Stationary and Nonstationary Equilibria of Duel and Truel with Random Shooting Order

Athanasios Kehagias () and Symeon Mastrakoulis
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Athanasios Kehagias: Aristotle University of Thessaloniki: Aristoteleio Panepistemio Thessalonikes
Symeon Mastrakoulis: Aristotle University of Thessaloniki: Aristoteleio Panepistemio Thessalonikes

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 47, 30 pages

Abstract: Abstract We study duel and truel variants in which two or three players, respectively, shoot each other in random order (or abstain from shooting). Depending on the final outcome of the game (number of survivors), each player may receive both positive, zero or negative payoff. We compute payoffs under stationary strategies by solving a system of linear equations, which always has a unique solution. Then we compute Nash equilibria under stationary strategies and shown that there is always a shooting NE and, under appropriate conditions, the truel also has a nonshooting stationary NE. We also provide a number of nonstationary NE, obtained by using a “grim triggering mechanism” to punish deviations from equilibrium. Finally, we briefly discuss: (a) extensions to the case of more than three players (nuel) (b) the connection of our model to applied problems and (c) the relationship to the Prisoner’s Dilemma and to the family of contest games.

Date: 2026
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DOI: 10.1007/s10957-025-02873-4

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