Cumulative search-evasion games

Cumulative search-evasion games

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Article ID: iaor1993543
Country: United States
Volume: 38
Issue: 4
Start Page Number: 495
End Page Number: 510
Publication Date: Aug 1991
Journal: Naval Research Logistics
Authors: ,
Keywords: gaming, game theory
Abstract:

Cumulative search-evasion games are two-person zero-sum search-evasion games where play proceeds throughout some specified period without interim feedback to either of the two players. Each player moves according to a preselected plan. If (Xt,Yt) are the positions of the two players at time t, then the game’s payoff is the sum over t from 1 to T of A(Xt,Yt,t). Additionally, all paths must be ‘connected.’ That is, the finite set of positions available for a player in any time period depends on the position selected by that player in the previous time period. One player attempts to select a mixed strategy over the feasible T-time period paths to maximize the expected payoff. The other minimizes. Two solution procedures are given. One uses the Brown-Robinson method of fictitious play and the other linear programming. An example problem is solved using both procedures.

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