Quasi-robust multiagent contracts

A criticism of mechanism design theory is that the optimal mechanism designed for one environment can produce drastically different actions, outcomes, and payoffs in a second, even slightly different, environment. In this sense, the theoretically optimal mechanisms usually studied are not “robust.” To study robust mechanisms while maintaining an expected utility maximization approach, we study a multiagent model in which the mechanism must be designed before the environment is as well understood as is usually assumed. The particular model is of an auction setting with binary private values. Our main result is that if the prior belief about the correlation in the agents' values is diffuse enough, the optimal Bayesian-Nash auction must also satisfy dominant strategy incentive constraints. Furthermore, when the optimal auction does provide dominant strategy incentives, it takes one of two forms: (i) if perfect correlation and negative correlation are excluded as possibilities, the auction incorporates all information about the prior belief over the possible correlations, and (ii) if either perfect correlation or negative correlation is a possibility, the auction does not incorporate any correlation information and can be described as a modified Vickrey auction.