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On the Nash Equilibria of a Simple Discounted Duel
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On the Nash Equilibria of a Simple Discounted Duel
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On the Nash Equilibria of a Simple Discounted Duel
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Paper
On the Nash Equilibria of a Simple Discounted Duel
2023
Overview
We formulate and study a two-player static duel game as a nonzero-sum discounted stochastic game. Players \\(P_{1},P_{2}\\) are standing in place and, in each turn, one or both may shoot at the other player. If \\(P_{n}\\) shoots at \\(P_{m}\\) (\\(m\\neq n\\)), either he hits and kills him (with probability \\(p_{n}\\)) or he misses him and \\(P_{m}\\) is unaffected (with probability \\(1-p_{n}\\)). The process continues until at least one player dies; if nobody ever dies, the game lasts an infinite number of turns. Each player receives unit payoff for each turn in which he remains alive; no payoff is assigned to killing the opponent. We show that the the always-shooting strategy is a NE but, in addition, the game also possesses cooperative (i.e., non-shooting) Nash equilibria in both stationary and nonstationary strategies. A certain similarity to the repeated Prisoner's Dilemma is also noted and discussed.
Publisher
Cornell University Library, arXiv.org
Subject
