Efficiently characterizing games consistent with perturbed equilibrium observations
We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes of games and observation models of interest. Our approach provides a sharp, computationally efficient characterization of the extent to which a particular set of observations constrains the space of games that could have generated them. This allows us to solve a number of variants of this problem as well as to quantify the power of games from particular classes (e.g., zero-sum, potential, linearly parameterized) to explain player behavior. We illustrate our approach with numerical simulations.
Additional InformationWe thank Federico Echenique, Denis Nekipelov, Matt Shum, and Vasilis Syrgkanis for extremely helpful comments and suggestions. Ziani's research was funded in part by NSF grant CNS-1254169. Chandrasekaran's research was funded in part by NSF awards CCF-1350590 and CCF-1637598, Air Force Office of Scientific Research grants FA9550-14-1-0098 and FA9550-16-1-0210, and the Sloan research fellowship. Ligett's research was funded in part by ISF grant 1044/16, NSF grants CNS-1254169 and CNS-1518941, a subcontract under the DARPA Brandeis Project, and the Hebrew University Cybersecurity Research Center in conjunction with the Israel National Cyber Bureau in the Prime Minister's Office. Ligett's work was done in part while the author was visiting the Simons Institute for the Theory of Computing at Berkeley.
Submitted - 1603.01318.pdf