SECRECY AND DECEPTION AT EQUILIBRIUM, WITH APPLICATIONS TO ANTI‐TERRORISM RESOURCE ALLOCATION

Abstract

In this work, we develop a game‐theoretic model for whether and how a first mover should disclose her resource allocation. Our model allows us to explore whether the first mover should disclose correct information about her resource allocation, incorrect information, or no information. Although we study secrecy and deception specifically in the homeland‐security context where the first mover is assumed to be the defender, our work can also provide insights in other contexts, such as business competition.

Keywords:

• Secrecy and deception
• Truthful disclosure
• Homeland security
• Resource allocation
• Game theory

ACKNOWLEDGMENTS

This research was supported by the United States Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE) under grant number 2007‐ST‐061‐000001. However, any opinions, findings, and conclusions or recommendations in this document are those of the authors and do not necessarily reflect views of the United States Department of Homeland Security. We also thank Professor Larry Samuelson (Yale University), Professor Todd Sandler (University of Texas at Dallas) and Mr Stephen Campbell (Tufts University), and two anonymous referees for their helpful comments. Any errors are ours, of course.

Notes

¹ For a general discussion of first‐mover advantage in the economic literature, see for example Lieberman & Montgomery (1988, 1998).

² The case in which the actual defense is guaranteed to be observed by the attacker can be obtained as a degenerate case of our model, by setting the deception and secrecy costs large enough that the defender will always choose truthful disclosure in any equilibrium.

³ Note that the defender utility can in principle also reflect the cost of implementing the signal s (i.e., the cost of implementing secrecy, truthful disclosure, or deceptive disclosure).

⁴ Several bodies of literature provide refinements on equilibrium concepts for out‐of‐equilibrium signals. These include sequential equilibrium (Kreps and Wilson, 1982), divine equilibrium (Banks and Sobel, 1987), and stable equilibrium (Cho and Kreps, 1987). However, we do not further address this issue in our work, for reasons of simplicity.

⁵ Note that we no longer need to update the attacker’s belief about the defender type θ_D , since there is no private information in this game. Therefore, equation (8) in Definition 1 is not needed. For simplicity, we also remove θ_D from equations (9) and (10), because it is a constant and common knowledge in this case.

⁶ As in Section 3, for simplicity, we remove θ_A from equations (13) and (14), because it is a constant and common knowledge.

⁷ Recall that θ_D was suppressed in the function ũ_D in equation (11) for simplicity. Similarly, we suppress A from the function ũ_D in equation (15).

⁸ For more general contest success functions, see for example Skaperdas (1996).