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Bryce Wiedenbeck

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5 papers

1 author row

AAMAS Conference 2023 Conference Paper

Data Structures for Deviation Payoffs

Bryce Wiedenbeck
Erik Brinkman

We present new data structures for representing symmetric normalform games. These data structures are optimized for efficiently computing the expected utility of each unilateral pure-strategy deviation from a symmetric mixed-strategy profile. The cumulative effect of numerous incremental innovations is a dramatic speedup in the computation of symmetric mixed-strategy Nash equilibria, making it practical to represent and solve games with dozens to hundreds of players. These data structures naturally extend to rolesymmetric and action-graph games with similar benefits.

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AAMAS Conference 2023 Conference Paper

Learning Parameterized Families of Games

Madelyn Gatchel
Bryce Wiedenbeck

Nearly all simulation-based games have environment parameters that affect incentives in the interaction but are not explicitly incorporated into the game model. To understand the impact of these parameters on strategic incentives, typical game-theoretic analysis involves selecting a small set of representative values, and constructing and analyzing separate game models for each value. We introduce a novel technique to learn a single model representing a family of closely related games that differ in the number of symmetric players or other ordinal environment parameters. Prior work trains a multi-headed neural network to output mixed-strategy deviation payoffs, which can be used to compute symmetric 𝜀-Nash equilibria. We extend this work by making environment parameters into input dimensions of the regressor, enabling a single model to learn patterns which generalize across the parameter space. For continuous and discrete parameters, our results show that these generalized models outperform existing approaches, achieving better accuracy with far less data. This technique makes thorough analysis of the parameter space more tractable, and promotes analyses that capture relationships between parameters and incentives.

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AAAI Conference 2019 Conference Paper

Learning Deviation Payoffs in Simulation-Based Games

Samuel Sokota
Caleb Ho
Bryce Wiedenbeck

We present a novel approach for identifying approximate role-symmetric Nash equilibria in large simulation-based games. Our method uses neural networks to learn a mapping from mixed-strategy profiles to deviation payoffs—the expected values of playing pure-strategy deviations from those profiles. This learning can generalize from data about a tiny fraction of a game’s outcomes, permitting tractable analysis of exponentially large normal-form games. We give a procedure for iteratively refining the learned model with new data produced by sampling in the neighborhood of each candidate Nash equilibrium. Relative to the existing state of the art, deviation payoff learning dramatically simplifies the task of computing equilibria and more effectively addresses player asymmetries. We demonstrate empirically that deviation payoff learning identifies better approximate equilibria than previous methods and can handle more difficult settings, including games with many more players, strategies, and roles.

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AAAI Conference 2018 Conference Paper

A Regression Approach for Modeling Games With Many Symmetric Players

Bryce Wiedenbeck
Fengjun Yang
Michael Wellman

We exploit player symmetry to formulate the representation of large normal-form games as a regression task. This formulation allows arbitrary regression methods to be employed in in estimating utility functions from a small subset of the game's outcomes. We demonstrate the applicability both neural networks and Gaussian process regression, but focus on the latter. Once utility functions are learned, computing Nash equilibria requires estimating expected payoffs of pure-strategy deviations from mixed-strategy profiles. Computing these expectations exactly requires an infeasible sum over the full payoff matrix, so we propose and test several approximation methods. Three of these are simple and generic, applicable to any regression method and games with any number of player roles. However, the best performance is achieved by a continuous integral that approximates the summation, which we formulate for the specific case of fully-symmetric games learned by Gaussian process regression with a radial basis function kernel. We demonstrate experimentally that the combination of learned utility functions and expected payoff estimation allows us to efficiently identify approximate equilibria of large games using sparse payoff data.

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AAMAS Conference 2012 Conference Paper

Scaling Simulation-Based Game Analysis through Deviation-Preserving Reduction

Bryce Wiedenbeck
Michael Wellman

Multiagent simulation extends the reach of game-theoretic analysis to scenarios where payoff functions can be computed from implemented agent strategies. However this approach is limited by the exponential growth in game size relative to the number of agents. Player reductions allow us to construct games with a small number of players that approximate very large symmetric games. We introduce \emph{deviation-preserving reduction}, which generalizes and improves on existing methods by combining sensitivity to unilateral deviation with granular subsampling of the profile space. We evaluate our method on several classes of random games and show that deviation-preserving reduction performs better than prior methods at approximating full game equilibria.

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