Abstract
Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In many situations, we would like to compute strategies that can actually be implemented by humans, who may have computational limitations and may only be able to remember a small number of features or components of the strategies that have been computed. For example, a human poker player or military leader may not have access to large precomputed tables when making real-time strategic decisions. We study poker games where private information distributions can be arbitrary (i.e., players are dealt cards from different distributions, which depicts the phenomenon in large real poker games where at some points in the hand players have different distribution of hand strength by applying Bayes’ rule given the history of play in the hand thus far). We create a large training set of game instances and solutions, by randomly selecting the information probabilities, and present algorithms that learn from the training instances to perform well in games with unseen distributions. We are able to conclude several new fundamental rules about poker strategy that can be easily implemented by humans.
Highlights
Large-scale computation of strong game-theoretic strategies is important in many domains.For example, there has been significant recent study on solving game-theoretic problems in national security from which real deployed systems have been built, such as a randomized security check system for airports [1]
We presented a novel formulation of the problem of computing strong game-theoretic strategies that are human understandable as a machine learning problem
Computing strong strategies in games has fallen under the domain of specialized equilibrium-finding algorithms that produce massive strategy files which are unintelligible to humans
Summary
Large-scale computation of strong game-theoretic strategies is important in many domains. We observed that we are able to obtain low testing error even when training on a relatively small fraction of the data, which suggests that it is possible for humans to learn strong strategies by memorizing solutions to a carefully selected small set of presolved games. This approach would require humans to quickly be able to compute the distance between a new game and all games from the training database in order to determine the closest neighbor, which could be computationally taxing. The problem of constructing human-interpretable rules has been studied recently in machine learning, e.g., [4,5], for medical applications [6,7,8]
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