Three-part partition games on rectangles

Abstract

A partition game on a rectangle is a two-person zero-sum game in which the rectangle is partitioned into a finite number of regions and the payoff function is constant in each region. A special case with four regions is essentially Silverman's game, which has been extensively studied in recent years. In this paper, we examine three-part partition games where the boundaries separating the regions are the graphs of two continuous functions. Various conditions under which optimal mixed strategies and game value do or do not exist are found, as are optimal strategies and value in case they exist. Some games of this type have in the classical game theory literature been interpreted as continuous Colonel Blotto games.