The place of game theory in contemporary scholarship is problematic. Although its inventors have presented it by the names "Theory of Games and Economic Behaviour" it is as related to economics as to sociology, politology, and even peace studies. It is not clear at all how what it adds to these fields integrates in them. Discussions of games begin with descriptions of them, not descriptions of who plays them and why. If we know about any interaction between people, what they expect of it, what rules they follow, and how their assessments of each other's possible move influence their decisions, then there is hardly any difficulty to present it as a game in the format of game theory. We may have little difficulty to assume that people interact for some purposes and that their assessments of each other's moves may influence their own decisions. (Even though these assumptions are not always true, they are true often enough to justify the study of such cases.) Still, why should we assume that the rules of any game are given? Perhaps when discussing the economic behaviour of entrepreneurs we may admit that they often take the rules for their conduct as given. But when discussing interactions between delegations that negotiate peace, for a different kind of example, such an assumption is scarcely ever tenable. The same goes for legislation. Yet these days game theoretical discussions often spill over to matters of legislation and of peace making.
Game theorists recommend the strategy of the Pax Romana: if you want peace, prepare for war. It is conditional aggressiveness. The better alternative is the conditional generosity that the European Union (EU) practices with great success.AQ1 These strategies may belong to the game known as the repeated prisoner's dilemma: peace (or mutual cooperation) rests on a threat to punish; to that end, players should maintain their threat. In the repeated prisoner's dilemma, the best response to the strategy of "always cooperate" is to always defect. Yet, these strategies may belong to the game known as the stag hunt. In it, the best response to the strategy of "always cooperate" is cooperating with the other player through each round of the game. The game played by the European Union, we contend, is nearer to the stag hunt game than to the prisoner's dilemma game. Every European Union country recently (rightly, of course) recognizes peace as best—and thus as better than an attack on a defenceless neighbour that would lead to an immediate victory.
What must be avoided during a cold war? The reply of Bertrand Russel (1959) was that the game of chicken must be avoided. He described the game between the USSR and US as a super-game in which every country can refuse playing the (repeat) game of chicken. We will discuss some subsets of the chicken game: the simultaneous one versus the sequential one, one with free information and one without free information, one with an option of communication versus one without this option. Some games are clearly much more dangerous than others; they can be prevented easily by the flow of credible information. We will also contrast the replies of Schelling (1960) and (2006), who supported MAD strategy, with that of Ellsberg (1968). Schelling and Aumann have proposed to apply the strategy of attacking if and only if the other side attacks, while Ellsberg has pointed out that the commitment to attack with big enough probability is sufficient in order to prevent the other side from attacking. (Ellsberg actually proposed to minimize the price of deterrence, while Schelling did not see the price). We argue that Russel's proposal is better, and Ellsberg's is a better choice of the plan of action in the bad game. We propose that even small changes in the choice of the chicken game may make the game less risky. There are many variants of the chicken game, some are much less risky than the others, and some changes of the game can be done with ease.
In this book we have presented an extended version of game theory and its possible application to international relations. Game theory presents games as given; mechanism design theory presents the social planer as one who attempts to acquire complete information and then to decide in its light what game to play; by contradistinction, extended game theory rests on the supposition that a player makes the most important strategic decision when deciding what game to play. This includes, particularly, the decision what game not to play and, more particularly, what group of game to play (for example, a kind of trade), and with whom (for example, in what market). Obviously, it is much easier to choose what game not to play than what game to play. For, the readiness to play may depend on a few independent conditions, whereas for the readiness to avoid playing that game suffice it to cancel one of them. We recommend a methodology that renders game theory part-and-parcel of social science. Also, we distinguish pure game theory which is a branch of mathematics from applied game theory which is a part of the social sciences. Pure game theory is certain and does not refer to reality, whereas applied game theory refers to reality and is uncertain. Particularly uncertain is the answer the question what game is being played in a specific real situation. It is advisable to make it clear whether a given discussion belongs to pure or applied game theory. It is a big and harmful mistake to confuse them. The claim that a theory about society has the status of mathematics makes it closed for empirical testimonies, and then it is pseudo-scientific; it is particularly pernicious when used as a platform for recommendations that are against the public interest, including recommendations to make war. The interest of this book is in peace. We resist the aggressive recommendations that leading game theoreticians make, and even repeatedly. Some hawkish recommendation rest on arbitrary or distorted descriptions of real-life situations, and on the tacit assumption that a description is true and that the game in question is unchangeable. Our interest is to diffuse threats of war. To that end we recommend the following strategies. First, analyzing a real-life situation, we should ask, what game is being played. Being a question of fact, this question is not mathematical but social, and we should see to it that it be social-scientific, namely, testable: the answer to it should always be open for empirical examination. Game theory as social science, we claim, can help see how exactly a cooperative policy is much better in international relations, and why a policy is much better peaceful than aggressive, and how democracies are able to enjoy peace much more than dictatorships, and why freedom of information and transparency and public debates contribute to national security.
Realpolitik is the claim that agreements in international relations are worthless since there is no institution to enforce them. Game theoretician Robert J. Aumann suggests in his Nobel lecture (2006) that “The fundamental insight is that repetition is like an enforcement mechanism” . The application of this insight to international relations allows for the improvement of their applicability and thus it refutes Realpolitik.Early game theory appeared as an alternative to the social sciences; it is better anchored within the social science — as a useful tool. This renders game-theoretical recommendations irenic. Aumann (1990) argues that there is no a priori reason to expect that agreement to cooperate should have practical results. His claim rests on an additional assumption: at times no improvement is observed. Yet at times significant improvement is observed. This should encourage the search for the conditions that lead to improvement; it goes well with the proposal to consider game theory part-and-parcel of social science: how does playing in a given game depend the culture within which it takes place.
Game theory recommends the preference of a strategy over an action; instead, we propose to precede to this the very choice to play or not to play any given game. This renders game theory applicable to real situations. We recommend a combination of Abraham Wald's recommendation to choose between different potential errors with Herbert Simon's recommendation considering our acceptance of any offer we find sufficiently satisfactory. This renders what is found satisfactory revisable and thus it renders Simon's proposal more realistic.
In the realist game of international negotiations, each state attempts to promote their interest regardless of international law. Thus, it is a negotiation in the shadow of the sword, i.e. a negotiation in which each side knows that if the parties do not achieve an agreement, the alternative may be a war, and thus the bargaining position of its party is function of their capacities in a case of war. Negotiation in the shadow of international law is an alternative to it: in this alternative the parties negotiate according to their international legal rights. It reduces injustice and incentives to armament and to terror. It thus promotes peace. A state can choose unilaterally to play the game of negotiations in accord with international law by merely respecting the rights of one's neighbours regardless to their waving swords, and by this have much more peace and generate incentives against terror and armament. This efficiently brings much more security and peace. A policy of respecting international law, combined with conditional generosity, is more efficient. The wish for peace should make a country encourage its neighbours to avoid armament. The best way to do so is to adopt a policy of unilateral respect for international law and conditional generosity towards one's neighbours. The international community should enforce, or at least encourage, negotiations in accord with international law.
The most useful move in playing any game is often the decision, which games to avoid playing. This includes the avoidance of declaring war. The best encouragement to this is providing incentives for enhancing peaceful expectations. Game theory reveals the big advantage of trust, even of minimal trust, in situations that display characteristics such as those of the repeated prisoner's dilemma game, and of the stag-hunt game. Moreover, mutual cooperation is a possible result of the repeated prisoner's dilemma off the moves are visible during the game—at least partially. Without reputation, the players cannot make the necessary difference between the repeated and the one-time game, and then defection remains the dominant strategy. This is so since in this case each player knows that their actions will not influence the actions of the opponent. This invites institutions that promote freedom of information. Thus, game theory leads to much more peaceful, liberal, and friendly approach than some prominent experts on the theory propose.
The different equilibria that game theory proposes concerns plans of action. However, players may choose not only plans of action for given particular games but also what game to play. We propose different new equilibria of super-games that comprise choices of plans for what games to play and for how to play them. Nash theory allows for equilibria for games and for achieving inefficient equilibria in some games. Similarly, the theory should allow for equilibria for super-games: equilibria of the choice of a game. This paper concerns inefficient equilibria in some super-games of the choice of a game to play: possibly all players will stay with a particular game even though they will all benefit from moving from that game to another possible game. People may adhere to the equilibrium of war even when they have an option of peace: they may avoid peace negotiations out of ignorance of the need to change both the game and the strategy.
A repeated game without communication between players is in Nash equilibrium if no player has incentive to change strategy unilaterally. Game-theoretical equilibrium is different. It occurs when no player sees incentives to change strategy unilaterally. A game may be in Nash equilibrium and not in game-theoretical equilibrium due to mistaken judgment. The advantage of Nash equilibrium over game-theoretical one is obvious. The advantage of game-theoretical equilibrium over Nash equilibrium is this. A mistaken move is commoner than the choice of the best move available. Considerations of both kinds bring game theory nearer to Wald's decision theory.
How can cooperative game theory contribute to the prevention of wars? Some scholars who appreciate cooperative game theory express frustration at the paucity of its applications. Yet, some small changes in the theory, particularly enabling small changes in games, may change both the theory and the games for the better. Abstaining from playing risky games is clearly commendable, and so is the search for peaceful means for the prevention of playing risky games. Games that tend to discourage cooperation and to promote war are better not played. It has been seen that so far, cooperative game theory, namely, the theory of games with perfectly enforceable contracts, has no significant use. It will be more useful, however, particularly for social planners, if it is armed with a toolkit for the choice of games to play in order to promote peace and cooperation, and for the choice of games to avoid playing for the same reason. Also, integrating cooperative game-theory into the social sciences may encourage study of the conditions that help promote peace and cooperation. In addition, it is commendable to import these achievements of non-cooperative game theory to cooperative game theory. The application of the theory of Nash equilibrium, mutatis mutandis, to cooperative game theory, may help prevent playing games that may incite war.
The International Criminal Court (the ICC) has neither universal jurisdiction (jurisdiction that is not dependent on the consent of the parties), nor consent-based jurisdiction (jurisdiction that depends on the mutual consent of the two involved states). The ICC does have jurisdiction in cases in which the conduct to be judged took place in a State that accepts the Rome Statute (that declares that the crimes within the jurisdiction of the Court shall not be subject to anystatute of limitations).Universal jurisdiction would provide the best protection of human rights. Universal jurisdiction does not obtain. It obtains only partially. That is to say, the ICC, which is the institution that is closest to having universal jurisdiction, has only partial universal jurisdiction. The assumption is common that partial jurisdiction is second best. This is not always true. The shift of the ICC from traditional consent- based jurisdiction to a partially universal jurisdiction might weaken human rights protection in some scenarios. The ICC may provide the following undesirable incentives: it might encourage an occupying state to continue the occupation in order to prevent the emerging free state from becoming a party to the Rome Statute and, especially, from accepting its jurisdiction retroactively. It may likewise encourage the occupying state to initiate a civil war in the occupied state as a means of discouraging it from joining the ICC. Moreover, it may encourage
We argue that there is a stream in the Talmud that attributes the responsibility to one player alone in the case of a joint crime/joint tort, and even in dividing the credits for a joint Mitzvah. We used the game theory to investigate which incentives are provided by this approach, which games are created, which games are blocked, and to which results this approach leads. In this paper, we present some Talmudic games. Although in Jewish law, a sinner cannot be a witness, one Talmudic rabbi proposes a rule that, in the case of a joint crime, one of the criminals may testify against their friend (who is the other criminal), but the court will not recognize the self-incriminating part of the testimony. The testimony of the criminal will also neutralize the friend’s capacity to testify against the criminal since the friend will be considered a sinner after the initial testimony. We argue that this rule may lead to maximal deterrence. We also investigate other Talmudic rules that impose responsibility on (only) one partner in the case of a joint deed: the halachic rule, which imposes responsibility in the case of bribery on the taker only. Another Talmudic rule that imposes the responsibility on the last player and only on them in the case of a joint murder/tort/mitzvah that was performed sequentially, and the rule that imposes responsibility (only) on the agent and not on the sender. We also investigate the different rules about imposing responsibility on the partners who did not cover a pit. Surprisingly, there are rules that impose responsibility on only one partner, and we argue that this prevents a prisoner’s dilemma. This paper is a part of the developing field of the Talmud and Game Theory.
In this article, I begin with the question, what should be the agenda of political economy and of law and economics? I argue that the agenda should include humanistic economic questions, such as how to protect weak workers and how to minimize suffering. Humanistic economics is especially important when we discuss legal questions. Then, I discuss this article’s central question: How should power gaps be handled in the labour market? I examine the various answers to this question and discuss the fundamental controversies in political economy. In particular, I examine the solution of a free market vis-a-vis the social-democratic solutions of labour legislation—especially the minimum wage law, encouragement of organized labour, and transfer of wealth through tax laws.
It is a commonly held intuition that increasing punishment leads to less crime. Let's move our glance from the punishment for the crime itself to the punishment for the attempt to commit a crime, or to the punishment for the threat to carry it out. We'll argue that the greater the punishment for the attempt to rob, i.e. for the threat, give me your money or else…, the greater the number of robberies and attempts there will be. The punishment for the threat makes the withdrawal from it more expensive for the criminal, making the relative cost of committing the crime lower. In other words, the punishment of the attempt turns the attempt into a commitment by the robber, while at the same time turning an incredible threat into a credible one. Therefore, the robber has a strong interest in a legal system that increases the punishment of the attempt.
The International Criminal Court (The ICC) exercises partial universal jurisdiction, which means that its jurisdiction lies between a completely universal jurisdiction and a purely state-consent-based jurisdiction. Whereas a completely universal jurisdiction gives the strongest legal incentive for not violating human rights, it is not clear that a partially universal jurisdiction is the second-best possibility; the shift from the traditional consent-based jurisdiction to partially universal jurisdiction at the ICC might weaken human-rights protection. First, it might encourage an occupying state to continue the occupation in order to prevent the emerging free state from becoming a party to the Rome Statute and, especially, from accepting its jurisdiction retroactively. Second, it may encourage the occupying state to initiate a civil war in the occupied state in order to discourage it from joining the ICC. Third, it may encourage the occupying state to promote a terrorist leadership for the occupied people in order to discourage them from joining the ICC. Later, we will discuss some possible solutions to those problems.
This paper makes the point that a court decision that is open for appeal is actually equivalent to a take-it-or-leave-it settlement proposal to both parties. In order that the case will not be appealed they both need to "take", i.e., accept, this proposal. Thus, a right to appeal actually activates the regressive effects that characterize settlements, also with respect to lower-court decisions. Legal Uncertainty has a regressive effect on lower court decisions: if the judge wishes to block appeals in order to protect one party's interest, her own self-interest, or the system's interest, her decision will be regressively biased relative to the higher-court decision. In fact this could happen also without strategic judges, but as an evolutionary process: the survival power of regressive decisions is stronger in a legally uncertain regime.
Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form small cancellation theory we show that the groups in this family are bi-automatic.
