Madelyn Gatchel

Madelyn Gatchel, Michael P. Wellman

Learning or estimating game models from data typically entails inducing separate models for each setting, even if the games are parametrically related. In empirical mechanism design, for example, this approach requires learning a new game model for each candidate setting of the mechanism parameter. Recent work has shown the data efficiency benefits of learning a single parameterized model for families of related games. In Bayesian games -- a typical model for mechanism design -- payoffs depend on both the actions and types of the players. We show how to exploit this structure by learning an interim game-family model that conditions on a single player's type. We compare this to the baseline approach of directly learning the ex ante payoff function, which gives payoffs in expectation of all player types. By marginalizing over player type, the interim model can also provide ex ante payoff predictions, as necessary for Bayes-Nash equilibrium approximation. We also leverage the interim model to compute new beneficial piecewise best-response strategies, without any additional sample data. We validate our method through a case study of a dynamic sponsored search auction. For both payoff accuracy and Nash-approximation error, the interim model matches the ex ante model on the trained range, and outperforms ex ante in extrapolation. Our case study demonstrates that Bayesian game-family models can support comprehensive mechanism design, and that through interim-stage modeling we can enhance expressivity and reliability.

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 $\varepsilon$-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.