Efficiency and Equilibrium Selection in an Allocation Problem

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