Rank-dependent choice equilibrium: A nonparametric generalization of QRE

Quantal response equilibrium (QRE) builds the possibility of errors into an equilibrium analysis of games. One objection to QRE is that specific functional forms must be chosen to derive equilibrium predictions. As these can be chosen from an infinitely dimensional set, another concern is whether QRE is falsifiable. Finally, QRE can typically only be solved numerically. We address these concerns through the lens of a novel set-valued solution concept, rank-dependent choice equilibrium (RDCE), which imposes a simple ordinal monotonicity condition: Equilibrium choice probabilities are ranked the same as their associated expected payoffs. We first discuss important differences between RDCE and QRE and then show that RDCE envelopes all QRE models. Finally, we show that RDCE (and, hence, QRE) is falsifiable since the measure of the RDCE set, relative to the set of all mixed-strategy profiles, converges to zero at factorial speed in the number of available actions.