Escalation and Cooperation in Conflict Situations

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Abstract
We present a new game-theoretic analysis of an abstract auction game that captures essential strategic aspects of escalation phenomena. Two competitive adversaries commit resources irreversibly in order to win an indivisible prize; the winner will take the prize while both winner and loser incur the cost of their bids (investments). Following O'Neill (1986), we first reexamine a discrete version of the game and emphasize some strategic considerations that give rise to new bidding strategies of players. These new strategies, however, confirm O'Neill's result qualitatively: Rational players should not bid against each other. We then introduce a more general model of the game and show that escalatory competitive bids are compatible with equilibrium play. Equilibria with escalating bidding eventually realize a “draw”: Initial firmness (leading to escalation) is followed by conciliatory behavior that eventually implements a common commitment level.

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