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On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games
We propose a two-timescale algorithm for finding local Nash equilibria i...
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Multiagent Evaluation under Incomplete Information
This paper investigates the evaluation of learned multiagent strategies ...
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Fast Algorithms for Rank-1 Bimatrix Games
The rank of a bimatrix game is the matrix rank of the sum of the two pay...
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Efficient Nash Computation in Large Population Games with Bounded Influence
We introduce a general representation of large-population games in which...
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Real World Games Look Like Spinning Tops
This paper investigates the geometrical properties of real world games (...
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Actor-Critic Algorithms for Learning Nash Equilibria in N-player General-Sum Games
We consider the problem of finding stationary Nash equilibria (NE) in a ...
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Large Scale Learning of Agent Rationality in Two-Player Zero-Sum Games
With the recent advances in solving large, zero-sum extensive form games...
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A Generalized Training Approach for Multiagent Learning
This paper investigates a population-based training regime based on game-theoretic principles called Policy-Spaced Response Oracles (PSRO). PSRO is general in the sense that it (1) encompasses well-known algorithms such as fictitious play and double oracle as special cases, and (2) in principle applies to general-sum, many-player games. Despite this, prior studies of PSRO have been focused on two-player zero-sum games, a regime wherein Nash equilibria are tractably computable. In moving from two-player zero-sum games to more general settings, computation of Nash equilibria quickly becomes infeasible. Here, we extend the theoretical underpinnings of PSRO by considering an alternative solution concept, α-Rank, which is unique (thus faces no equilibrium selection issues, unlike Nash) and tractable to compute in general-sum, many-player settings. We establish convergence guarantees in several games classes, and identify links between Nash equilibria and α-Rank. We demonstrate the competitive performance of α-Rank-based PSRO against an exact Nash solver-based PSRO in 2-player Kuhn and Leduc Poker. We then go beyond the reach of prior PSRO applications by considering 3- to 5-player poker games, yielding instances where α-Rank achieves faster convergence than approximate Nash solvers, thus establishing it as a favorable general games solver. We also carry out an initial empirical validation in MuJoCo soccer, illustrating the feasibility of the proposed approach in another complex domain.
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