Pavlovian Prisoner's Dilemma—Analytical results, the quasi-regular phase and spatio-temporal patterns

Abstract

The Prisoner's Dilemma (PD) game is applied in several research fields due to the emergence of cooperation among selfish players. In this work the PD is studied in a one-dimensional lattice, where each cell represents a player, which in turn can interact with the neighbors playing the PD (cooperate or defect). The update of states adopts the Pavlovian Evolutionary Strategy (PES) or Darwinian Evolutionary Strategy (DES). Adopting PES, if a player receives a positive payoff greater than his/her aspiration level, he/she keeps the current state, and switches otherwise. Adopting DES, player compares his/her payoff with payoff of opponents. If it is not the highest, he/she copies the state of fittest player, switching the state if it is different of his/her current state. The critical temptation values obtained analytically are reported, and the cluster patterns that emerge from the interactions among the players are shown. Also we defined analytical functions that calculate the maximum/minimum size of defective/cooperative clusters. Also, the parameter space is explored with exhaustive computational simulations, which confirm the analytical results and reinforce that Pavlovian strategy foments cooperation among players. In steady state, system can reach the cooperative or quasi-regular phases, when adopting the PES, and cooperative, defective or chaotic phases, adopting the DES. The new quasi-regular phase occurs when several players switch their states in each round, but the proportion of cooperators does not show significant variation. Additionally, the present work shows that the lowest temptation level (T=1) may be considered a trivial case only for the particular case where the players interact with only one neighbor, otherwise system presents the same features that for higher temptation values.

A simple game-theoretic model for upstream fish migration

“…The model focuses on prolonged swimming behavior of fishes rather than burst ones, the latter being relevant for much shorter timescale. Game-theoretic models have extensively been utilized for ecological and biophysical modelling of animals (Kabalak et al 2015;Mariani et al 2016;Metz et al 1992;Pereira and Martinez 2010;Riechert and Hammerstein 1983;Tanaka et al 2011); however, application of such models to biophysics of fish migration is still rare. The variables to be optimized in the present model contain the swimming speed and school size that should be chosen by the fish school, so that the net cost of migration is minimized.…”

Dilema do prisioneiro contínuo com agentes racionais e classificadores de cooperação

“…No entanto, redes unidimensionais possuem as mesmas transições de fase de redes bidimensionais, istoé, apresentam os mesmos valores de tentação crítica onde ocorrem mudanças abruptas na proporção assintótica de cooperadores [46,47,48]. Neste capítulo, apresentamos o modelo adotado nesta tese em três seções: a primeira seção traz a descrição do modelo em detalhes; a segunda, o modelo analítico e aúltima, o modelo computacional.…”

“…[46,47,48] apresentamos uma nova abordagem para o DPI, a qual foi utilizada na presente tese. Esta abordagem utiliza um autômato celular em uma rede unidimensional regular, onde cada célula do autômato celular representa um jogador ou uma família (vários membros no mesmo sítio).…”

“…Esta função generalizada de ganho foi primeiramente apresentada na Ref. [48]. O ganho total G ié dado pela soma dos ganhos das interações com todos seus vizinhos (κ i ):…”

“…Esperávamos compreender o efeito da personalidade dos jogadores e agregar elementos como a inconsistência intertemporal [112], a assimetria na tomada de decisão frente a ganhos e perdas [15]. Para isso, utilizamos o dilema do prisioneiro contínuo na estrutura que propusemos [46,47,48] com novas estratégias.…”