These Studies on Security contain only the results of my scientific views, research, analyses and models. In other words, they provide a SUMMARY of my MAJOR contributions to the Science of Security.
STUDY 18. APPLICATIONS OF GAME THEORY IN SECURITY AND CONFLICT SITUATIONS (CONFLICTS)
Different classes of games are analyzed in relation to conflict situations (conflicts) with increased uncertainty, and strategies for behavior in such situations are discussed as an effective mix of elements of both confrontation (prioritizing one's own interests) and cooperation (considering the interests of the other party to an acceptable degree).
The following monograph of mine is devoted to examining various aspects of Game Theory in relation to security and conflicts:
Николай Слатински. Сигурността – животът на Мрежата. София: Военно издателство, 2014.
[Nikolay Slatinski. Sigurnostta – zhivotut na Mrezhata. Sofia: Voenno iztadelstvo, 2014].
Nikolay Slatinski. Security – the Life of the Network. Sofia: Military publishing house, 2014 (in Bulgarian)
Rarely in a conflict the only possible relationship is one of constant and escalating confrontation. Rather, we can speak of the presence of elements of both confrontation and cooperation. They are always intertwined and there is both unity and opposition between them. Confrontation is filled with negative (destructive) energy and with aggressive intentions. Cooperation is filled with positive (constructive) energy and with peaceful intentions. In any conflict, the choice of behavior – whether confrontational or cooperative attitudes will prevail – depends on a number of factors: external and internal, political and economic, ethical and cultural and other factors.
The development of the conflict can be represented on a diagram using a coordinate system with two axes (Figure 1). One axis marks the corresponding magnitude of Cooperation at the given point in the development of the conflict, and the other axis marks the corresponding magnitude of Confrontation for this point. The curve connecting the successive points of conflict development is called the „Conflict Curve in the Cooperation–Confrontation Axes“. To avoid the same abbreviation for the axes names Co. (Cooperation) and Co. (Confrontation) , this Conflict Diagram can be (jokingly) called the „Coca–Cola Conflict Diagram“.
Figure 1. Conflict Development Chart („Coca-Cola“)
To continue our analysis of the relationship between confrontation-dominant strategies and cooperation-dominant strategies in conflict situations (conflicts), we will turn to Game Theory.
Game Theory is a mathematical method (or class of mathematical methods) for studying optimal strategies in conflict situations and competitive interactions called games.
„Game“ in this case is a process expressed in strategic interaction (through confrontation and/or cooperation), in which two or more parties („players“) participate, leading a struggle to realize their interests. Each party, using its available resources, pursues its goals with the help of a certain rational strategy by choosing among alternative solutions and considering the moves of the opponents. This can result in a win or a loss depending on the behavior and unknown prior decisions of the other parties, as well as a number of other conditions accompanying any such game.
Mathematical Game Theory traces its origins to the classic book Theory of Games and Economic Behavior (1944) by the Hungarian-Jewish mathematician John von Neumann (1903 – 1957) and the German-American economist Oscar Morgenstern (1902 – 1977).
It is interesting from a mathematical point of view and instructive from the point of view of our individual and group human ambitions to note that in cases of incompatible or very poorly compatible interests of the two parties to the conflict, the likely relatively stable (and in principle relatively fair) solution is achieved when each player strives for the best of the worst solutions or the worst of the best solutions. Then one could arrive at the ideal case for the particular game of strategic rivalry, when the minimum of the maxima of one player coincides with the maximum of the minima of the other player – the „maximin“ or „minimax“ solutions [1].
According to the interaction between the elements of confrontation and cooperation in conflicts, their content and their final outcome, two types of conflicts or games, as they are often called in conflict modeling, can be considered: „zero-sum conflicts (games)“ and „non-zero-sum conflicts (games)“.
■ Zero-sum conflicts (games) are of the type „win–lose“, „yes–no“, „either–or“, where a win for one side means a loss for the other.
In Game Theory, this type of game is called a „strategic rivalry game“ or a „zero-sum game“.
■ Conflicts (games) with non-zero sum have two variants – with a positive value and with a negative value of the non-zero sum:
▪ When the non-zero sum is positive, the conflicts (games) are of the type „win-win“, „yes-yes“, „and-and“, i.e. in them, both parties can win, achieving an outcome that is beneficial (albeit to varying degrees) to both parties.
In Game Theory, such a game is called a „strategic cooperation game“ or a „positive non-zero-sum game“.
▪ When the non-zero sum is negative, the conflicts (games) are of the type „lose-lose“, „no-no“, „neither-neither“, i.e. in them, both parties can lose, with an outcome that is disadvantageous (albeit to varying degrees) for both parties.
In Game Theory, such a game is called a „strategic antagonism game“ or a „negative non-zero-sum game“.
In describing different conflict situations related to security, different behavioral strategies are used, as a result of which one of the two sides wins (it has a successful strategy) and the other side loses (its strategy is unsuccessful).
In fact, this is the goal of any game (of any conflict situation, of any conflict) – both parties pursue different interests, take actions according to the accepted rules, and each strives to make its profit as large as possible (that is, to the maximum extent to protect its interests and realize its goals) and, if possible, to minimize the profit of the other party (that is, to make it so that the other party can protect its interests and achieve its goals as little as possible).
It is accepted to believe that what our strategy of behavior in the conflict will be – whether predominantly confrontational or predominantly cooperative, is determined by our attitude towards the other side. In fact, the nature of the chosen strategy is determined not by the attitude towards the other, but mainly by the nature of the conflict.
If conflict is a zero-sum game (i.e., either–or), then no matter how we treat our opponent, and even if we feel the best we can, our strategy must nevertheless be dominated by elements of confrontation.
Example – two people get divorced and the court has to decide which of them to give their only child to. In this case, even if the divorcing spouses have kept the good attitude one to and want and after the divorce to remain friends, if the child will be given only to one, each of the two parents has to pursue a strategy with confrontation content to the other parent, to maximize his/her disadvantages and to convince the court with her (his) arguments that the other is the worse parent and she herself (he himself) is the better parent, therefore the court should award the child to her (him).
Relying on a strategy of cooperation by highlighting the good traits and positives in the character of the other spouse can „mislead“ the court into awarding the child to him (her).
If the conflict is a non-zero-sum game (i.e. and–and), then despite the possible very bad attitude towards the other side, everyone must put substantial elements of cooperation into the conflict strategy so that both sides actually win (not lose).
Let's take the divorce case again, only in this case there are two children. It is clear that the court will be guided by a decision in which each of the parents will be awarded one child. In this case, even if the two spouses feel a strong hatred for each other and blame each other for the ruined life, they should orient themselves to strategies with predominant elements of cooperation – so that each of them can spend several days of the month with the other child, so that the two children can communicate with each other as much as possible, have common holidays and feel the strongest brotherly and/or sisterly feelings for each other.
These examples suggest the Message from Game Theory – the strategy for behavior in a conflict is determined not so much by the attitude of the two parties to each other, but by the nature of the conflict – whether it is zero (i.e., either–or) or nonzero (i.e., and–and) sum.
Some of the most important model tasks for studying strategic behavior in Game Theory are Prisoner's Dilemma, Deadlock, Stag Hunt, and Chicken. In fact, Prisoner's Dilemma is the main task from which the other three can be obtained. We will pay special attention to it, especially since it is fruitful as an explanatory mechanism and results when it comes to a phenomenon (social practice) central to this Study – reciprocal altruism.
Explanation:
Altruism (from Latin other, others) – principle or practice of concern for the well-being of someone else; a traditional virtue in many cultures and a foundational aspect of many religious traditions; the opposite of selfishness.
Reciprocal (mutual) altruism – social behavior in which individuals make gestures, provide help, perform self-sacrifice to a certain extent to each other, expecting a similar gesture, help, self-sacrifice in return. The term was coined by the American evolutionary biologist and sociobiologist Robert Trivers (1943).
Actually, let's first talk about reciprocal altruism.
Trust is the basis of the development of a number of social practices, which in different animals are realized to some extent on an instinctive level, and in humans they are „uploaded“ to a social level, i.e. they are transformed into normal social actions and judgments of reality of humans. The role of these trust-based practices is huge, they are part of the most essential reasons that allowed man to separate very sharply from the rest of the animal species, even from the apes with whom he has common ancestors, and to become the true King of the Earth. Reciprocal altruism is one such practice. Robert Trivers defines altruistic behavior as such behavior of one organism A towards another not closely related to it organism B, which benefits B and is detrimental to A, and benefit and harm being defined in terms of everything involving the efficient functioning of these organisms [2].
Reciprocal altruism is also found in various animal species, but there it is on an instinctive level. For example, there is a species of vampire bats that suck blood from victims. When they return from hunting, if a bat (because female bats form social groups, so here all bats are actually female) has not been able to eat and is hungry, immediately one of the fed bats will give it (vomit) some of the blood it has sucked. The next time the roles are reversed, the bat that was fed returns the gesture to the bat that fed it. Here is a standard practice of reciprocal altruism. Such an interaction is mainly carried out by bats, which during daytime rest usually line up next to each other, i.e. they have established closer contact and their mutual trust seems to have grown. In addition, this reciprocal altruism, although instinctive, meets the conditions for the Prisoner's Dilemma, which we will consider later – when the benefit that the hungry bat receives for it is greater than the harm that the full bat suffers (i.e., the blood given will save from starvation or severe emaciation the unsuccessful hunting bat, the recipient, but will not fatally affect the donor, and therefore, if one bat „plays“ altruistically, the reward it will receive if the other bat also „plays“ altruistically is greater than the loss it will suffer if the second bat cheats him, i.e. refuses to play altruistically – here we are talking about multiple interactions between them [3]). It is probably not for nothing that vampire bats have the most complex social organization among all bat species.
The realization of reciprocal altruism requires complexity of the organization and it itself complicates it, because in its essence reciprocal altruism is a social function that can be sustained in the presence of the corresponding complicated social structure.
Reciprocal altruism with its positive outcome can be considered as a consequence of extremely good, constructive intentions. In this case, it is the result that is important. And the reasons that led to it can have different grounds. Conscious coercion could also be such a reason. In the sense that an action so positive as a result may have been born of compulsion or of the realization that it will be arrived at.
Indeed, suppose that some bats decide not to return the gesture in principle, i.e. to have egoist rather than altruistic behavior. This means that in others, i.e. altruistic bats, there will be a need to remember egoist bats. And because the altruistic bats will feel threatened by the behavior of the egoist bats, they will have to build new habits and procedures of interaction with each other to minimize the negative effects of the actions of the egoist bats and find appropriate compensations as victims of this behavior. In altruistic bats, the dynamics of their social memory will intensify and their interaction bonds will be strengthened. If they get into trouble after an unsuccessful „hunt“, egoist bats will not receive food, while bats harmed by this behavior will be compensated by other donors (altruists). So, even at the first time, in the short term, it seems that the egoist bats are in a more favorable position (they have received food from the altruistic bats in their unsuccessful hunting, but did not return the gesture next time) and temporarily to strengthen themselves physically, to improve their chances of survival and continuation of the family, and therefore to improve the chances of reproduction of their genes, in the long run they, the egoist bats, will be in a negative, disadvantageous position. This is because, on the one hand, they will not receive food when they have had an unsuccessful hunt (recall that the loss of food from the donor has a lower cost than the benefit that the fed bat receives), and also they will be isolated from social ties and will not enjoy the advantages that the community provides. With such a development, in the short term, egoist bats will gain an advantage and begin to increase in number, but in the long term, they will be in a very disadvantageous position and will begin to sharply decrease in number, until their practical disappearance, i.e. to making the group (flock, herd) of bats almost entirely, if not entirely, altruistic bats.
A „reasonable“ vampire bat will prefer to participate in the game of „reciprocal altruism“, even if it is not to the taste of his valuable inner world. The „unreasonable“ bats, because of their worse chances of survival, will be minimized or extinct, so the community actually works in favor of the „reasonable“ bats, who voluntarily or under compulsion practice reciprocal altruism. One to whom altruistic behavior is demonstrated will respond with altruistic behavior and not cheat, i.e. to act egoistic. Such examples can be given for many other living beings of different classes, species and genera. In humans, it is more complicated, since it is not only about existential values such as sustenance, reproduction and protection from enemies, but also about other social values – honor, dignity, self-respect, good name, reputation, etc.
Reciprocal altruism can be seen as a repeatedly repeated interaction between two individuals (players) in symmetric reciprocal situations, which can be represented by the following table of benefits and losses / gains and damages:
Table 1. Reciprocal altruism – Benefits and Losses: R – Reward, D – Damage, G – Gain, P – Punishment
In Table 1, the relevant designations are as follows:
♦ R – the Reward each individual receives in an altruistic exchange when no one cheats the other;
♦ D – the Damage the altruist suffers for having been cheated;
♦ G – the Gain that the cheater secures for himself, because he cheats the altruist;
♦ P – the Punishment that each of the two receives for both not acting altruistically and deceiving each other.
The following inequality holds for this class of tasks:
D < P < R < G [4].
Prisoner's Dilemma was developed in 1950 by the researchers of the RAND Corporation (RAND Corporation), the American mathematician Merrill Flood (1908 – 1991) and the American mathematician of Polish origin Melvin Drescher (1911 – 1992), and was named so by the Canadian mathematician Albert Tucker (1905 – 1995).
Prisoner's Dilemma can be viewed in two ways:
‣ both positive as an incentive for cooperative behavior towards the authorities (reduction or cancellation of the sentence, i.e. years of imprisonment);
‣ both negatively as a punishment for refusing to cooperate with the authorities (increasing the sentence).
Similarly, the point of view may not be that of the authorities, but that of the other partner (player). For example, when we talk about reciprocal altruism, then the benefits and losses are already considered depending on whether each of the players has an altruistic behavior or cheats his partner (renounces altruistic behavior).
But the idea of the Dilemma is the same: if each player acts solely on his individual self-interest, in the end both will be dissatisfied with the outcome.
Although we are talking about a prisoner, even two prisoners, this Dilemma is not only considered in relation to prisoners. It is a general and generalizable task that can be viewed as a game in which two players can cooperate or not cooperate at the same time, or one can cooperate and the other can cheat.
In a „real“ case (this type of case gave rise to the name of this game Prisoner's Dilemma), the police in a city known for its serious crime situation capture two criminals who act together in numerous serious violations of the law. The arrested are taken to cells at both ends of the pre-trial detention center and are not allowed to communicate with each other.
Each of them is said to:
‣ If one makes a full confession of the crimes of both and the second refuses to admit anything, then the first will receive a sentence of 1 year and the other will be sentenced to 10 years in prison.
‣ If both remain silent and do not make any confessions, they will each be sentenced to 2 years in prison.
‣ However, if they both make full confessions about their joint gang activity, they will each receive 5 years in prison.
So, each of the two is faced with the dilemma of keeping quiet or making full confessions. The table of possible years of imprisonment for the two (with their increase from 1 to
Table 2. Prisoner's Dilemma Type Game, „real“ case – years in prison
It can be seen that if everyone thinks only of his own interests and does not consider the other, in the end they both lose. They lose too much. Thinking only of his own interests, everyone is in a hurry to make full confessions. It would be tempting to remain silent, but if the other person speaks, then 10 years in prison await him.
In this „real“ case, the losses and benefits to the actors are punishments (i.e., they are negative), although different in magnitude. The American political scientist Robert Axelrod (1943) considered a specific case of the same type of game, only when the benefits and harms are incentives (i.e., they are positive). Then the corresponding table of distribution of benefits and damages has a slightly different appearance.
Table 3. Prisoner's Dilemma Type Game, „specific“ case – Benefits and Losses (rewards can be in, for example, [thousands] of dollars), by Robert Axelrod [5]
In Game Theory, in the general case, Prisoner's Dilemma game has the following distribution matrix of benefits and losses.
Table 4. Prisoner's Dilemma Type Game, General Case – Benefits and Losses
Brief commentary on Table 4.
♦ The Reward that each player receives if it cooperates with the other (e.g. they show reciprocal altruism), as seen by comparing with Table 1 for reciprocal altruism, here is R=2 (in the „real“ case, Table 2, it is also R=2, but let's remember – as a punishment, and in the „specific“ case, Table 3, it is R=3).
♦ The Damage suffered by each player if he cooperates (altruism) and the other cheats him (refusal of altruism) is D=0 (in the „real“ case it is D=10, and in the „specific“ case it is also D=0).
♦ The Gain for the player when he cheats (refusal of altruism) and the other cooperates (altruism) is G=3 (in the „real“ case it is G=1, but it is also like a punishment, and in the „specific“ case it is G=5).
♦ The Punishment received by both players for each deceiving the other (mutual denial of altruism) is P=1 (in the „real“ case it is P=5, and in the „specific“ case it is P=1).
Here, the order of increasing value of the four main quantities is the Damage, the Punishment, the Reward, the Gain (D/P/R/G), i.e. 0/1/2/3 (in the „real“ case as penalties, i.e. with a „minus“ sign we have -10/-5/-2/-1, and in the „specific“ case 0/1/3/5) or as already said, the ratio is always valid:
D < P < R < G.
In other words, in terms of the original Prisoner's Dilemma game:
♦ The Gain (for the player who cheats while the other cooperates) must be greater than the Reward (for both of them cooperating);
♦ The Reward must be greater than the Punishment (for both in case of mutual cheating);
♦ The Punishment must be greater than the Damage (for the player who cooperates while the other cheats).
And so:
The Damage < The Punishment < The Reward < The Gain.
• If in Prisoner's Dilemma the Punishment and the Reward are exchanged in terms of value, i.e. when the Punishment becomes greater than the Reward, Deadlock game results.
• If in Prisoner's Dilemma the Reward and the Gain are exchanged in terms of value, i.e.when the Reward becomes greater than the Gain, Stag Hunt game results.
• If in Prisoner's Dilemma the Damage and the Punishment are exchanged in terms of value, i.e. when the Damage becomes greater than the Punishment, Chicken game results.
Let's take a look at these three strategy games.
• Deadlock is a strategy game that would hardly be of interest, since it best rewards mutual deception, and therefore each of the two players always and under all circumstances refuses to play cooperatively.
In this game, the dominant behavior strategy of both players is that they gain the most by refusing to play cooperatively, i.e. they seek to cheat the other party (i.e., not to show altruism). This is why this game is boring because there is no distinction between selfish interest and mutual benefit. It is called Deadlock for this reason, because both sides decide not to play cooperatively, they refuse to cooperate.
An example. Two countries (more likely and more understandably – during the Cold War) due to mutual distrust refuse to comply with the agreement reached to eliminate their nuclear arsenals, therefore it is impossible for this agreement to achieve its goal and to have effective mutual control over its compliance and over their armaments. Cooperation here is equivalent to each country complying with the agreement (removing its arsenal). The cheat is to break it (keeping the arsenal) as it is supposed to – secretly. In this scenario, the best outcome for each country is to retain its nuclear arsenal while the other eliminates its own. The second most important outcome is that each country retains its arsenal. Next is for both sides to remove their arsenals (complying with the agreement). The worst outcome is that one state abides by the agreement (removes its arsenal) while the other violates it (retains its arsenal) [6, 7].
Table 5. Deadlock Type Game, general case – Benefits and Losses [8]
As stated, Deadlock results from Prisoner's Dilemma when the Punishment and the Reward are exchanged in value, i.e. the Punishment becomes greater than the Reward.
♦ The Reward that each player receives for cooperating with the other, as seen by comparing with the reciprocal altruism table, Table 1, here is R=1.
♦ The Damage suffered by each player if he cooperates and the other cheats him is D=0.
♦ The Gain that the player makes when he cheats and the other cooperates is G=3.
♦ The Punishment both players receive for cheating each other is P=2.
Here, the order of increasing value of the four main quantities is the Damage, the Reward, the Punishment, Gain, (D/R/P/G), i.e. 0/1/2/3 or the ratio is in effect:
D < R < P < G.
In other words, in Deadlock game conditions:
♦ The Gain (for the player who cheats while the other cooperates) must be greater than the Punishment (for both of them cheating on each other);
♦ The Punishment must be greater than the Reward (for both in case of mutual cooperation);
♦ The Reward must be greater than the Damage (for the player who cooperates while the other cheats).
And so:
The Damage < The Reward < The Punishment < The Gain.
• Stag Hunt can be illustrated with a fable from as far back as 1755 by the French philosopher and thinker Jean-Jacques Rousseau (1712 – 1778), in which he tells how five primitive hunters try to kill a stag enough to feed them and their families. While hunting the stag promises lunch for all of them, they pursue it with a concerted effort and surround it. But at that moment a rabbit runs past one of the hunters, who runs after him, kills him and secures food for himself and his relatives. Unfortunately, the stag escaped through the gap he opened and the other hunters were left empty-handed. The treacherous hunter did this because he knew that if he did not kill the rabbit, then running up to another of the hunters, the latter would not hesitate and chase him, leaving a gap through which the stag would escape and thus leave him empty-handed. This is how, as long as this is possible, everyone pursues the goal with a common effort, but if an either-or situation arises (either the self-interest or the common interest), the hunter will always choose the self-interest. Not because he is egoist, but because it is the only way to satisfy his interests, and anyone in his place would do the same – „Stag Hunt is a classic illustration of the problem of securing a public good in the face of the individual temptation to give it up in favor of his selfish interest“ [9].
Such are the interstate relations according to the views of the school of political realism – with the difference that in them the egoism of the state is not simply an initial negative quality, but is characterized as sacred. In an either-or situation, the statesman is doomed to choose the national interest, because in such a situation, each of his opponents would act in the same way and protect his own interests at the expense of interests of others. Acting on trust can prove fatal. It is not possible to consider the interests of others because they would never consider your interests. According to political realists, „absence of trust dominates international relations. Therefore, every state strives to increase its power“ [10, 11].
Explanation:
The school of political realism places the protection of national interests and security with all its available power in the first place in the foreign, security and defense policy of a country, and everything else – morality, law, principles, duty, compliance with commitments, with a given word, remains in the background. If people's egoism is considered a bad, unattractive trait of human character, in international relations they speak of „sacred egoism of nations“, i.e. it goes without saying that nations, states, should be egoistic, or at least have a healthy dose of egoism.
Let us now imagine the specific situation of this hunt and estimate the effect of the hunt as calories. Let's say there are two hunters and (notional) the stag has 6 calories and the rabbit has 2. Then if both of them catch the stag and share it they will each get 3 calories, and if one of them catches a rabbit (and they drop the stag) they will get 2 calories.
Table 6. Stag Game Type Game, a specific case (analogue of hunting) – Benefits and Losses (in calories) [12]
In Game Theory, in the general case, Stag Hunt has the following distribution matrix of benefits and losses.
Table 7. Stag Hunt Type Game, general case – Benefits and Losses
As stated, Stag Hunt is obtained from Prisoner's Dilemma when Reward and Gain are exchanged in value, i.e. Reward becomes greater than Gain.
♦ The Reward each player receives for cooperating with the other, as seen by comparing with the reciprocal altruism table, Table 1, here is R=3.
♦ The Damage suffered by each player if he cooperates and the other cheats him is D=0.
♦ The Gain that the player makes when he cheats and the other cooperates is G=2.
♦ The Punishment received by both players for cheating each other in the general case of the game is P=1 (and in the „specific“ case, Table 6, is P=2).
Here, the order of increasing value of the four main quantities in the general case of the game is the Damage, the Punishment, the Gain, the Reward (D/P/G/R), i.e. 0/1/2/3 or the ratio is in effect:
D < P < G < R
(in the „specific“ case the order is the same, but as 0/2/2/3 or the ratio applies:
D < P = G < R).
In other words, in the terms of Stag Hunt game:
♦ The Reward (for both in mutual cooperation) must be greater than the Gain (for the player who cheats while the other cooperates);
♦ The Gain must be greater than the Punishment (for both in the case of mutual cheating – in the specific case it is equal, but this does not change the logic of the game);
♦ The Punishment must be greater than the Damage (for the player who cooperates while the other cheats).
And so:
The Damage < The Punishment < The Gain < The Reward.
• Chicken game – the name of the game can be explained as „Who is the coward?“.
The American economist and prominent specialist in the field of international relations and national security, Thomas Schelling (1921 – 2016), cites the example of how, after the Second World War, the American youth were entertained by the „game of chicken“. Two of them are driving trucks (or cars, motorbikes) at high speed against each other, and the one who turns first and deviates from the road is the „chicken“, i.e. a coward. For the other, this night is the happiest because all the girls are dancing with him and looking at him with ecstatic eyes.
And in the American film „Rebel Without a Cause“ (1955) with the untimely death of the talented actor James Dean (1931 – 1955) in the main role of the confused, but honest, principled and brave James „Jim“, „Jimbo“ Stark, the game of „Chicken“ has a slightly different appearance – two young men, at a given signal, set off in their cars at maximum speed towards the edge of the Millertown cliff, overhanging the sea, and the first one to jump out of his car is a coward (he's the chicken). Jimbo jumps out of the car at the last moment, and his opponent Buzz Henderson fails, flies into the abyss and dies.
In this game, each of the two drivers is faced with the dilemma of whether to go ahead boldly and become the hero of the night, or back down and embarrass themselves in front of the girls. The table of profits and damages that this „game“ brings to the two young men (with a reduction of +100 or a complete victory, a hero of the evening, through -10, a „chicken“, a coward to -1000 or an accident with serious injuries or even death) can be presented as follows:
Table 8. Chicken Type Game, specific case – Benefits and Losses
In Game Theory, in the general case, Chicken game has the following distribution matrix of benefits and losses.
Table 9. Chicken Type Game, general case – Benefits and Losses
As stated, Chicken game is obtained from Prisoner's Dilemma when the Damage and the Punishment are exchanged in value, i.e. the Damage becomes greater than the Punishment.
♦ The Reward each player receives for cooperating (i.e., turning) with the other, as seen by comparing with the reciprocal altruism table, Table 1, here in the general case is R=2 (in the particular case, Table 8, it is R=-1).
Actually, for this game, we should rather be talking about the „Reward“ (i.e. in quotes, because it is a negative score for the players – each of them took a turn).
♦ The Damage suffered by each player if he „cooperates“ (turns) and the other „cheats“ him (in this case moves forward) in the general case is D=1 (in the „concrete“ case it is D=-10).
♦ The Gain that the player makes when he „cheats“ (continues) and the other „cooperates“ (turns) is in the general case G=3 (in the concrete case it is G=+100).
♦ The Punishment received by both players for „cheating“ each other (proceeding to a collision) is in the general case P=0 (in the concrete case it is P=-1000).
Here, the order of increasing value of the four main quantities is Punishment, Damage, Reward, Gain (P/D/R/G) i.e. 0/1/2/3 or the ratio is in effect:
P < D < R < G
(in the concrete case the order is the same but as -1000/-10/-1/+100).
In other words, in the terms of Chicken game:
♦ The Gain (for the player who „cheats“, i.e. moves on while the other player „cooperates“ i.e. turns) must be greater than the Reward (for both in mutual „cooperation“, i.e. both turn);
♦ The Reward must be greater than the Damage (for the player who „cooperates“, i.e. turns, while the other player „cheats“, i.e. moves on);
♦ The Damage must be greater than the Punishment (for both of them when „cheating“ each other, i.e. moving on).
And so:
The Punishment < The Damage < The Reward < The Gain [13].
That being said, in three of the four games (not including Deadlock game), when both sides pursue only their own interests, they both lose – this is especially clear in Chicken game. It is these situations that are particularly attractive to study by Game Theory, and it develops them as classes of model tasks – tasks that describe extreme cases, they show what can happen if the game gets out of control, if both sides „forget“ that it is a game with two players, if they ignore the need to balance goals and resources invested in their achievement (in other words, they do not seek to act effectively) or if they cease to act as rational players (for example, show over-emotionality) and lose control of their own strategy.
Among these model tasks there are two main classes (types):
▪ the first class (of super-egoism) includes the tasks where each of the two parties pursues, as it was above, only their own interests;
▪ the second class (of super-altruism) is from the tasks where each of the two parties cares only for the interests of the other party.
▪ In the tasks (games, conflicts) of the first class (super-egoism), each of the two parties pursues only its own interests, and in the end both parties suffer a loss.
The simplest case is called „The Two Sisters and the Orange“. In this place, two sisters are fighting over an orange, the mother comes and divides it equally between them. But instead of calming down, both sisters start to cry in an emotional sign of disagreement with this symmetrical decision of the mother, since the younger sister just wanted to eat the orange and the older one needed its peel because her boyfriend is coming to visit, she wants to make a cake for the occasion in order to show off her skills, and probably because she has already heard the maxim that the way to a man's heart is through his stomach...
Situations in which each side thinks only of its own interests, and as a result both sides lose, are usually divided into three types of „games“:
⁕ „Game“ with a small loss;
⁕ „Game“ with a recoverable large loss – when the loss is large but recoverable;
⁕ „Game“ with a unrecoverable great loss – when the loss is great and unrecoverable.
⁕ In the first case (a „game“ with a small loss), the game „Walk“ or "He, She and the Two Dogs" can be considered.
In this „game“, each of the two lovers feels great joy when walking with the other, but is also filled with great pleasure when walking with his/her dog. However, the problem is that if both lovers go out for a joint walk with their dogs, then the whole positive experience fails completely, because their dogs can't stand it and start barking, attacking, biting, and the walk becomes simply impossible.
The table of experienced positive emotions (by their increase from 1 to 4) can be presented in the following form [14]:
Table 10. „He, She and the Two Dogs" – experienced positive emotions
It can be seen that if everyone thinks only of his/her own interests and does not consider the other, then everyone will go for a common walk with his/her dog, but in the end the walk will be totally ruined. However, the loss is small, because they met each other, they told each other again and again that they love each other, and the two can agree to take turns with the dogs when going out. In that case, things will fall into place.
In fact, as can be easily ascertained, this is a Prisoner's Dilemma type of game. Indeed – the Damage is 1, the Punishment is 2, the Reward is 3, the Gain is 4.
And indeed the condition is met:
D < P < R < G.
⁕ In the second case (a „game“ with a large but recoverable loss), the „real“ case (see Table 2) of the Prisoner's Dilemma game can be considered again. Instead of both keeping quiet, gritting their teeth and not confessing, so that they get away with 2 years in prison each, each thinks only of how to get out of prison sooner, and in the end they both get 5 years effective sentence.
Table 2. Prisoner's Dilemma type game, „real“ case – years in prison
This is how, again, if each thinks only of his own interests and does not consider the other, in the end they both lose. They lose too much. Thinking only of his own interests, everyone is in a hurry to make full confessions. It would be tempting to remain silent, but if the other person speaks, then 10 years in prison await him. The loss as a final result is great (5 years in prison), but still not unrecoverable.
⁕ The third case (a „game“ with a great and unrecoverable loss) naturally falls within the scope of Chicken type games. As an example, we can cite the „specific case“ discussed above in the study of this type of game, when each of the drivers is only interested in winning, and in the end there is a serious accident.
Table 8. Chicken Type Game, specific case – Benefits and Losses
It can be seen that if everyone thinks only of his own interests and does not consider the other, in the end they both lose, and unrecoverable – the loss for both is fatal.
The situation can develop further, making it even more complicated and difficult to solve.
And what would happen if one of the drivers demonstratively threw the steering wheel out the window, i.e. when this player suicidal?
What if the discarded steering wheel is not the real one, but a false, i.e. when this player is bluffing [15]?
Explanation:
Bluff – deliberate creation of a false impression; deception, delusion.
Here is the place for a „lyrical digression“.
The starting presumption in Game Theory is that the participants are rational players (actors). In particular, in the „Chicken“ Coward game, their goal is not to crash, so it is implicitly assumed that one will always back down.
Let us now imagine that one participant is an irrational player…
What can he do? There are two alternatives and they were just mentioned.
• In the first alternative, the irrational player throws the steering wheel out the window. Therefore, he will not turn in any case.
This player has a suicidal mentality.
Does the other, rational player have a choice in such a situation? Well, if he doesn't turn, a crash with terrifying consequences is inevitable.
In this case, the „rational choice“ of the rational player – not to turn – would be a pure example of an irrational decision. But this player is rational and will by no means make an irrational decision... And then? Theory doesn't help him, unfortunately. And for now.
• In the second alternative, the irrational player again throws the steering wheel out the window of the truck, but it is a false, not real steering wheel. In other words, he's bluffing.
What should a rational player do in this case? And again, unfortunately, the theory does not suggest to him – because it has not yet been developed.
The reason has been stated – all previous Game Theory is based on the presumption that players are rational actors.
It is for this reason that today the West experiences an acute deficit of a developed Science of Security to deal with irrational players.
The West falls into a stupor when one actor – for example, the terrorist – is an irrational player willing to die for his goals. What should the West do with such a player? How to „punish“ him when this player is ready to go all the way and sacrifice even his life?
The West also falls into a stupor when one actor – for example, Putin – is an irrational player bluffing with blackmail that he will resort to nuclear weapons in the War against Ukraine.
If modern Science of Security had developed a qualitatively new Game Theory, when one of the participants is an irrational player (or more than one, and in the extreme case – when all the actors are irrational), then this modern Game Theory would point out the huge role of early warning and even more of strategic forecasting, thanks to which an optimally in-depth analysis of the behavior of the irrational player and making the most reliable prediction – whether in the particular case he is ready to go all the way, or actually „just“ bluffing.
This would be a condition to largely overcome the hesitation about the behavior of the irrational player and make the right decision that guarantees victory over him.
If we go back to today in international security, we can say that:
• The first alternative – throwing away the real wheel (suicide) – corresponds to the actions of modern religiously motivated terrorism in its cruelest and most brutal version – the Islamist one.
• The second alternative – throwing away the false wheel (bluffing) – corresponds to the actions of Putin – the Coward from the bunker, the rashist King Rat.
This Coward, this bane of international security, this war criminal blackmails with nuclear threats. But his insane behavior is based on the illusion that if he throws away the false wheel, the West will „squat“ and turn... The Rat King is bluffing!
The West must overcome the fear of Putin's nuclear blackmail; to overcome the Fear of the very fear that Putin might use a nuclear weapon. If it frees itself from this Fear, from the Fear of fear itself, the West will not only help Ukraine in a limited way, so that the War continues for a long time and exhausts Russia, but it will help Ukraine as it should be helped this brave, heroic country, fighting against rashism and for democracy and peace – in the name of itself, in the name of Europe, in the name of the West, in the name of the world.
A very important thing – in all these games (tasks), the interaction was considered as a one-time act. And in life, the players, the actors, the subjects are in continuous or at least in frequent interaction. And when there is such an interaction, it becomes possible to work out certain of its rules, it is possible to create trust, to increase the degree of predictability about how the partner (opponent) would act in a given situation, i.e. a mechanism for reconciling interests can be developed.
This is exactly what Robert Axelrod is done: he arranges a kind of competition – a tournament between specialists (economists, mathematicians, psychologists, sociologists, political scientists) in conflicts (games) from around the world, by presenting different strategies – a total of 15 – for behavior in the conditions of an oft-repeated Prisoner's Dilemma – so each person chooses at each turn whether to cooperate with the partner or betray him, the benefits and losses being determined according to the relevant matrix (Table 4).
Robert Axelrod „translated“ these 15 strategies into a common computer language and started a competition between them in a large computer. Each of the strategies/programs competes with each of the others, including a copy of itself, i.e. 15 x 15 = 225 different „matches“ in Prisoner's Dilemma conditions lasting 200 turns.
To everyone's surprise, the competition was won by the Russian-born American specialist in mathematical psychology, general systems theory, mathematical biology and modeling of social interactions Anatol Rapoport (1911 – 2007) with the shortest and simplest program consisting of literally one line, which can be called „Tit-for-Tat“ – TfT, i.e. what you do to me, that I do to you – starting with cooperation and then every move you respond with the opponent's previous move – you do what he just did, i.e. for treason punishing with treason, for cooperation encouraging with cooperation.
Robert Axelrod is incredibly surprised, he organizes a competition with even more participants (it attracts evolutionary biologists, physicists, computer specialists), and the situation with the Prisoner's Dilemma is repeated 200 times. And again the winner is the same [16, 17, 18].
Such a strategy shows that in order to synchronize behaviors and choices with a person, he must feel what you felt – if he betrayed you, you betray him next time, if he cared for you, next time show him that you care for him; only by feeling the pain of betrayal and the happiness of love can he understand you too. Never forget that the other is also a living being, but never think that he is more important than you. With such a strategy, each player („prisoner“) responds in the next game with an identical move to the previous move of the opponent (the second „prisoner“) – if the first was silent, now the second is silent, if the first „soaked“ the second, now the second „soaks“ the first too. It turns out that responding to the other in a way analogous to his actions, the players („prisoners“) most quickly work out a common, successful for both of them, strategy, i.e. with such a strategy, the two players most quickly synchronize their actions, their interests are most quickly integrated into a joint, cooperative strategy, through which they think not only about themselves, but also about each other, and begin to cooperate, and thus help each other [19].
For Robert Axelrod, there is a really fundamental problem that he has pondered for a long time – how and if cooperation can occur when egoists interact and without a coercive (disciplining) central authority.
This problem is related to three very important questions:
(1) How can a potentially cooperative strategy take hold in an environment that is fundamentally uncooperative?
(2) What type of strategy can succeed in a diverse environment composed of other individuals widely using more or less complex strategies?
(3) Under what conditions could such a strategy, once established among a group of people, resist the invasion of a less cooperative strategy [20]?
The Tit-for-Tat strategy can also be seen as an eye-for-an-eye strategy.
In the Book of the Old Testament „Exodus“ God spoke to Moses: „If people are fighting and hit a pregnant woman and she gives birth prematurely but there is no serious injury, the offender must be fined whatever the woman’s husband demands and the court allows. But if there is serious injury, you are to take life for life, eye for eye, tooth for tooth, hand for hand, foot for foot, burn for burn, wound for wound, bruise for bruise“ (Ex. 21:22-25).
In the New Testament, a more cooperative behavior is suggested: Jesus tells his disciples: „You have heard that it was said, ‘Eye for eye, and tooth for tooth’. But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also“ (Matt. 5:38-39), and also „Do to others as you would have them do to you“ (Luke 6:31).
This is how you go from „do unto others as they do unto you“ to „do unto others as you would have them do unto you“ [21].
Explanation:
Moses – character from the Bible, religious leader, lawgiver and the most important prophet in Judaism.
Robert Axelrod's analysis of a computer tournament simulation game demonstrates that, under the right conditions, cooperation can indeed occur in a community made up of egoists with no central authority.
For this to happen, cooperation must go through three stages in its evolution:
(1) It can start even in a community in which unconditional cheating reigns (mass distribution of non-cooperative strategies) as long as individuals can enter into relationships more than 0 or 1 time. Cooperation can develop from a small cluster of individuals who base their cooperation on reciprocity, even if their cooperation occurs very rarely, i.e. they don't have frequent contact.
(2) A strategy based on reciprocity can develop in a community where many and different types of strategies are used. Those who rely on cooperation and reward it in this way begin to accumulate points (benefits) much faster than those who cheat, i.e. ignore cooperative strategies. Therefore, strategies that rely on reciprocal responses prove to be able to survive in a non-cooperative environment.
(3) Cooperation, once established on the basis of reciprocity, can be defended against the invasion of less cooperative strategies, and thus the wheel of evolution gains momentum and a mechanism is built into it, as Robert Axelrod writes – a „ratchet“, that does not allow it to move backwards, in the opposite direction [22, 23].
Explanation:
Ratchet - sharp-toothed brake, thumb, tongue, mechanism that allows movement of the wheel in one direction only.
A very interesting and instructive case of reciprocal altruism as a „Live and let others live“ strategy arose during the First World War. French or British and German soldiers are in trenches located not far from each other on the front line and hold their positions for a long period of time. When there is no combat, soldiers on both sides refrain from shooting at opposing soldiers as they move around the front line. In other words, the strategy of cooperation should not always be tied to the personal qualities, goals and relations of the representatives of both parties to each other [24].
▪ In the tasks (games, conflicts) of the second class (super-altruism), completely opposite to the ones considered so far, each of the two parties cares only for the interests of the other party, completely subordinating their interests to it (or even completely ignoring them), and in the end both parties again suffer a loss. Therefore, if in the previous class of games the idea is that, in the general case, if each side in the conflict pursues only its own interests, both sides lose as a result, in this class of games, the idea is that if each side puts the interests of the other side first, in the general case, both sides also lose.
A model situation of the second class is the so-called game „O. Henry“, after the literary pseudonym O. Henry of the American writer William Sidney Porter (1862 – 1910). This play is based on his short story „The Gift of the Magi“ (1906), in which the two spouses, Della and James Dillingham Young, are deeply in love. They have two treasures they are proud of – her gorgeous hair and his gold watch. Each of the two decides to give a gift to the beloved person for Christmas. She cuts off her hair and sells it, and with the money she buys him a platinum watch chain. He sells his watch and buys her a set of real tortoiseshell hair combs with glittering stones on the end – the combs she's admired so many times in a Broadway window. So in Christmas Eve she has combs but no hair and he has a watch chain but no watch.
The bottom line of these game classes (conflicts, tasks) is all the same. In general, the optimal solution is always found as a mix of elements of confrontation and cooperation, i.e. as an aspiration of each of the parties to the conflict to think about defending its interests, taking into account the interests of the other party at the same time.
Of course, as in the game „O. Henry“, where each of the two sides in the conflict is driven solely by the interests of the other side (in practice, it is difficult to even call such a game a conflict), it is logical to assume that the loss will be small. When each partner is driven by the thought of doing good to the other partner and forgets to think about their own interests, the common loss can ultimately be seen more as the result of a misunderstanding, and much faster the two parties will learn to synchronize the interests of each of them, as well as their common interests.
Therefore, in Game Theory, far more attention is paid to games (conflicts) in which each of the two parties pursues its own interests first of all, and then, if ways are not found to regulate relations without giving the opportunity for the conflict to flare up, and if each of the players „forgets“ that there are two parties involved in the game, or as said above, the game begins to acquire irrational elements, it will most likely enter one of the above three cases:
‣ little loss (relationships can easily be resumed);
‣ major but recoverable loss (relationships can be resumed, albeit with great effort);
‣ great and unrecoverable loss (the relationship cannot be restored because it has broken down irreparably).
The two tables below offer additional opportunities for information and reflection regarding the principle of matching the type of conflict (zero-sum or non-zero-sum) with the strategy of behavior of each party to the conflict (with elements of cooperation and elements of confrontation).
For those who believe that the final result is most important, the probability (chance) of achieving a positive result can be defined as follows:
Table 11. Probability of a positive result
This table is deciphered as follows:
→ in a zero-sum conflict if the participant relies on cooperative behavior, the most likely outcome is that he fails to protect his interests;
→ in a zero-sum conflict, if the participant relies on confrontational behavior, the probability that he will protect his interests is greater than or at least equal to 1/2 (i.e., at least 50%);
→ in a non-zero-sum conflict, if the participant relies on confrontational behavior, the probability that he will protect his interests is less than or at most equal to 1/2 (i.e., no more than 50%);
→ in a non-zero-sum conflict, if the actor relies on cooperative behavior, the most likely outcome is that he succeeds in protecting his interests.
The conclusion is (as we pointed out earlier in this Study) that in zero-sum conflicts the key to success is a predominance of confrontational elements, and in non-zero-sum conflicts, the key to success is a predominance of cooperative elements in the participant's behavior.
Explanation:
In mathematics, probability is usually measured between 0 (i.e. 0%) and 1 (i.e. 100%).
For those who believe that preserving the relationship with the other participant is most important, the table takes the following form:
Table 12. Probability of keeping relationships
This table is deciphered as follows:
→ in a zero-sum conflict if the participant relies on confrontational behavior, the most likely outcome is that he fails to preserve his relationship with the other participant, i.e. he will destroy the relationship;
→ in a zero-sum conflict, if the participant relies on cooperative behavior, the probability that he will be able to maintain his relationship with the other participant is less than or at most equal to 1/2 (i.e. no more than 50%);
→ in a non-zero-sum conflict, if the participant relies on confrontational behavior, the probability that he will be able to maintain his relationship with the other participant is greater than or at least equal to 1/2 (i.e. at least 50%);
→ in a non-zero-sum conflict, if the participant relies on cooperative behavior, the most likely outcome is that he manages to preserve his relationship with the other party.
The conclusion is that in zero-sum conflicts, one actor may find it very difficult to maintain relations with the other actor, regardless of whether cooperative or confrontational elements predominate in his behavior, and in non-zero-sum conflicts, one actor can largely maintain his relationship with the other actor, regardless of whether cooperative or confrontational elements predominate in his behavior.
In conclusion, we will provide another table of the probability of achieving a workable and sustainable solution to a conflict, related to Anatole Rapoport's classification of the three types of conflict by the tactics of the participants („fights“, „games“ and „debates“) and by the type of conflict as the outcome (zero-sum game or non-zero-sum game).
But first let us clarify that Anatole Rapoport gives a classification of the types of conflicts according to which they are „fights“, „games“ and „debates“ [25].
> „Fights“ are a type of conflict where the contradictions between the parties are antagonistic and both sides strive for total victory because the other possible outcome for them is total loss. Such are the conflicts related to values, on which compromise is impossible – either you are for abortion or you are against it; you are either for or against the death penalty; either you accept my God, or you remain a believer in your God;
> „Games“ are a type of conflict in which there are strictly defined rules for the behavior of the parties, such as e.g. of chess. Participants in such conflicts are rational players. Each of them strives to „win“ by optimizing their benefits and minimizing damage, observing these rules;
> „Debates“ are a type of conflict in which „bargaining“, the ability to trade, to maneuver, to carry out successful diplomacy, to find compromises, to search for the deep cause of the conflict, takes precedence.
Table 13. Probability of a workable and sustainable solution
The meaning of this table is as follows:
→ in the case of a „Fights“ type conflict (as a tactic of the participants) and a „zero-sum game“ (as an outcome), the probability of achieving a workable and sustainable solution to this conflict is negligible – from 0 to 1/6.
→ in the case of a „Games“ type conflict (as a tactic of the participants) and a „zero-sum game“ (as an outcome), the probability of achieving a workable and sustainable solution to this conflict is very small – from 1/6 to 2/6 (i.e. to 1/3);
→ in the case of a „Debates“ type conflict (as a tactic of the participants) and a „zero-sum game“ (as an outcome), the probability of achieving a workable and sustainable solution to this conflict is small – from 2/6 (i.e. from 1/3) to 3/6 (i.e. to 1/2);
→ in the case of a „Fights“ type conflict (as a tactic of the participants) and a „non-zero sum game“ (as an outcome), the probability of achieving a workable and sustainable solution to this conflict is high – from 3/6 (i.e. from 1/2) to 4/6 (i.e. to 2/3);
→ in the case of a „Games“ type conflict (as a tactic of the participants) and a „non-zero sum game“ (as a result), the probability of obtaining a workable and sustainable solution to this conflict is very high – from 4/6 (i.e. from 2/3) to 5/6;
→ in the case of a conflict of the type „Debates“ (as the type of tactics of the participants) and „non-zero sum game“ (as the result), the probability of obtaining a workable and sustainable solution to this conflict is huge – from 5/6 to 1.
In other words, the probability of achieving a workable and sustainable solution to a conflict (i.e., the conflict being resolved) can be ranked from highest to lowest in the following order:
1. The conflict is of a type of „Debate“ (as the tactics of the participants) and „non-zero sum game“ (as the outcome).
2. The conflict is of a type of „Game“ (as the tactics of the participants) and „non-zero-sum game“ (as the outcome).
3. The conflict is of a type „Fight“ (as the tactics of the participants) and „non-zero-sum game“ (as the outcome).
4. The conflict is of a type of „Debate“ (as the tactics of the participants) and „zero-sum game“ (as the outcome).
5. Conflict is of a type of „Game“ (as the tactics of the participants) and „zero-sum game“ (as the outcome).
6. The conflict is of a type of „Fight“ (as the tactics of the participants) and „zero-sum game“ (as the outcome).
References:
1. Deutsch, Karl. The Analysis of International Relations. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., Harvard University, 1968, 116 – 117.
2. Trivers, Robert L. The Evolution of Reciprocal Altruism. // The Quarterly Review of Biology, Vol. 46, №. 1 (Mar., 1971), 35—57, The University of Chicago Press, p. 35.
3. Dawkins, Richard. Selfish Gene. New York: Oxford University Press Inc., 2006, p. 231.
4. Trivers, Robert L. The Evolution of Reciprocal Altruism, ibid., 38 – 39.
5. Axelrod, Robert. The Evoliution of Cooperation. New York: Basic Books, Inc., Publishers, 1984, p. 8.
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9. Rheingold, Howard. Smart Mobs. The Next Social Revoliution. Cambridge, MA.: Basuc Books, 2002, p. 42.
10. Русо, Жан-Жак. Избрани съчинения. Т. 1. С.: Наука и изкуство, 1988, 624 – 625.
Ruso, Zhan-Zhak. Izbrani suchinenia. T. 1. Sofia: Nauka I izkustvo, 1988, 624 – 625. (in Bulgarian)
(Rousseau, Jean-Jacques. Selected works)
11. Кулагин, Владимир. Современные теории международных отношений. // Международная жизнь, 1998, №. 1, с. 82.
Kulagin, Vladimir. Sovremennye teorii mezhdunarodnyh otnosheniy. // Mezhdunarodnaya zhizn, 1998, №. 1, s. 82. (in Russian)
(Kulagin, Vladimir. Modern theories of international relations)
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Kola, Dominik. Politicheskaya sociologia. M.: Ves mir, Infra-M, 2001, 65 – 66. (in Russian)
(Cola, Dominic. Political sociology)
13. Nicholson, Michael. Rationality and the analysis of international conflict. Cambridge University Press, 1992, р. 76.
14. By Nicholson, Michael. Rationality and the analysis of international conflict, ibid., р. 65.
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16. Dawkins, Richard. Selfish Gene, ibid., 209 – 210.
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(Friedman, David. Theory on Appreciate)
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Nay, Dzhouzef. Mezhdunarodnite konflikti. Teoria I istoria. Sofia: Pragama, 1998, 29 – 31. (in Bulgarian)
(Nye, Joseph S. International Conflicts)
20. Axelrod, Robert. The Evoliution of Cooperation, ibid., VIII – IX.
21. Dexit, Avinash K., Barry J. Nalebuff. Thinking Strategicaly, ibid., р. 106.
22. Axelrod, Robert. The Evoliution of Cooperation, ibid., 20 – 21.
23. Rheingold, Howard. Smart Mobs, ibid., 43 – 45.
24. Axelrod, Robert. The Evoliution of Cooperationibid., 73 – 75.
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Afanasiev, S. D., B. A. Babak I drugie. Sosvremennye burzhuaznye teorii mezhdunarodnyh otnosheniy (kriticheskiy analiz). M.L Nauka, 1976, s. 336. (in Russian)
(Afanasiev, S. D., V. A. Babak and others. Modern bourgeois theories of international relations (critical analysis)
07/25/2023
Brief explanation:
The texts of my Studies have been translated into English by me. They have not been read and edited by a native English speaker, nor by a professional translator. Therefore, all errors and ambiguities caused by the quality of the translation are solely mine. But I have been guided by the thought that the purpose of these Studies is to give information about my contributions to the Science of Security by presenting them in a brief exposition, and not to demonstrate excellent English, which, unfortunately, I cannot boast of.
