Holding power in sequential games

Holding power is simply the ability of a player to stay at one position longer than his opponent, thereby forcing the opponent to make the next move in a sequential game. In this paper, we illustrate the real world relevance of this concept by examining the Berlin crisis of 1948 and showing that only a holding power interpretation provides a satisfying explanation of the eventual resolution. We define holding power formally and find that, when one player has holding power, the outcome of the conflict is determined. We develop a simple procedure for identifying the holding power outcome in every strict ordinal 2x2 game, and draw several interesting conclusions about the nature of this power. We find that a horizon of six moves or less always ensures that the eventual holding power outcome is reached. We also find that holding power outcomes are always Pareto-superior, except in a Prisoners’ Dilemma game when the initial position of the player without holding power is associated with the noncooperative Nash equilibrium. Finally, we determine that the holding power outcome depends on which player has this power in just 15 of the 78 distinct 2x2 ordinal games. In 9 of these games, holding power is effective in the sense that a player does better when he has holding power. In the remaining 6 cases, though, the possession of holding power is actually a disadvantage-a player prefers that his opponent have holding power rather than himself. We provide an explanation for this occasional phenomenon.