Game theory method improves utility recovery from noisy equilibrium data
Suboptimality Loss for Inverse Learning from Imperfect Equilibria
Computer Science and Game Theory
Summary
Many systems involve multiple people or agents making strategic decisions together. Often, we want to figure out their hidden preferences or goals by looking at their actions, but the data can be noisy or inconsistent. The authors propose a new way to measure how far observed actions are from perfect strategies, which is more reliable under imperfect data. They show that their method works better than previous ones when there is noise or conflicting information.
What this means in practice
- •For market analysts: Improve estimation of competitor preferences in noisy market data to better predict pricing and production strategies in oligopolistic industries.
- •For supply chain managers: Analyze strategic behaviors in supply networks using imperfect data to design more robust resource allocation.
Authors
Andreas Feik, Pierre Pinson, Dario Paccagnan
Abstract
Many modern systems involve the strategic interaction of multiple agents. In such settings, observed actions typically reflect equilibrium behavior under utilities that are only partially known. Recovering these hidden utilities from data - the central goal of inverse game theory - is key for prediction, counterfactual analysis, and mechanism design. However, existing approaches based on inverse variational inequalities are highly sensitive to noisy and inconsistent equilibrium observations, thus limiting their applicability. In this paper, we resolve this issue by introducing a game-theoretic suboptimality loss that measures the aggregate utility gain players could obtain by unilaterally deviating from an observed strategy profile. First, we show that this loss is convex and admits an efficient decomposition into player-wise best-responses. Second, we show this loss is sandwiched between the predictability loss and the inverse variational inequality loss, making it a tractable surrogate for equilibrium prediction. Third, we develop a mirror descent algorithm to minimize it and demonstrate on a heterogeneous networked Cournot competition that our approach remains accurate under noisy observations and inconsistent equilibrium data while inverse variational inequality methods produce degenerate estimates.