Cumulative search‐evasion games

James N. Eagle and Alan R. Washburn

Naval Research Logistics (NRL), 1991, vol. 38, issue 4, 495-510

Abstract: Cumulative search‐evasion games (CSEGs) 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.

Date: 1991
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