Bayesian incentive compatible mechanisms

Abstract

We study the problem of optimal mechanism design for incomplete information Stackelberg games with several followers in which each follower, guided by his own probability assessments concerning the characteristics of the other followers, behaves as a Bayesian in choosing a reporting strategy. Allowing for uncountably many types and infinite dimensional type descriptions, we present a new, general existence result for Bayesian incentive compatible (BIC) mechanisms. Because the existence problem is infinite dimensional, novel existence arguments are required. Our existence proof is based on two results: one on the sequential closure of the subset of BIC mechanisms with respect toK-convergence, and the other, a new result on sequential compactness in spaces of vector-valued functions.