Hide and seek game with multiple resources

Abstract

We study a generalization of hide and seek game of von Neumann [14], where each player has one or more resources. We characterize the value and Nash equilibria of such games in terms of their unidimensional marginal distributions. We propose a $$\mathcal {O}(n \log (n))$$ time algorithm for computing unidimensional marginal distributions of equilibrium strategies and a quadratic time algorithm for computing mixed strategies given the margins. The characterization allows us to establish a number of interesting qualitative features of equilibria.