Estimation of Games under No Regret

69 Pages Posted: 21 Nov 2022

See all articles by Niccolò Lomys

Niccolò Lomys

CSEF - University of Naples Federico II

Lorenzo Magnolfi

University of Wisconsin-Madison

Date Written: November 5, 2022


We develop a method to estimate a game’s primitives in complex dynamic environments. Because of the environment’s complexity, agents may not know or understand some key features of their interaction. Instead of equilibrium assumptions, we impose an asymptotic ε-regret (ε-AR) condition on the observed play. According to ε-AR, the time average of the counterfactual increase in past payoffs, had each agent changed each past play of a given action with its best replacement in hindsight, becomes small in the long run. We first prove that the time average of play satisfies ε- AR if and only if it converges to the set of Bayes correlated ε-equilibrium predictions of the stage game. Next, we use the static limiting model to construct a set estimator of the parameters of interest. The estimator’s coverage properties directly arise from the theoretical convergence results. The method applies to panel data as well as to cross-sectional data interpreted as long-run outcomes of learning dynamics. We apply the method to pricing data in an online marketplace. We recover bounds on the distribution of sellers’ marginal costs that are useful to inform policy experiments.

Keywords: Empirical Games, Bayes (Coarse) Correlated Equilibrium, Learning in Games, Regret Minimization, Partial Identification, Incomplete Models

JEL Classification: C1, C5, C7, D4, D8, L1, L8

Suggested Citation

Lomys, Niccolò and Magnolfi, Lorenzo, Estimation of Games under No Regret (November 5, 2022). Available at SSRN: or

Niccolò Lomys

CSEF - University of Naples Federico II ( email )

via Cinthia, 4
Naples, Caserta 80126

Lorenzo Magnolfi (Contact Author)

University of Wisconsin-Madison ( email )

1180 Observatory Drive
Madison, WI Wisconsin 53706
United States
6082628789 (Phone)


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