How democracy resolves conflict in difficult games

Democracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative outcome. In the transformed game, it is always rational for voters to vote for the cooperative outcome, because cooperation is a weakly dominant strategy independent of the decision rule and the number of voters who choose it. Such games are illustrated by 2-person and n-person public-goods games, in which it is optimal to be a free rider, and a biblical story from the book of Exodus.Democracy; voting; social choice; public goods; game theory; Prisoners' Dilemma; Bible

Every Normal-Form Game Has a Pareto-Optimal Nonmyopic Equilibrium

It is well-known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: Every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis

The Stable Set of the Social Conflict Game with Delegations: Existence, Uniqueness, and Efficiency

We investigate the stable sets of social conflict games by employing the framework of the (abstract) system by Greenberg (Theory of Social Situations: An Alternative Game theoretic Approach, Cambridge University Press, 1990).The social conflict game includes the prisoners\u27 dilemma and the chicken game.We show that the stable set may fails to exist in the system directly derived from the social conflict game.The stable set exists if and only if the strong equilibrium exists in the underlying game.We consider another system where an agent is prepared and each player is allowed to delegate his decision to the agent. Then, the stable set always exists and consists of Pareto efficient outcomes with a certain property. We also discuss the relationship between the strong equilibrium and the stable set for the model with delegations

Farsightedness in Games: Stabilizing Cooperation in International Conflict

We show that a cooperative outcome—one that is at least next-best for the players—is not a Nash equilibrium (NE) in 19 of the 57 2 x 2 strict ordinal conflict games (33%), including Prisoners’ Dilemma and Chicken. Auspiciously, in 16 of these games (84%), cooperative outcomes are nonmyopic equilibria (NMEs) when the players make farsighted calculations, based on backward induction; in the other three games, credible threats induce cooperation. More generally, in all finite normal-form games, if players’ preferences are strict, farsighted calculations stabilize at least one Pareto-optimal NME. We illustrate the choice of NMEs that are not NEs by two cases in international relations: (i) no first use of nuclear weapons, chosen by the protagonists in the 1962 Cuban missile crisis and since adopted by some nuclear powers; and (ii) the 2015 agreement between Iran, and a coalition of the United States and other countries, that has been abrogated by the United States but has forestalled Iran’s possible development of nuclear weapons

Single-payoff farsighted stable sets in strategic games with dominant punishment strategies

We investigate the farsighted stable set in a class of strategic games with dominant punishment strategies. In this class of games, each player has a strategy that uniformly minimizes the other players’ payoffs for any given strategies of other players. We particularly investigate a special class of the farsighted stable sets each of which consists of strategy profiles yielding a single payoff vector. We call such farsighted stable sets as the single-payoff farsighted stable sets. We propose a concept called the inclusive set that completely characterizes the single-payoff farsighted stable sets in the strategic games with dominant punishment strategies. We also show that the set of payoff vectors yielded by the single-payoff farsighted stable sets is closely related to the strict -core in strategic games. Further, we apply the results to the strategic games where each player has two strategies and　strategic games associated with some market models.First version: September 30, 2016Revised version: October 24, 201

How democracy resolves conflict in difficult games

Democracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative outcome. In the transformed game, it is always rational for voters to vote for the cooperative outcome, because cooperation is a weakly dominant strategy independent of the decision rule and the number of voters who choose it. Such games are illustrated by 2-person and n-person public-goods games, in which it is optimal to be a free rider, and a biblical story from the book of Exodus

A Political Reciprocity Mechanism

We consider the problem of designing legislative mechanisms that guarantee equilibrium existence, Pareto-efficiency, and inclusiveness. To address this question, we propose a finite-horizon voting procedure that embeds clauses of reciprocity. These clauses grant voters the right to oppose actions that are not in their interest, retract actions that face opposition, and punish harmful actions. We study voters\u27 strategic behavior under this voting procedure using two classical approaches. Following the blocking approach, we introduce two related solution concepts---the reciprocity set and the sophisticated reciprocity set---to predict equilibrium policies. We then show that these solution concepts (1) are always non-empty; (2) only select Pareto-efficient policies; (3) strategically protect minority interests; and (4) are compatible with classical notions of fairness and Rawlsian justice in distributive problems. Following the non-cooperative approach, we provide an implementation of each of these solution concepts in subgame perfect equilibrium, which makes them applicable in a wide range of legislative settings. We also extend them to effectivity functions, a large class of games that includes strategic form games. A comparative analysis shows that the reciprocity mechanism has other desirable features and properties that distinguish it from other well-known voting mechanisms and solution concepts