A Multi-Stage Model of Searching for Two Mobile Objects on a Graph

Abstract

We are dealing with a search game where one searcher looks for two mobile objects on a graph. The searcher distributes his searching resource so as to maximize the probability of detecting at least one of the mobile objects. Each mobile object minimizes its own probability of being found. In this problem the Nash equilibrium, i.e. the optimal transition probabilities of the mobile objects and the optimal values of the searcher’s resource, was found. The value of the game in a single-stage search game with non-exponential payoff functions was found.