A Learning Framework for Distribution-Based Game-Theoretic Solution Concepts
Tushant Jha, Yair Zick
TL;DR
The paper develops a general PAC-learning framework for distribution-based game-theoretic solution concepts by introducing the solution dimension $\mathit{Sd}(\Psi)$, a unifying measure that extends graph and VC dimensions to the domain of solution concepts. It proves uniform convergence and learnability results for consistent solvers, showing how low $\mathit{Sd}(\Psi)$ yields polynomial-sample PAC guarantees, and extends these ideas beyond consistency to agnostic settings. The framework is applied to hedonic games (where $\mathit{Sd}(\Psi) \le n$), competitive equilibria in Fisher markets (where $\mathit{Sd}(\Psi_{CE}) = O(k)$), and Condorcet winners (where $\mathit{Sd}(\Psi_{Cond}) \le \log_2(k+2)$), deriving concrete sample complexity bounds and discussing constructive versus non-constructive aspects. The work highlights the potential of a unified theory for learning economic solutions from data, while acknowledging open challenges in algorithm design for consistent solutions and extensions to non-realizable settings and PMAC-style guarantees.
Abstract
The past few years have seen several works on learning economic solutions from data; these include optimal auction design, function optimization, stable payoffs in cooperative games and more. In this work, we provide a unified learning-theoretic methodology for modeling such problems, and establish tools for determining whether a given economic solution concept can be learned from data. Our learning theoretic framework generalizes a notion of function space dimension -- the graph dimension -- adapting it to the solution concept learning domain. We identify sufficient conditions for the PAC learnability of solution concepts, and show that results in existing works can be immediately derived using our methodology. Finally, we apply our methods in other economic domains, yielding a novel notion of PAC competitive equilibrium and PAC Condorcet winners.