Statistical Relational Learning for Game Theory

Abstract

In this paper, we motivate the use of models and algorithms from the area of Statistical Relational Learning (SRL) as a framework for the description and the analysis of games. SRL combines the powerful formalism of first-order logic with the capability of probabilistic graphical models in handling uncertainty in data and representing dependencies between random variables: for this reason, SRL models can be effectively used to represent several categories of games, including games with partial information, graphical games and stochastic games. Inference algorithms can be used to approach the opponent modeling problem, as well as to find Nash equilibria or Pareto optimal solutions. Structure learning algorithms can be applied, in order to automatically extract probabilistic logic clauses describing the strategies of an opponent with a high-level, human-interpretable formalism. Experiments conducted using Markov logic networks, one of the most used SRL frameworks, show the potential of the approach.