Strong Equilibria in Bayesian Games with Bounded Group Size

Qishen Han, Grant Schoenebeck, Biaoshuai Tao, Lirong Xia

Track: Economics, online markets and human computation

Keywords: Algorithmic game theory, information elicitation

TL;DR: We propose a solution concept that characterizes coalitional strategic behavior with a bounded number of players. We apply this solution concept to study peer prediction and propose other applications, including voting and Blotto game.

Abstract:

We study the group strategic behaviors in Bayesian games. Equilibria in previous work do not consider group strategic behaviors with bounded sizes and are too ``strong'' to exist in many scenarios. We propose the ex-ante Bayesian $k$-strong equilibrium and the Bayesian $k$-strong equilibrium, where no group of at most $k$ agents can benefit from deviation. The two solution concepts differ in how agents calculate their utilities when contemplating whether a deviation is beneficial. Intuitively, agents are more risk-averse in the Bayesian $k$-strong equilibrium than in the ex-ante Bayesian $k$-strong equilibrium. With our solution concepts, we study collusion in the peer prediction mechanisms, as a representative of the Bayesian games with group strategic behaviors. We characterize the thresholds of the group size $k$ so that truthful reporting in the peer prediction mechanism is an equilibrium for each solution concept, respectively. Our solution concepts can serve as criteria to evaluate the robustness of a peer prediction mechanism against collusion. Besides the peer prediction problem, we also discuss two other potential applications of our new solution concepts, voting and Blotto games, where introducing bounded group sizes provides more fine-grained insights into the behavior of strategic agents.

Submission Number: 1265