2023/04/11 by Athanasios Kehagias, Kehagias, Athanasios
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #Combinatorics #Computer Science and Game Theory (cs.GT) #Discrete Mathematics (cs.DM) #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Game theory #Mathematical economics #Mathematics #Nash equilibrium #Normal-form game #Optimization and Control (math.OC) #Philosophy #Repeated game #Risk dominance #Simple (philosophy) #Stochastic game #Strategy #Symmetric game #Traveler's dilemma
paper · pdf · doi:10.48550/arxiv.2304.05024
openalex publication_date 2023/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate and study a two-player static duel game as a nonzero-sum discounted stochastic game. Players P1,P2 are standing in place and, in each turn, one or both may shoot at the other player. If Pn shoots at Pm (m≠ n), either he hits and kills him (with probability pn) or he misses him and Pm is unaffected (with probability 1-pn). 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.