A solution for a two-person zero-sum game with a concave payoff function (Q2753307)

\noindent The authors consider a two-person zero-sum game where the strategy set \(\Phi\) of the maximizer is an \(n\)-dimensional closed convex set in \(\mathbb{R}^n\) represented by a finite set of inequalities: \(\Phi=\{\phi\in\mathbb{R}^n: g_i(\phi)\geq 0\), \(i=1,\ldots,m\}\), and that of the minimizer is a finite set \(\Omega\). For each pure strategy \(\omega\) in \(\Omega\), the payoff function \(R(\phi,\omega)\) is assumed to be strictly concave as a function of \(\phi\). The problem of finding optimal strategies and the game value is formulated as a min-max and max-min problem, and a numerical method of solving the problem is proposed. The method is illustrated in a search-evasion game where the hider moves on a finite set of points over a discrete set of times and the searcher has a continuum of ways to distribute the search effort.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].