Imperfect best-response mechanisms

TL;DR

This paper examines how best-response mechanisms perform when players occasionally deviate from optimal strategies, analyzing the robustness of convergence and incentive compatibility under imperfect play.

Contribution

It provides new insights into the robustness of best-response mechanisms when players make mistakes, extending the understanding of their convergence and incentive properties.

Findings

Convergence is affected by the probability of players deviating from best responses.

Incentive compatibility can be maintained under certain bounds of imperfect play.

The results quantify the robustness of these mechanisms to noise and errors.

Abstract

Best-response mechanisms (Nisan, Schapira, Valiant, Zohar, 2011) provide a unifying framework for studying various distributed protocols in which the participants are instructed to repeatedly best respond to each others' strategies. Two fundamental features of these mechanisms are convergence and incentive compatibility. This work investigates convergence and incentive compatibility conditions of such mechanisms when players are not guaranteed to always best respond but they rather play an imperfect best-response strategy. That is, at every time step every player deviates from the prescribed best-response strategy according to some probability parameter. The results explain to what extent convergence and incentive compatibility depend on the assumption that players never make mistakes, and how robust such protocols are to "noise" or "mistakes".