October 2011 to September 2012
game theory risk analysis
Adversarial Risk Analysis (ARA) builds a model for the decision-making process of one’s opponent, and then selects the action which maximizes one’s expected utility under that model. This approach differs from the traditional game theoretic formulation, in which one seeks a joint equilibrium strategy under strong common knowledge assumptions about all players. The research supported by this grant extended the emerging theory of ARA to several applications, particularly auction theory and level-k models. A key aspect of this work relies upon the combination of elicited expert opinion from multiple experts. Standard theory shows that no such combination is strictly possible (aside from clones, no non-dictatorial pooling of Bayesian priors can simultaneously represent the mutual judgment of all experts). However, use of covariate information and multidimensional scaling enables creation of a “pseudo-expert” that approximately integrates the opinion that would be held by an agent with multiple areas of expertise, or other specified characteristics. The thrust of this research is to explore an alternative to classical game theory which enables analysts to develop strategy under more realistic assumptions (e.g., that their opponent is not as smart as John von Neumann, is not perfectly rational, and has different probabilistic beliefs than oneself). That alternative has been developed in several “toy” contexts previously published, such as the Borel game and a convoy routing game through a road network with IEDs. The research supported by this grant continues that exploration by extension to applications that are richer and more realistic. The primary results from this research will appear in two ways: as chapters in a book on ARA, which is currently about 75% complete, and in an article that has been accepted (possibly as a discussion paper) and will soon appear in Statistics, Politics and Policy.