STOCHASTIC DUEL WITH THREE OR MORE PLAYERS

Consider a stochastic duel with many players. Each player chooses an opponent to shoot at, makes a hit after a random amount of time that follows an exponential distribution, and is killed as soon as being hit for the first time. The duel continues until all but one player is killed, and the lone survivor is declared the winner. The goal of each player is to decide which opponent to target at any given time in order to maximize their winning probability. We develop an algorithm to compute each player’s optimal strategy and winning probability. In particular, the strongest player—the one having the largest kill rate—need not be the most likely to win, and it is not necessarily optimal for each player to shoot at their strongest opponent. We also consider a variation of the game in which players arrive sequentially to select their own kill rates, knowing the selections made by players who arrived earlier. In this sequential-move game with three players, the first player wants to be mediocre and the third player has the best chance to win. Our findings enable further understanding of military conflicts that involve three or more adversaries in the same area of operations.
Outstanding Thesis
Major, United States Marine Corps
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