Efficiency and Equilibrium Selection in an Allocation Problem

We study two variants of an allocation problem where two parties lay proportional claims to an asset, and an arbiter has a final say on allocation. The two variants we study vary by the incentives to the arbiter. In one variant, the arbiter is incentivized proportional to the payoff to the lowest paid claimant and in the other, the arbiter is incentivized proportional to the payoff to the highest paid claimant. While neither incentive scheme changes the set of equilibria, they alter expected payoff in off-equilibrium outcomes, with implications for equilibrium selection. Accordingly, the first variant leads to egalitarian claims whereas the second leads to claims of the entire pot, and subsequently to high incidence of impasse. A level-k model of bounded rationality fits the observed outcomes. Thus, in bargaining with multiple equilibria, the level-k model is useful in designing arbiter incentives to maximize efficiency