Blotto games with costly winnings

Irit Nowik^a, Tahl Nowik<sup>b

a</sup> Department of Industrial Engineering and Management, Lev Academic Center, P.O.B 16031, Jerusalem 9116001, Israel
^b Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel

Abstract: We introduce a new variation of the stochastic asymmetric Colonel Blotto game, where the n battles occur as sequential stages of the game, and the winner of each stage needs to spend resources for maintaining his win. The limited resources of the players are thus needed both for increasing the probability of winning and for the maintenance costs. We show that if the initial resources of the players are not too small, then the game has a unique Nash equilibrium, and the given equilibrium strategies guarantee the given expected payoff for each player.

Language: English

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