Four-part partition games isomorphic to Silverman's game

Abstract

A four-part partition game on a rectangle S I × S II is a two-person zero-sum game, where the strategy sets S I and S II are intervals and the rectangle is partitioned by three curves into four regions on each of which the payoff function is constant. These games generalize Silverman's game, where the boundary curves are of the form y= Tx, y= x and y= x/ T. In this paper it is shown that two increasing nonintersecting curves may be chosen arbitrarily and there is a uniquely determined third increasing curve such that if the payoffs are properly related, the game is isomorphic to Silverman's game.