Empirical Distribution of Equilibrium Play and Its Testing Application
Yakov Babichenko, Siddharth Barman, Ron Peretz

TL;DR
This paper demonstrates that in large normal-form games, approximate equilibria can be efficiently obtained and tested through sampling, with bounds that improve previous support size estimates.
Contribution
It provides new bounds on the number of samples needed to find and test approximate equilibria for Nash, correlated, and coarse correlated equilibria.
Findings
Sample-based methods can efficiently approximate equilibria.
Supports of approximate equilibria are polylogarithmic in game size.
New bounds improve previous polynomial support size estimates.
Abstract
We show that in any -player -action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse correlated. For each one of them we obtain upper and lower bounds on the number of samples required for the empirical distribution over the sampled action profiles to form an approximate equilibrium with probability close to one. These bounds imply that using a small number of samples we can test whether or not players are playing according to an approximate equilibrium, even in games where and are large. In addition, our results substantially improve previously known upper bounds on the support size of approximate equilibria in games with many players. In particular, for all the three types of equilibria we show the existence of approximate…
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Taxonomy
TopicsGame Theory and Applications · Economic theories and models · Experimental Behavioral Economics Studies
