N-person Prisoner's Dilemma Research Articles

Prosocial values and group assortation : Within an N-person prisoner's dilemma game.

Ninety-five freshmen each recruited three peers to play a "group bidding game," an N-person prisoner's dilemma in which anyone could win movie tickets depending on their scores in the game. Prior to playing, all participants completed a measure of prosocial value orientation. Replicating and extending earlier findings (Sheldon and McGregor 2000), our results show that prosocial participants were at a disadvantage within groups. Despite this vulnerability, prosocial participants did no worse overall than asocial participants because a counteracting group-level advantage arose for prosocials, who tended to be concentrated in groups. Implications of this assortative process for the egoism/altruism debate, and for hierarchical selection theory, are discussed.

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.

Threshold Effects and the Decline of Cooperation

Game-theoretical analyses of the n-person Prisoner's Dilemma (PD) and of group production have largely ignored the impact of threshold effects on the evolution of cooperation. This article introduces a model where uncooperative action cannot be detected as long as it does not exceed a certain level. The resulting breakdown of cooperation parallels the backward induction effect of a finitely repeated PD and might illustrate pessimistic social theories like Olson's “institutional sclerosis.” But surprisingly, cooperation remains at an intermediate level if simple random variations of population size occur. This hints at the possibility that the mentioned pessimism is an often overrated position.

Causal attribution of choice behavior in three N-Person Prisoner's Dilemmas

The major purpose of the present study was to compare the causal attributions made by Cooperators and Defectors for a cooperative and a noncooperative target in an N-Person Prisoner's Dilemma. Factor analyses of attributions yielded two factors associated with the target's intrapersonal processes. One intrapersonal factor was a combination of weakness and lack of intelligence, labeled Ignorance, and the second was related to good versus bad, labeled Concern for Others. Among Cooperators, noncooperation was attributed more than cooperation to Ignorance. Defectors did just the opposite. This supports the idea that one's own predisposition prescribes criteria for rational choice in Prisoner's Dilemma. Both Cooperators and Defectors attributed cooperation more than noncooperation to Concern for Others. However, Cooperators made the largest discriminations on this factor. The above findings were observed in three N-Person Prisoner's Dilemmas varying in the extent to which Fear and Greed could be the cause of noncooperation. In addition to Ignorance and Concern for Others, factor analyses revealed two factors associated with the situational pressures of Fear and Greed in the payoff matrix itself. The different dilemmas appeared to affect both Cooperators' and Defectors' attributions to Fear and Greed in a manner consistent with their underlying game theoretical differences.

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.

A Planning Model for a Water Quality Management Agency

The Canada Water Act provides for the establishment of regional management agencies in areas designated as water quality management areas. These agencies must establish water quality standards within their area and design a control program to meet these standards efficiently. This paper describes a model for planning an efficient water quality program within a river basin. The waste abatement control employed is called the rent allotment control, whose merit is that its implementation provides a solution to the information problem of efficient waste abatement. The control is implemented through a bargaining process or game between the agency and the waste dischargers that may be characterized as an n-person prisoner's dilemma. The game provides the agency with information about individual waste abatement costs, and terminates in a set of agreements on rents and allotments which depend upon the bidding strategies adopted by each player. “Optimal” bidding strategies are examined under the assumption that waste dischargers are risk averse and cost minimizing. An example of the operation of the control is provided using data from the Ottawa River Basin.

To join or not to join: An approach to the unionization decision

The problem of joining or not joining a (faculty) union is analyzed via a simplified analogy. The effects of group size are discussed and it is shown that the decision structure is an n-person prisoner's dilemma. Several possible solutions to the dilemma are discussed but the ultimate solution appears to be more a matter of social ethics than logic.

The N-person prisoner's dilemma: some theory and a computer-oriented approach.

The two-person, two-strategy prisoner's dilemma is, by now, well known. The purpose of the research reported here is to start an investigation of the more interesting multiple-person, multiple-strategy analogue of the prisoner's dilemma. The multiple-person, two-strategy game is the subject of this study. Four interpretations of the game are possible. Each of these is presented and one is selected for further study. The rationale for a combined laboratory-computer approach is given, some decision-making models for the game are constructed, and the results of the simulations of the models are reported.