N-person Prisoner's Dilemma Game Research Articles

Universals, Knowledge Claims, and Methods

Research Article| July 01 2011 Universals, Knowledge Claims, and Methods Joe Oppenheimer Joe Oppenheimer Joe Oppenheimer has written extensively on issues of social justice and rational choice theory. His latest works include three co-authored articles in the Journal of Politics reinterpreting all behavioral results in n-person prisoner dilemma games and Political Principles: A Rational Choice Theory Guide to Politics and Social Welfare. Search for other works by this author on: This Site Google The Good Society (2011) 20 (2): 249–280. https://doi.org/10.5325/goodsociety.20.2.0249 Cite Icon Cite Share Icon Share Facebook Twitter LinkedIn MailTo Permissions Search Site Citation Joe Oppenheimer; Universals, Knowledge Claims, and Methods. The Good Society 1 July 2011; 20 (2): 249–280. doi: https://doi.org/10.5325/goodsociety.20.2.0249 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All Scholarly Publishing CollectivePenn State University PressThe Good Society Search Advanced Search The text of this article is only available as a PDF. Copyright © 2012 The Pennsylvania State University2012The Pennsylvania State University Article PDF first page preview Close Modal You do not currently have access to this content.

Chaos, oscillation and the evolution of indirect reciprocity in n-person games

Evolution of cooperation among genetically unrelated individuals has been of considerable concern in various fields such as biology, economics, and psychology. The evolution of cooperation is often explained by reciprocity. Under reciprocity, cooperation can prevail in a society because a donor of cooperation receives reciprocation from the recipient of the cooperation, called direct reciprocity, or from someone else in the community, called indirect reciprocity. Nowak and Sigmund [1993. Chaos and the evolution of cooperation. Proc. Natl. Acad. Sci. USA 90, 5091–5094] have demonstrated that directly reciprocal cooperation in two-person prisoner's dilemma games with mutation of strategies can be maintained dynamically as periodic or chaotic oscillation. Furthermore, Eriksson and Lindgren [2005. Cooperation driven by mutations in multi-person Prisoner's Dilemma. J. Theor. Biol. 232, 399–409] have reported that directly reciprocal cooperation in n-person prisoner's dilemma games (n>2) can be maintained as periodic oscillation. Is dynamic cooperation observed only in direct reciprocity? Results of this study show that indirectly reciprocal cooperation in n-person prisoner's dilemma games can be maintained dynamically as periodic or chaotic oscillation. This is, to our knowledge, the first demonstration of chaos in indirect reciprocity. Furthermore, the results show that oscillatory dynamics are observed in common in the evolution of reciprocal cooperation whether for direct or indirect.

Punishing free riders: direct and indirect promotion of cooperation

Human cooperation in a large group of genetically unrelated people is an evolutionary puzzle. Despite its costly nature, cooperative behavior is commonly found in all human societies—a fact that has interested researchers from a wide range of disciplines, including biology, economics, and psychology, to name a few. Many behavioral experiments have demonstrated that cooperation within a group can be sustained when free riders are punished. We argue that punishment has both a direct effect and an indirect effect on promoting cooperation. The direct effect of punishment alters the consequences of cooperation and defection in such a way as to make a rational person prefer cooperation. The indirect effect of punishment promotes cooperation among conditional cooperators by providing the condition necessary for their cooperation (i.e., the expectation that other members will also cooperate). Here we present data from two one-shot n-person prisoner's dilemma games, demonstrating that the indirect effect of punishment complements the direct effect to increase cooperation in the game. Furthermore, we show that direct and indirect effects are robust across two forms of punishment technology: either when punishment is voluntarily provided by game players themselves or when it is exogenously provided by the experimenter.

The Dilemma of Prisoners

Stalin's Great Terror was one of history's most massive political purges. In its form, the Terror resembled a one-shot, n-person prisoner's dilemma game. Although the Terror could not have been sustained if prisoners cooperated, most prisoners defected against one another, as the model would predict. Yet the record of the Terror also demonstrated that in a mass purge there exists a wider strategy set than that of the prisoner's dilemma game. Using an illustrative case and a generalized model of purges, it is shown that if prisoners implicate their interrogators and play what is called a “transformation” strategy, they raise the cost to the authority of conducting the purge. In fact, the authority has no consistent best response to the transformation, and the purge should not be sustainable for long thereafter. The Great Terror was apparently limited by employment of this transformation. Limitations on the formation and use of such a strategy are also considered.

AN ANALYSIS OF CHOICE BEHAVIOR IN 2-ALTERNATIVE N-PERSON HOMOGENEOUS GAMES

The choice behavior in 2-Alternative N-Person homogeneous games was exhaustively investigated using a questionnaire method.Two complete sets of 39 games, the one set was based on linear payoff functions (L condition), and the other on two-interval step-wise payoff functions Scondition, were chosen on the basis of a game classification method developed by Takigawa (1989).The 39 games all for 11 players were defined respectively by the combinations of each level of four endpoints of payoff functions. Each of the 39 games was made identifiable by 4 alphabets representing the level of the endpoint (A>B>C>D). For example, the N-Person Prisoner's Dilemma game is coded DBCA. The subjects participated consisted of 132 college students, each of whom was assigned randomly to either of the two conditions. Table 3 shows the choice distributions and the degree of difficulties rated by the subjects on a 7-point scale. There was little difference between the 2 conditions in the choice distributions and the degree of difficulties. An efficiency factor was calculated for each game in order to evaluate the subjects' choice in terms of collective payoff. Figs. 1 and 2 show the two dimensional distributions of the 39 games in each condition, where the ordinate denotes the efficiency and the abscissa the experienced degree of difficulty. Based on the obtained two dimensional distributions, each game was classified into one of the 4 categories, highdifficulty high-efficiency, high-difficulty lowefficiency, low-difficulty high-efficiency, and lowdifficulty lowefficiency categories. Some noteworthy non-trivial games such as BBBA, CABA, CBAD, and CBCA were found in addition to N-Person PD (DBCA). Seven decision motives were extracted from the reasons given by subjects for their choice of alternatives in each game. The extracted motives were: type of alternative, maximax, minimax, collective payoff, α comparison, β comparison, and maximization of difference. Table 4 shows the alternatives in each game chosen by each of the 7 motives.The types of dilemmas, the equivalent and the exclusive, can be discriminated in the framework of the decision motive model. The relations between the types of dilemmas and the conflict situations were also analyzed. Finally, some methodological problems in the experimental game studies were discussed.

The evolution of reciprocity in sizable groups

Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, we consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. We show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases.

“Public” Choice and Cooperation in n-Person Prisoner's Dilemma

Four-person groups played repeated trials of an n-Person Prisoner's Dilemma game under two information conditions. In one condition, each player's choice was made known to the others following each trial. In the other information condition each subject was informed only of the number of others who cooperated or competed on each trial. The first condition was a “public choice” situation while the second was an “anonymous choice” situation. The data supported the hypothesis that there would be greater cooperation in the “public choice” condition than in the “anonymous choice” condition since the former created a situation in which the individual would be made accountable to the group for the consequences of his choices. The results are discussed in terms of the various manipulations of group process which can produce deindividuation, that is, a lessening of the individual's propensity to behave in a socially approved manner.