A Learning Framework for Distribution-Based Game-Theoretic Solution Concepts
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The past few years have seen several works establishing PAC frameworks for solving various problems in economic domains; these include optimal auction design, approximate optima of submodular functions, stable partitions and payoff divisions in cooperative games and more. In this work, we provide a unified learning-theoretic methodology for modeling these problems, and establish some useful 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 general methodology. Finally, we apply our methods in other economic domains, yielding a novel notion of PAC competitive equilibrium and PAC Condorcet winners.
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