Embedding social dilemmas in intergroup competition reduces free-riding

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Abstract

We study a class of multi-level collective actions, in which each individual is simultaneously engaged in an intragroup conflict and intergroup competition. The intragroup conflict is modeled as an n-person Prisoner’s Dilemma game, in which the dominant strategy is to contribute nothing. The intergroup competition is for an exogenous and commonly known prize shared by members of the winning group. We focus on the effects on the level of contribution of the two most common sharing rules for dividing the prize, equal and proportional. Our results show that (1) embedding the intragroup conflict in intergroup competition markedly reduces free riding; (2) the proportional profit sharing rule significantly outperforms the egalitarian rule, and the difference between the two increases with experience; (3) under egalitarian but not under proportional sharing, there is over-contribution compared to theoretical predictions, and (4) a simple reinforcement-based learning model accounts for the aggregate results of all five experimental conditions.

Section snippets

Model

Denote the number of groups competing for the prize by n (n  2), the number of players in group k by m (k) (k = 1, 2,  , n), and the total number of players across all n groups by N. Assume each of the N players has the same budget (henceforth “endowment”) that we denote by e. The strategy space is continuous; each member i of group k can invest (contribute) any fraction of her endowment. Denote the individual contribution by xik (0  xik  e), the total contribution of group k by Xk (Xk = xik), and the

Subjects

A total of 112 undergraduate subjects participated. They had volunteered to take part in a 2-h computer-controlled experiment on interactive decision making with payoff contingent on performance. Individual earnings, not including the $5.00 show-up fee, ranged between $17.75 and $31.00. Experimental earnings for each round were originally computed in tokens and converted into US$ at the end of the experiment according to conversion rates included in the subjects’ experimental instructions (see

Results

We observed no significant differences between the mean contributions per round of Sessions 1 and 2 of Condition EG2. The mean contributions in Session 2 of Condition PR2 exceeded the ones in Session 1 by about 4 tokens, but the trend across rounds was the same. Therefore, the two sessions in Condition EG2 were combined, as were the two sessions in Conditions PR2. In equilibrium, individual contributions in Conditions PR1 and PR2 should exceed contributions in Conditions EG1 and EG2, which, in

Discussion

We have presented evidence that embedding independent within-group social dilemmas of the PD kind in a between-group competition for an exogenous prize alleviates free-riding, the size of the effect depending on the prize sharing rule. In fact, the mean total contribution by all the N = 8 cohort players in Conditions PR1 and PR2—about 320 for Condition PR1 and 265 for Condition PR2—exceeds the value of the prize S (S = 208 in Condition PR1 and S = 152 in Condition PR2) by about 60 and 70%,

Acknowledgments

We gratefully acknowledge financial support from the Research Grant Council to the Hong Kong University of Science and Technology (Grant HKUST6307/04H).

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