Bayesian incentive compatibility (source code)

= Bayesian incentive compatibility
{c}
{title2=$vX_i(v)-P_i(v)\geq vX_i(z)-P_i(z)$}

Truthful reporting is Bayesian incentive compatible when every type maximizes its expected utility over the other players' types by reporting truthfully. In an <independent private values model>, the displayed inequality uses the same interim allocation and payment functions for every possible true type.