Chess-like Games Are Dominance Solvable in at Most Two Steps

During the pioneering time of game-theoretic research in the first half of the past century, it was proved that the game of chess has a value, i.e., that either there is a winning strategy for White, or there is a winning strategy for Black, or both players can secure themselves a draw. Since then, a rich theory has developed for general games of perfect information,2 yet surprisingly little is implied by this theory for specific games such as chess; e.g., the question as to which of the three possible values of chess is the actual value continues to be unsettled. In this paper we show that chess-like games, i.e., strictly competitive, finite games of perfect information with at most three outcomes, can be solved by applying only two rounds of elimination of dominated strategies in the strategic form. In plain words, our result says that these games (one of which is chess) have the following property. Consider the strategic form of the game. Eliminate all dominated strategies from the strategy sets of each