Brian Wallace

The impact of the termination rule on cooperation in a prisoner’s dilemma experiment

Cooperation in prisoners dilemma games can usually be sustained only if the game has an infinite horizon. We analyze to what extent the theoretically crucial distinction of finite vs. infinite-horizon games is reflected in the outcomes of a prisoners dilemma experiment. We compare three different experimental termination rules in four treatments: a known finite end, an unknown end, and two variants with a random termination rule (with a high and with a low continuation probability, where cooperation can occur in a subgame-perfect equilibrium only with the high probability). We find that the termination rules do not significantly affect average cooperation rates. Specifically, employing a random termination rule does not cause significantly more cooperation compared to a known finite horizon, and the continuation probability does not significantly affect average cooperation rates either. However, the termination rules may influence cooperation over time and end-game behavior. Further, the (expected) length of the game significantly increases cooperation rates. The results suggest that subjects may need at least some learning opportunities (like repetitions of the supergame) before significant backward induction arguments in finitely repeated game have force.

Asymmetric Enforcement of Cooperation in a Social Dilemma

We use a public-good experiment to analyze behavior in a decentralized asymmetric punishment institution. The institution is asymmetric in the sense that players differ in the effectiveness of their punishment. At the aggregate level, we observe remarkable similarities between outcomes in asymmetric and symmetric punishment institutions. Controlling for the average punishment effectiveness of the institutions, we find that asymmetric punishment institutions are as effective in fostering cooperation and as efficient as symmetric institutions. At the individual level, we find that players with higher punishment effectiveness contribute similar amounts to the public account, but have higher earnings and punish more than their weak counterparts.

Power Asymmetries and Punishment in a Prisoner's Dilemma with Variable Cooperative Investment.

In many two-player games, players that invest in punishment finish with lower payoffs than those who abstain from punishing. These results question the effectiveness of punishment at promoting cooperation, especially when retaliation is possible. It has been suggested that these findings may stem from the unrealistic assumption that all players are equal in terms of power. However, a previous empirical study which incorporated power asymmetries into an iterated prisoners dilemma (IPD) game failed to show that power asymmetries stabilize cooperation when punishment is possible. Instead, players cooperated in response to their partner cooperating, and punishment did not yield any additional increase in tendency to cooperate. Nevertheless, this previous study only allowed an all-or-nothing–rather than a variable–cooperation investment. It is possible that power asymmetries increase the effectiveness of punishment from strong players only when players are able to vary their investment in cooperation. We tested this hypothesis using a modified IPD game which allowed players to vary their investment in cooperation in response to being punished. As in the previous study, punishment from strong players did not increase cooperation under any circumstances. Thus, in two-player games with symmetric strategy sets, punishment does not appear to increase cooperation.

The Effect of Power Asymmetries on Cooperation and Punishment in a Prisoner’s Dilemma Game

Recent work has suggested that punishment is detrimental because punishment provokes retaliation, not cooperation, resulting in lower overall payoffs. These findings may stem from the unrealistic assumption that all players are equal: in reality individuals are expected to vary in the power with which they can punish defectors. Here, we allowed strong players to interact with weak players in an iterated prisoners dilemma game with punishment. Defecting players were most likely to switch to cooperation if the partner cooperated: adding punishment yielded no additional benefit and, under some circumstances, increased the chance that the partner would both defect and retaliate against the punisher. Our findings show that, in a two-player game, cooperation begets cooperation and that punishment does not seem to yield any additional benefits. Further work should explore whether strong punishers might prevail in multi-player games.

Financial Contagion in Networks: A Market Experiment

We investigate how the network structure of ?nancial linkages and uncer- tainty about the location of a shock a?ect the likelihood of contagion and the formation of prices in a double auction market experiment. Core-periphery networks are highly susceptible to contagion and generate ?re sales of assets that exacerbate ?nancial contagion beyond the mechanical role of network structure. In contrast, contagion is minimal on circle networks and market prices remain stable. Uncertainty on the location of the shock has little in?uence. The tradersi¯ comprehension level of the network-driven risk is predictive of their behavior and the likelihood of bankruptcy.