The optimal control for promoting the cooperation in evolution game generated by Prisoner's Dilemma

We discuss the effect of the punishment in the prisoner’s dilemma game. We propose a new evolution strategy rule which can reflect the external factor for both players in the evolution game. In general, if the punishment exists, the D (defection-defection) structure (i.e., both of the two players choose D-D strategy) which is the Nash equilibrium for the game can keep stable and never let the cooperation emerge. However, if a new evolution strategy rule is adopted, we can find that the D-D structure can not keep stable and it will decrease during the game from the simulations. In fact, the punishment mainly affects the C-D (cooperation-defection) structure in the network. After the fraction of the C-D structure achieved some levels, the punishment can keep the C-D structure stable and prevent it from transforming into C-C (cooperation-cooperation) structure. Moreover, in light of the stability of structure and the payoff of the individual gains, it can be found that the probability which is related to the payoff can affect the result of the evolution game.

Download Full-text

Punishment and Feedback Mechanism for the Evolution Game on Small-World Network Based on Varying Topology

Mathematical Problems in Engineering ◽

10.1155/2014/148915 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6

Author(s):

Yuntao Shi ◽

Bo Liu ◽

Xiaoliang Kou ◽

Xiao Han

Keyword(s):

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Small World ◽

Feedback Mechanism ◽

Small World Network ◽

Prisoner’S Dilemma Game ◽

Prisoner's Dilemma Game ◽

Updating Rule ◽

Set Up ◽

Evolution Game

We address the problem of the punishment and feedback mechanism for the evolution game on small-world network with varying topology. Based on the strategy updating rule, we propose a new punishment and feedback mechanism; that is, all the individuals of the network will play ann-round Prisoner’s Dilemma Game firstly and then, for the most defectors, their neighbors will punish them and break the connecting link with them and set up the new connecting link for themselves. The mechanism can make the degree of the whole network decrease. We find that the mechanism can help keep the cooperators surviving and make them avoid being wiped out by the defectors. With the mechanism being adopted, the number ofn-round Prisoner’s Dilemma Game (PDG) almost has no effect on the evolution game. Furthermore, the probability of the average connectingkand the scale of the network is related to the result of the evolution game.

Download Full-text

Maximizing cooperation in the prisoner’s dilemma evolutionary game via optimal control

10.1101/2020.07.13.201400 ◽

2020 ◽

Author(s):

P.K. Newton ◽

Y. Ma

Keyword(s):

Optimal Control ◽

Prisoner's Dilemma ◽

Evolutionary Game ◽

Optimal Schedule ◽

Stable State ◽

Prisoner’S Dilemma ◽

Payoff Matrix ◽

Optimal Timing ◽

Initial Population ◽

Asymptotically Stable

The prisoner’s dilemma (PD) game offers a simple paradigm of competition between two players who can either cooperate or defect. Since defection is a strict Nash equilibrium, it is an asymptotically stable state of the replicator dynamical system that uses the PD payoff matrix to define the fitness landscape of two interacting evolving populations. The dilemma arises from the fact that the average payoff of this asymptotically stable state is sub-optimal. Coaxing the players to cooperate would result in a higher payoff for both. Here we develop an optimal control theory for the prisoner’s dilemma evolutionary game in order to maximize cooperation (minimize the defector population) over a given cycle-time T, subject to constraints. Our two time-dependent controllers are applied to the off-diagonal elements of the payoff matrix in a bang-bang sequence that dynamically changes the game being played by dynamically adjusting the payoffs, with optimal timing that depends on the initial population distributions. Over multiple cycles nT (n > 1), the method is adaptive as it uses the defector population at the end of the nth cycle to calculate the optimal schedule over the n + 1st cycle. The control method, based on Pontryagin’s maximum principle, can be viewed as determining the optimal way to dynamically alter incentives and penalties in order to maximize the probability of cooperation in settings that track dynamic changes in the frequency of strategists, with potential applications in evolutionary biology, economics, theoretical ecology, and other fields where the replicator system is used.PACS numbers02.50.Le; 02.30.Yy; 05.45.-a; 87.23.Kg; 87.23.Cc

Download Full-text

Zu brav oder zu böse? Mobbing-Opfer und Abgelehnte im Prisoner's Dilemma-Paradigma

Zeitschrift für Sozialpsychologie ◽

10.1024//0044-3514.30.23.179 ◽

1999 ◽

Vol 30 (2/3) ◽

pp. 179-193 ◽

Cited By ~ 2

Author(s):

Beate Schuster

Keyword(s):

Prisoner's Dilemma ◽

Prisoner’S Dilemma

Zusammenfassung: Der soziometrische Status und der Viktimisierungsstatus von 5. bis 11. Klässlern wurde ermittelt, der Status hypothetischer InteraktionspartnerInnen sowie deren angebliche Wahlen variiert, und die Reaktionen im Gefangenendilemma erfaßt. Die Reaktionen wurden sowohl durch die experimentell vorgegebenen als auch durch die erwarteten Wahlen der InteraktionspartnerInnen bestimmt: Kooperative Zuege wurden eher kooperativ, und kompetitive Zuege eher kompetitiv beantwortet. Darüber hinaus vermieden Mobbingopfer kompetitive Züge, während zwei Untergruppen der Abgelehnten gegensätzliche Strategiepräferenzen aufwiesen: Versuchspersonen, die sowohl Ablehnung als auch Mobbing erfahren («Viktimisiert-Abgelehnte») verhielten sich besonders kooperativ; abgelehnte ProbandInnen, die nicht viktimisiert werden («Nicht-viktimisiert-Abgelehnte») dagegen vergleichsweise kompetitiv. Die kooperativen Wahlen viktimisierter Versuchspersonen wurden nicht erwidert: Die Versuchspersonen reagierten gegenüber den Viktimisierten kompetitiver als sich die Viktimisierten ihrerseits gegenüber ihren InteraktionspartnerInnen verhielten. Diese Befunde bestätigen die Notwendigkeit, bei «Abgelehnten» zwei Untergruppen auf der Basis der Viktimisierungsdimension zu unterscheiden. Die Befunde werden ferner vor dem Hintergrund der Hypothese diskutiert, daß die Submissivität potentieller Opfer mit zu ihrer Viktimisierungs-Erfahrung beiträgt.

Download Full-text

Facial Likability and Smiling Enhance Cooperation, but Have No Direct Effect on Moralistic Punishment

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000338 ◽

2016 ◽

Vol 63 (5) ◽

pp. 263-277 ◽

Cited By ~ 6

Author(s):

Laura Mieth ◽

Raoul Bell ◽

Axel Buchner

Keyword(s):

Conditional Probability ◽

Direct Effect ◽

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Prisoner’S Dilemma Game ◽

Costly Punishment ◽

Prisoner's Dilemma Game ◽

Moralistic Punishment

Abstract. The present study serves to test how positive and negative appearance-based expectations affect cooperation and punishment. Participants played a prisoner’s dilemma game with partners who either cooperated or defected. Then they were given a costly punishment option: They could spend money to decrease the payoffs of their partners. Aggregated over trials, participants spent more money for punishing the defection of likable-looking and smiling partners compared to punishing the defection of unlikable-looking and nonsmiling partners, but only because participants were more likely to cooperate with likable-looking and smiling partners, which provided the participants with more opportunities for moralistic punishment. When expressed as a conditional probability, moralistic punishment did not differ as a function of the partners’ facial likability. Smiling had no effect on the probability of moralistic punishment, but punishment was milder for smiling in comparison to nonsmiling partners.

Download Full-text