On the Nash Equilibria of a Simple Discounted Duel
We formulate and study a two-player, duel game as a nonzero-sum discounted stochastic game. Players P1, and 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...
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Wrocław University of Science and Technology
2024-01-01
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| Series: | Operations Research and Decisions |
| Online Access: | https://ord.pwr.edu.pl/assets/papers_archive/ord2024vol34no2_5.pdf |
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| author | Athanasios Kehagias |
| author_facet | Athanasios Kehagias |
| author_sort | Athanasios Kehagias |
| collection | DOAJ |
| description | We formulate and study a two-player, duel game as a nonzero-sum discounted stochastic game. Players P1, and 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 a unit payoff for each turn in which he remains alive; no payoff is assigned to killing the opponent. We show that the always-shooting strategy is a NE but, in addition, the game also possesses so-called 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. (original abstract) |
| format | Article |
| id | doaj-art-b2da98303fd04f0f888632fb52f489e6 |
| institution | DOAJ |
| issn | 2081-8858 2391-6060 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wrocław University of Science and Technology |
| record_format | Article |
| series | Operations Research and Decisions |
| spelling | doaj-art-b2da98303fd04f0f888632fb52f489e62025-08-20T02:40:21ZengWrocław University of Science and TechnologyOperations Research and Decisions2081-88582391-60602024-01-01vol. 34no. 26584171694159On the Nash Equilibria of a Simple Discounted DuelAthanasios Kehagias0Aristotle University, Thessaloniki, GreeceWe formulate and study a two-player, duel game as a nonzero-sum discounted stochastic game. Players P1, and 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 a unit payoff for each turn in which he remains alive; no payoff is assigned to killing the opponent. We show that the always-shooting strategy is a NE but, in addition, the game also possesses so-called 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. (original abstract)https://ord.pwr.edu.pl/assets/papers_archive/ord2024vol34no2_5.pdf |
| spellingShingle | Athanasios Kehagias On the Nash Equilibria of a Simple Discounted Duel Operations Research and Decisions |
| title | On the Nash Equilibria of a Simple Discounted Duel |
| title_full | On the Nash Equilibria of a Simple Discounted Duel |
| title_fullStr | On the Nash Equilibria of a Simple Discounted Duel |
| title_full_unstemmed | On the Nash Equilibria of a Simple Discounted Duel |
| title_short | On the Nash Equilibria of a Simple Discounted Duel |
| title_sort | on the nash equilibria of a simple discounted duel |
| url | https://ord.pwr.edu.pl/assets/papers_archive/ord2024vol34no2_5.pdf |
| work_keys_str_mv | AT athanasioskehagias onthenashequilibriaofasimplediscountedduel |