Decision Making In Prisoner’s Dilemma

8.8 Discussion

The hypothesis that subjects in iterated Prisoner’s Dilemma games were more cooperative than subjects in single-move Prisoner’s Dilemma games was previously confirmed for example by Andreoni & Miller, 1993.

We reached the same conclusion, when we:

- compared the frequency of cooperation in single-move games and the averaged frequency of cooperation in all iterated Prisoner’s Dilemma games taken together (H1);

- compared the frequency of cooperation in single-move games and the frequency of cooperation in the last five moves for all closed-end iterated Prisoner’s Dilemma games taken together (H2);

- compared the frequency of cooperation in single-move games and the frequency of cooperation in strategy-specific games (H4’).

In other words, hypotheses H1, H2, and H4’ were confirmed. Hypothesis H4 as originally formulated was confirmed only partially because the frequency of cooperation in single-move games is not significantly lower than the frequency of cooperation averaged for iterated games against Random strategy.
We also confirmed hypothesis H2 that frequency of cooperation in single-move games will be higher than the averaged frequency of cooperation in the last move in all closed-end iterated Prisoner’s Dilemma games taken together. This is interesting, because defection in the last move of a closed-end iterated game seems to be a more “dominant” strategy than defection in a single-move game.
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I would like to return to the problem of cooperation in single-move games. We handled this issue in sections 6.14, 6.15, 6.16 a 6.19. Luce & Raiffa (1957) stated axiomatically that defection in single-move Prisoner’s Dilemma is strictly dominant (see section 6.14, 6.19) – empirical findings of considerable amount of cooperation in this type of games thus warrants explanation.
We can think of at least three plausible explanations of cooperative behavior in single-trial games: 1) matching heuristic, 2) control heuristic (or illusion of control), and 3) a spillover from experience in preceding iterated Prisoner’s Dilemmas (encountered in real life or in laboratory – in our experiment, the single-shot games were administered before the iterated games to eliminate unnecessary further transfer of cooperativeness). And there is possibly a fourth reason: inattention. These explanations are discussed in more detail in section 6.16.
The participants in our study cooperated on average in 11,26 trials out of 30 in the single-move games, that means our subjects cooperated in 36,47% on average. Only seven people out of 43 did not cooperate at all in single-move games (that is they followed the strictly dominant strategy). Our results are more or less similar to older findings, for example:
Bó (2005) obtained cooperation rates of 9,17% and 10,34% in his two single-shot experiments.
In a study by Batson & Moran (1999) subjects cooperated in 33% of single-move Prisoner’s Dilemma games in the condition where no empathy for the other player was induced and in 75% of single-move games in the condition where empathy for the other player was induced. In the “no-empathy” condition, the cooperation was 20% when the dilemma was framed as business transaction and 45% when the same dilemma was framed as social exchange. In the “empathy” condition, the cooperation was 70% when the dilemma was framed as business transaction and 80% when it was framed as social exchange.
Subjects in Chater’s et al. (2008) single-move Prisoner’s Dilemma experiments cooperated in 45% when the payoffs were T = 21, R = 20, P = 2, S = 1 (this was a “nice” condition, where subjects had relatively little incentive to defect). In the “nasty” condition (payoffs were T = 0, R = -31, P = -34, S = -35, which means there was relatively big incentive to defect) subjects cooperated in 13% of trials. In mixed condition (50/50 probability of calculating each payoff as either in the “nice”, or in the “nasty” condition) the cooperation rate was 40% (these are the results for the first experiment).
In another experiment by Chater et al. (2008) subjects cooperated in 45% in the “nice” condition (T = 21, R = 20, P = 2, S = 1), the cooperation rate was 10% in the “nasty” condition (T = 36, R = 5, P = 2, S = 1), and 29% in the second mixed condition.
In a third experiment by Chater et al. (2008) subjects cooperated in 33% in the “nice” condition (T = 11, R = 10, P = 1, S = 0), in 18% in the “nasty” condition (T = 0, R = -5, P = -6, S = -11), and in 45% in mixed condition. Interestingly, in the third experiment the average cooperation rate in the mixed condition was significantly higher than in the “nice” condition (p < 0,01).
To conclude, although cooperativeness in an iterated Prisoner’s Dilemma game is usually higher than cooperativeness in a single-trial game, we also corroborated that there is substantial amount of cooperation in the single-trial games. We found that in the last move of a closed-end iterated game people cooperate significantly less often than in the single-trial game.

9. End-game effect

9.1 Task

The task of the present inquiry is to study the existence of the so called end-game effect (or end-effect) in the iterated Prisoner’s Dilemma game. Rapoport and Dale (1966), using data from Rapoport and Chammah (1965a), confirmed the existence of an end-effect, that is a decline of frequency of cooperation towards the end of an iterated Prisoner’s Dilemma game or its definite sequence. End-effect appears to be a typical feature of iterated Prisoner’s Dilemma of known finite length, although it has been called into question by some empirical results (for example Morehouse, 1966). More research on this topic is reviewed in discussion.