Publicação
Insuperable Strategies in Two-Player and Reducible Multi-Player Games
| Resumo: | Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction. |
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| Autores principais: | Chalub, Fabio A.C.C. |
| Outros Autores: | Souza, Max O. |
| Assunto: | Farkas’ lemma Finite populations Game-theory Insuperable strategies Nash equilibrium Statistics and Probability Economics and Econometrics Computer Science Applications Computer Graphics and Computer-Aided Design Computational Theory and Mathematics Computational Mathematics Applied Mathematics |
| Ano: | 2025 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction. |
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