A Search Game with Incomplete Information on Detective Capability of Searcher

Authors

  • Ryusuke Hohzaki National Defense Academy, Department of Computer Science

Abstract

This paper deals with a so-called search allocation games (SAG), which a searcher distributes search resources, such as detection sensors and search time, into a search space to detect a target and the target moves to evade the detection. Although there have been many published papers on the SAG, they almost dealt with complete information games. In this paper, we consider private information of the searcher about the detection effectiveness of the search resource and discuss a two-person zero-sum incomplete information SAG with the detection probability of the target as payoff. We derive its Bayesian equilibrium to evaluate the value of the incomplete information.

Keywords:

search theory, game theory, incomplete information

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References

Brown, S.S. (1980). Optimal search for a moving target in discrete time and space. Operations Research, 28, 1275–1286.

Dambreville, F. and J.P. Le Cadre (2002). Detection of a Markovian target with optimization of the search efforts under generalized linear constraints. Naval Research Logistics, 49, 117–142.

De Guenin, J. (1961). Optimum distribution of effort: an extension of the Koopman basic theory. Operations Research, 9, 1–9.

Hohzaki, R. (2006). Search allocation game. European Journal of Operational Research, 172, 101–119.

Hohzaki, R. (2007a). Discrete search allocation game with false contacts. Naval Research Logistics, 54, 46–58.

Hohzaki, R. (2007b). A multi-stage search allocation game with the payoff of detection probability. Journal of the Operations Research Society of Japan, 50, 178–200.

Hohzaki, R. (2008). A search game taking account of attributes of searching resources. Naval Research Logistics, 55, 76–90.

Hohzaki, R. (2009). A cooperative game in search theory. Naval Research Logistics, 56, 264–278.

Hohzaki, R. (2013a). The search allocation game. Wiley Encyclopedia of Operations Research and Management Science, John Wiley & Sons, Online-version, 1–10.

Hohzaki, R. (2013b). A nonzero-sum search game with two competitive searchers and a target. Annals of Dynamic Games, 12, 351–373.

Hohzaki, R. (2016). Search games: Literature and survey. Journal of the Operations Research Society of Japan, 59, 1–34.

Hohzaki, R. and K. Iida (1998). A search game with reward criterion. Journal of the Operations Research Society of Japan, 41, 629–642.

Hohzaki, R. and K. Joo (2015). A search allocation game with private information of initial target position. Journal of the Operations Research Society of Japan, 58, 353–375.

Ibaraki, T. and N. Katoh (1988). Resource Allocation Problems: Algorithmic Approaches. The MIT Press: London.

Iida, K. (1972). An optimal distribution of searching effort for a moving target. Keiei Kagaku, 16, 204–215 (in Japanese).

Iida, K., R. Hohzaki and S. Furui (1996). A search game for a mobile target with the conditionally deterministic motion defined by paths. Journal of the Operations Research Society of Japan, 39, 501–511.

Iida, K., R. Hohzaki and K. Sato (1994). Hide-and-search game with the risk criterion. Journal of the Operations Research Society of Japan, 37, 287–296.

Kadane, J.B. (1968). Discrete search and the Neyman-Pearson lemma. Journal of Mathematical Analysis and Applications, 22, 156–171.

Koopman, B.O. (1957). The theory of search III: the optimum distribution of searching effort. Operations Research, 5, 613–626.

Matsuo, T. and R. Hohzaki (2017). A search game with incomplete information about target's energy. Scientiae Mathematicae Japonicae, 79, to appear.

Morse, P.M. and G.E. Kimball (1951). Methods of Operations Research. MIT Press: Cambridge.

Nakai, T. (1988). Search models with continuous effort under various criteria. Journal of the Operations Research Society of Japan, 31, 335–351.

Pollock, S.M. (1970). A simple model of search for a moving target. Operations Research, 18, 883–903.

Stone, L.D. (1975). Theory of Optimal Search. Academic Press: New York.

Washburn, A.R. (1983). Search for a moving target: the FAB algorithm. Operations Research, 31, 739–751.

Washburn, A.R. and R. Hohzaki (2001). The diesel submarine flaming datum problem. Military Operations Research, 4, 19–30.

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Published

2022-04-17

How to Cite

Hohzaki, R. (2022). A Search Game with Incomplete Information on Detective Capability of Searcher. Contributions to Game Theory and Management, 10. Retrieved from https://gametheory.spbu.ru/article/view/13256

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