A 2-PLAYER N-REGION SEARCH GAME

Abstract : Given N regions with their associated conditional detection probabilities alpha sub 1 ..., alpha sub N, let player A choose one region to hide in, and let player B look in one region at a time until he finds A. The payoff, to player A, is the expected number of looks required of B to find A. The form of the optimal pure strategies for B is described, and the mixed extension of this game is shown to have a solution. Player B has a good strategy that is a mixture of at most N pure strategies. A numerical procedure for calculating the solution is given.