Decision Making In Prisoner’s Dilemma

13. Conclusions

In the practical part of my thesis we dealt with the difference between iterated and single-trial Prisoner’s Dilemma game in terms of the frequency of cooperation (section 8.), and we found that the amount of cooperation in singe-trial games was indeed lower than in the iterated games. On the other hand, we found that on the last move of an iterated game with known terminating point, people cooperate less than in single-trial games. This finding, although relatively new and original, would not surprise students of expirimental games, since the so called “end-effect” is a phenomenon quite characteristic for finite iterated games. In section 9. we formulated several hypotheses to test this effect and we confirmed its existence, we also specified that it occurs only in the very last moves of a close-end game, and that it influences actual decision making, as well as subjects’ expectations about their own and their opponents’ prospective decisions.

In section 10. we confirmed the existence of an effect of learning in repeated encounters with certain strategies in the Prisoner’s Dilemma game. No similar research was done previously. It remains to determine more precisely what form does the learning take (e. g. pattern recognition, probability assessing, heuristic/strategic rules adopted, etc.). We confirmed that nonbinding communication (cheap talk) can enhance subjects’ willingness to cooperate and their expectations about their opponent’s willingness to cooperate (section 11.). We found that friendly and ambiguity tolerant subjects tend to cooperate more in some circumstances (section 12.) – these findings corroborate some previous “personality” related research of strategic games; on the other hand more research is very much needed in this specific area. For example we did not find any relation between risk avoidance and cooperativeness in the Prisoner’s Dilemma game, neither was any such relation discovered by previous research. This might seem unexpected, because players of Prisoner’s Dilemma are influenced for example by manipulating the pay-off matrix (see section 6.24) and the length of the game (section 6.18) – both can be seen as manipulating the amount of risk present in the game. So further inquiry into risk perception in strategic games is necessary.
In theoretical part we discussed some important contributions to decision making theory: classical utility theory and classical decision making (section 2.), bounded rationality theory (section 3.), prospect theory (section 4.), heuristics and biases approach (section 5.), and, of course, experimental game theory (section 6.). Here I would like to acquaint the reader with a few new research questions for the strategic gaming study, that draw inspiration from these decision making theories:
1) What will happen if certain parameters (such as the pay-offs, or the discount parameter) of the game are given only probabilistically? Will cooperation be promoted, or reduced? Will we observe such phenomena as overestimation of low probabilities and underestimation of high probabilities, or risk seeking for gains and risk aversion for losses of low probability, and risk aversion for gains and risk seeking for losses of high probability (see section 4., paragraphs (1) and (2))?
2) The influence of uncomplete information on subjects’ decision making can be studied (as noted in section 3.2, the unavailability of information for determining optimal solution is the main reason why people are boundedly rational). Subjects can for example play one trial of Prisoner’s Dilemma game against all other subjects in a pool of players (round n), then they get a feedback about one randomly chosen encounter from this series (encounter e that belongs to round n). The encounter e is chosen randomly; another possibility is false feedback (if the opponent in encounter e played C, the subject is given information that he played D, and vice versa), or the feedback can be false and random in the sence that the experimentator tells each subject randomly that one of his opponents (the one in encounter e) played C, or D, without respect to the actual decisions made by players in the pool (and the player encontered in e). Can cooperation be sustained under such circumstances, and if so, under what conditions (number of players, pay-off matrix, total number of trials, etc.)?
3) We can think of several ways or degrees of introducing noise into the game (see section 4.1, and section 6.3, paragraph (2)). What systems are relatively immune from, and conversely relatively sensitive to noise (number of players, strategies employed, cheap talk present, w parameter, pay-off matrix, the time when noise is introduced)?
4) We may try to determine the exact ways in which base rates of expected cooperation on the opponent’s part are learned/developped by subjects (see sections 5.1, 5.2, 5.3). Do, for example, early encounters with a given opponent have a relatively more decisive influence on the formation of subject’s base rates? Are base rates really transfered from previous into latter encounters with different opponents? What is the relative influence of cooperative and competititve encounters on forming base rates, and what are the mediating influences there (such as the structure of pay-offs)?
5) Information assymetries can be studied (for instance, part of the subjects in the pool get noisy information about encounters with other subjects and about game parameters, part of the subjects get reliable information, and part of the subjects get incomplete information, part of the subjects get some “extra” information, such as cheap talk). Will differentially informed subjects behave differently? What will be the relative influence of differentially informed subjects on the whole system (pool of subjects)?
The results of the experimental part of my thesis were summarized in this section and some possibilities for further research were suggesed.