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Game Theory and Risk Analysis


*Address correspondence to Louis Anthony (Tony) Cox, Jr., Cox Associates and University of Colorado, 503 Franklin Street, Denver, CO 80218, USA, tel: (303)-388-1778; fax: (303)-388-0609;


Risk analysts often analyze adversarial risks from terrorists or other intelligent attackers without mentioning game theory. Why? One reason is that many adversarial situations—those that can be represented as attacker-defender games, in which the defender first chooses an allocation of defensive resources to protect potential targets, and the attacker, knowing what the defender has done, then decides which targets to attack—can be modeled and analyzed successfully without using most of the concepts and terminology of game theory. However, risk analysis and game theory are also deeply complementary. Game-theoretic analyses of conflicts require modeling the probable consequences of each choice of strategies by the players and assessing the expected utilities of these probable consequences. Decision and risk analysis methods are well suited to accomplish these tasks. Conversely, game-theoretic formulations of attack-defense conflicts (and other adversarial risks) can greatly improve upon some current risk analyses that attempt to model attacker decisions as random variables or uncertain attributes of targets (“threats”) and that seek to elicit their values from the defender's own experts. Game theory models that clarify the nature of the interacting decisions made by attackers and defenders and that distinguish clearly between strategic choices (decision nodes in a game tree) and random variables (chance nodes, not controlled by either attacker or defender) can produce more sensible and effective risk management recommendations for allocating defensive resources than current risk scoring models. Thus, risk analysis and game theory are (or should be) mutually reinforcing.