We examine the optimal size of risk pools with moral hazard. In risk pools, the effective share of the own loss borne is the sum of the direct share (the retention rate) and the indirect share borne as residual claimant. In a model with identical individuals with mixed risk‐averse utility functions, we show that the effective share required to implement a specific effort increases in the pool size. This is a downside of larger pools as it, ceteris paribus, reduces risk sharing. However, we find that the benefit from diversifying the risk in larger pools always outweighs the downside of a higher effective share. We conclude that, absent transaction costs, the optimal pool size converges to infinity. In our basic model, we restrict attention to binary effort levels, but we show that our results extend to a model with continuous effort choice.
We conduct an experiment where subjects are matched in groups of three and vote on a moral transgression. Analyzing different voting rules, the frequency of votes for the moral transgression increases with the number of votes required for it. This effect persists when considering pivotal votes only, which eliminates opportunities to save on own moral costs and to rely instead on sufficiently many votes for the transgression by other group members. A series of novel treatments allows us to identify guilt sharing and preferences for consensual voting as empirically relevant and independent drivers of voting behavior.
We extend the theoretical and experimental analysis of endogenous sorting in social dilemma games to decisions of trustees in trust games. Trustees first decide about the amount they send back if the trustor sends the money and then learn that they can exit the game for a payoff that is identical to the trustor’s endowment. We develop a behavioral model where trustors and trustees have reciprocal preferences, and hence put positive weight on the other player’s payoff if they perceive their behavior as kind. Our model yields two possible constellations: Only trustees with high reciprocity participate, or all types except those with intermediate reciprocity participate. Our data lend strong support for the second pattern, as we observe a U-shaped relation between the trustees’ participation rate and the amount they return. Trustors are hence left with an extreme pool of participants where they are either matched with particularly selfish or generous trustees.
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