Equilibria in Repeated Games under No-Regret with Dynamic Benchmarks

48 Pages Posted: 20 Dec 2022 Last revised: 19 Jul 2023

See all articles by Ludovico Crippa

Ludovico Crippa

Stanford Graduate School of Business

Yonatan Gur

Stanford Graduate School of Business; Netflix

Bar Light

Microsoft Research, NYC

Date Written: December 6, 2022

Abstract

In repeated games, strategies are often evaluated by their ability to guarantee the performance of the single best action that is selected in hindsight, a property referred to as Hannan consistency, or no-regret. However, the effectiveness of the single best action as a yardstick to evaluate strategies is limited, as any static action may perform poorly in common dynamic settings. Our work therefore turns to a more ambitious notion of dynamic benchmark consistency, which guarantees the performance of the best dynamic sequence of actions, selected in hindsight subject to a constraint on the allowable number of action changes. Our main result establishes that for any joint empirical distribution of play that may arise when all players deploy no-regret strategies, there exist dynamic benchmark consistent strategies such that if all players deploy these strategies the same empirical distribution emerges when the horizon is large enough. This result demonstrates that although dynamic benchmark consistent strategies have a different algorithmic structure and provide significantly enhanced individual assurances, they lead to the same equilibrium set as no-regret strategies. Moreover, the proof of our main result uncovers the capacity of independent algorithms with strong individual guarantees to foster a strong form of coordination.

Keywords: Repeated Games, Incomplete Information, No Regret, Price of Anarchy

Suggested Citation

Crippa, Ludovico and Gur, Yonatan and Light, Bar, Equilibria in Repeated Games under No-Regret with Dynamic Benchmarks (December 6, 2022). Available at SSRN: https://ssrn.com/abstract=4295141 or http://dx.doi.org/10.2139/ssrn.4295141

Ludovico Crippa

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, 94305
United States

Yonatan Gur (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Netflix ( email )

Los Gatos, CA
United States

Bar Light

Microsoft Research, NYC ( email )

NYC, CA
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
176
Abstract Views
1,749
Rank
314,652
PlumX Metrics