A carregar...
Publicação
Insuperable Strategies in Two-Player and Reducible Multi-Player Games
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 699.89 KB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
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.
Descrição
Part of this work was done during the stay of FACCC at Carnegie Mellon University, supported by the CMU-Portugal Program. Furthermore, part of this work was done during FACC stays at City University, London (UK), Universidade Federal do Cear\u00E1 (Brazil), and Instituto de Matem\u00E1tica Pura e Aplicada (Rio de Janeiro, Brazil). FACCC also acknowledges discussions on the concept of Hamiltonian spite with Andr\u00E9 d\u2019Almeida, which eventually led to preliminary ideas in the concept of insuperable strategies. MOS also acknowledges the support of CAPES/BR - Finance code 01 and FAPERJ through grant E-26/210.440.2019. All authors acknowledge the support of the CAPES PRINT program at UFF through grant 88881.310210/2018-01. Last, but not least, FACCC acknowledges the input of his daughter, Alice, to explain how the N-player generalization of the zerinho-ou-um game is played nowadays by school children.
Publisher Copyright:
© The Author(s) 2025.
Palavras-chave
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