Evidential reasoning in the prisoner's dilemma

Classic game theory considers defection to be the rational choice in the Prisoner's Dilemma. Although defection maximizes a player's gain regardless of the opponent's choice, many players cooperate. We suggest that cooperation can be explained in part by expectations of reciprocal behavior, that is, by the belief that players facing the same situation probably will come to the same decision. In Experiment 1, expectations of reciprocity were experimentally manipulated. As predicted, cooperation increased monotonically with these expectations. In Experiment 2, experimentally manipulated expectations of opponent cooperation were not associated with higher rates of cooperation. These findings are interpreted in light of a general model of payoff maximization, and implications for other models (e.g., social value orientation) are discussed.     

Self-control by pigeons in the prisoner's dilemma

Pigeons played a repeated prisoner's dilemma game against a computer that reflected their choices: If a pigeon cooperated on trial n, the computer cooperated on trial n + 1; if the pigeon defected on trial n, the computer defected on trial n + 1. Cooperation thus maximized reinforcement in the long term, but defection was worth more on the current trial. Under these circumstances, pigeons normally defect. However, when a signal correlated with the pigeon's previous choice immediately followed each current trial choice, some pigeons learned to cooperate. Furthermore, cooperation was higher when trials were close together in time than when they were separated by long intertrial intervals.     

Effects of initial choices in the prisoner's dilemma

In the two‐person prisoner's dilemma game (PDG), there is considerable evidence that the tit‐for‐tat (TFT) strategy is most effective in inducing the other person to cooperate. One of the important features of the TFT strategy is that it cooperates on the first trial. We varied the initial choices of a simulated other, and tested the effects of (a) initial choices (cooperation or defection), and (b) persistence of initial choices: unilateral cooperation (or defection) on the first trial, first two trials, or first four trials. Results showed that a cooperative strategy—one that starts with cooperative choices—induced greater cooperation than a strategy that started with defections. The results of this study clearly show that (a) a cooperative strategy—one that initiates unilateral cooperation at the outset and then adopts a TFT strategy—is very effective in inducing subsequent cooperation from the other party, (b) the effectiveness of a cooperative strategy varies directly with the cooperative orientation of the other party (a cooperative strategy is more effective against a cooperative than a competitive person), and (c) initial cooperation is more effective if it is repeated more than once. Copyright © 2002 John Wiley & Sons, Ltd.     

Dominance-ascendance and behavior in the reiterated prisoner's dilemma game

The reiterated prisoner's dilemma was played for 300 trials by 3 groups of subjects, each containing 12 single-sexed pairs — a group of high-dominance pairs, another of low-dominance pairs, and the third of mixed pairs.     

Commitment and self-control in a prisoner's dilemma game

Humans often make seemingly irrational choices in situations of conflict between a particular smaller-sooner reinforcer and a more abstract, temporally extended, but larger reinforcer. In two experiments, the extent to which the availability of commitment responses-self-imposed restrictions on future choices-might improve self-control in such situations was investigated. Participants played a prisoner's dilemma game against a computer that played a tit-for-tat strategy-cooperating after a participant cooperated, defecting after a participant defected. Defecting produced a small-immediate reinforcer (consisting of points convertible to gift cards) whereas cooperating increased the amount of subsequent reinforcers, yielding a greater overall reinforcer rate. Participants were normally free to cooperate or defect on each trial. Additionally, they could choose to make a commitment response that forced their choice for the ensuing five trials. For some participants, the commitment response forced cooperation; for others, it forced defection. Most participants, with either commitment response available, chose to commit repeatedly despite a minor point loss for doing so. After extended exposure to these contingencies, the commit-to-cooperate group cooperated significantly more than a control group (with no commitment available). The commit-to-defect group cooperated significantly less than the control group. When both commitment alternatives were simultaneously available-one for cooperation and one for defection-cooperation commitment was strongly preferred. In Experiment 2, the commitment alternative was removed at the end of the session; gains in cooperation, relative to the control group, were not sustained in the absence of the self-imposed behavioral scaffold.     

Contingencies of reinforcement in a five-person prisoner's dilemma

As in studies of self-control, a tit-for-tat contingency in an iterated prisoner's dilemma game creates a conflict between maximization of local and global reinforcement. The present experiments examine this conflict in a multiplayer prisoner's dilemma game. Versus tit for tat, cooperation corresponds to self-control; defection, always immediately reinforced, corresponds to impulsiveness. Three experiments examined sensitivity of behavior to the global reinforcement contingency imposed by tit for tat. Undergraduates played a five-player prisoner's dilemma game against four dummy players programmed to play tit for tat or randomly. With tit for tat, a player's cooperation (or defection) increased dummy players' cooperation (or defection) on subsequent trials-reinforcing cooperation and punishing defection in the long run. Participants cooperated at a higher rate when the dummy players played tit for tat than when the dummy players played randomly. These results are consistent with findings in corresponding studies of self-control. Some participants, caught in a trap of mutual defection with the tit-for-tat playing dummy players, came to cooperate when the tit-for-tat contingency was reset ("forgiving" participants' previous defections) during a pause in the game. This increase was a result of the combined effects of a pause and reset; neither pausing nor resetting independently resulted in an increase in cooperation.     

Probability of reciprocation in repeated prisoner's dilemma games

Both social cooperation and self‐control require reciprocation. In social cooperation situations a single person's cooperative act, if not reciprocated by others, would be unreinforced both immediately and in the long term. Similarly, a single act of self‐control (refusing a single cigarette, for example), if not followed up by other such acts, would also be unreinforced immediately and in the long term. The present experiments varied probability of reciprocation in a prisoner's dilemma‐like game that could resemble a social cooperation or a self‐control situation. Participants earned points by playing against a computer. The computer offered the participant a choice between 5 or 6 points (‘cooperation’ by the computer) or between 1 or 2 points (‘defection’ by the computer). The participant's choice of the lesser alternative (‘cooperation’) or the greater alternative (‘defection’) on the current trial led, respectively, to cooperation or defection by the computer on the next trial with a probability (probability of reciprocation, PR) which could vary. When PR was greater than 63%, consistent cooperation maximized the participant's earnings. When PR was less than 63%, defection maximized earnings. Three conditions were studied: PR signaled by spinners; PR unsignaled; PR unsignaled with participants believing that they were playing with another person, not the computer. With PR = 100% (‘tit‐for‐tat’) and PR = 50%, the modal participant maximized earnings under all three conditions. With PR = 75%, participants maximized earnings only when PR was signaled. These results indicate that differences between people's tendency to cooperate with other people (social cooperation) and their tendency to cooperate with their own future interests (self‐control) may lie in differences in subjective PR. Copyright © 2001 John Wiley & Sons, Ltd.     

Prior experience and patterning in a prisoner's dilemma game

Female college students first played a pseudo-prisoner's dilemma (PPD) game with the experimenter, who followed a fixed strategy. In the first experiment the experimenter's strategies for different groups of subjects were: (a) play tit-for-tat; (b) play randomly; (c) always cooperate; (d) always defect (‘cooperation’ and ‘defection’, defined as in an actual prisoner's dilemma game). Only the tit-for-tat group increased cooperation over trials; other groups decreased cooperation. After playing the PPD with the experimenter, subjects played an actual prisoner's dilemma (PD) game with each other. In the PD game, subjects began cooperating moderately but cooperation deteriorated regardless of what the experimenter's strategy had been in the earlier (PPD) game. In a second experiment, subjects again played a PPD game with the experimenter and then played a PD game with each other. Half played one trial at a time as in the first experiment while half played in patterns of four trials at a time. In the PD game, patterning of trials retarded the development of mutual defection regardless of previous experience. The cooperation-preserving effect of patterning of trials in this social task is compared with similar effects on individual tasks involving self-control and risk-aversion. © 1998 John Wiley & Sons, Ltd.