scholarly journals The evolution of payoff matrices: providing incentives to cooperate

2010 ◽  
Vol 278 (1715) ◽  
pp. 2198-2206 ◽  
Author(s):  
Erol Akçay ◽  
Joan Roughgarden
Keyword(s):  
Natural Selection ◽  
Time Scale ◽  
Prisoner's Dilemma ◽  
Genetic Model ◽  
Social Systems ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Social Situation ◽  
Payoff Matrix ◽  
Payoff Matrices

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk–dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.

Evolutionary game dynamics of death-birth process with interval payoffs on graphs

2021 ◽  
pp. 1-12
Author(s):  
Bichuan Jiang ◽  
Lan Shu
Keyword(s):  
Natural Selection ◽  
Dynamic Equation ◽  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Fixation Probability ◽  
Weak Selection ◽  
Birth Process ◽  
Prisoner’S Dilemma Game ◽  
Game Dynamics

In this paper, we study the evolutionary game dynamics of the death-birth process with interval payoffs on graphs. First of all, we derive the interval replication dynamic equation. Secondly, we derive the fixation probability of the B-C prisoner’s dilemma game based on the death-birth process under the condition of weak selection, analyze the condition of the strategy fixed in the population, that is the condition of strategy A being dominant is analyzed. So we can judge whether natural selection is beneficial to strategy A in the game process through this condition. Finally, the feasibility of this method is verified by several examples.

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

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

scholarly journals Evolving Ecological Social Dilemmas: A Spatial Individual-Based Model for the Evolution of Cooperation with a Minimal Number of Parameters

2007 ◽  
Vol 2007 ◽  
pp. 1-5
Author(s):  
H. Fort
Keyword(s):  
Game Theory ◽  
Natural Selection ◽  
Evolutionary Game Theory ◽  
Spatial Model ◽  
Evolutionary Game ◽  
Social Dilemmas ◽  
Payoff Matrix ◽  
Evolution Of Cooperation ◽  
Full Version ◽  
Payoff Matrices

Cooperation, both intraspecific and interspecific, is a well-documented phenomenon in nature that is not well understood. Evolutionary game theory is a powerful tool to approach this problem. However, it has important limitations. First, very often it is not obvious which game is more appropriate to use. Second, in general, identical payoff matrices are assumed for all players, a situation that is highly unlikely in nature. Third, slight changes in these payoff values can dramatically alter the outcomes. Here, I use an evolutionary spatial model in which players do not have a universal payoff matrix, so no payoff parameters are required. Instead, each is equipped with random values for the payoffs, fulfilling the constraints that define the game(s). These payoff matrices evolve by natural selection. Two versions of this model are studied. First is a simpler one, with just one evolving payoff. Second is the “full” version, with all the four payoffs evolving. The fraction of cooperator agents converges in both versions to nonzero values. In the case of the full version, the initial heterogeneity disappears and the selected game is the “Stag Hunt.”

EFFECTS OF LEARNING ACTIVITY ON COOPERATION IN EVOLUTIONARY PRISONER'S DILEMMA GAME

2008 ◽  
Vol 19 (09) ◽  
pp. 1377-1387 ◽  
Author(s):  
XIAOJIE CHEN ◽  
FENG FU ◽  
LONG WANG
Keyword(s):  
Prisoner's Dilemma ◽  
Cooperative Behavior ◽  
Social Systems ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Individual Learning ◽  
Intermediate Level ◽  
Learning Activity ◽  
Prisoner’S Dilemma Game ◽  
Prisoner's Dilemma Game

We study the evolutionary Prisoner's Dilemma game under individual learning activity mechanism on small-world and scale-free networks, respectively. Each player updates its strategy with quenched learning rate which characterizes the strength of individual learning activity during the evolutionary process. Simulation results show that the mechanism of learning activity presents nontrivial phenomena on both the two networks: optimal intermediate levels of learning activity can promote or sustain cooperation. Specifically, there exists an interesting resonance-like manner in the evolutionary game when the intermediate level of learning activity promotes cooperation, and there exists a plateau for cooperation in the favorable moderate region of learning activity when the intermediate level of learning activity sustains cooperation. Moreover, these interesting phenomena are not sensitive to the two networks with other topological parameters. Our work can be helpful in reflecting the effects of individual learning mechanism on cooperative behavior in social systems.

scholarly journals Evolution of cooperation: The analysis of the case wherein a different player has a different benefit and a different cost

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Shun Kurokawa
Keyword(s):  
Natural Selection ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolution Of Cooperation ◽  
Cost Ratio ◽  
Personal Cost ◽  
Model Setting

The existence of cooperation demands explanation in terms of natural selection. Prisoner’s dilemma is a framework often used when studying the evolution of cooperation. In prisoner’s dilemma, most previous studies consider the situation wherein an individual who cooperates will give an opponent an amount b at a personal cost of c, where b > c > 0 while an individual who defects will give nothing. This model setting is convenient; however, previous studies have not considered the case wherein a different player has a different benefit and different cost while in reality, it is natural to consider that a different player has a different benefit and different cost. Here, we raise the following question: Taking that a different individual has a different benefit and a different cost into consideration, what strategy is likely to evolve? In this paper, we focus on the direct reciprocity and analyze the case wherein a different player has a different benefit and a different cost. We obtain the condition for the evolution in the general case. And in addition, we have revealed that under a specific condition as the interaction repeats longer and the benefit-to-cost ratio is larger and the cooperating probability is more sensitive to the benefit the opponent provides, the establishment of cooperation is more likely.

THE EFFECT OF PINNING CONTROL ON EVOLUTIONARY PRISONER'S DILEMMA GAME

2010 ◽  
Vol 24 (25) ◽  
pp. 2581-2589 ◽  
Author(s):  
WEN-BO DU ◽  
HONG ZHOU ◽  
ZHEN LIU ◽  
XIAN-BIN CAO
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Pinning Control ◽  
Control Mechanisms ◽  
Control Cost ◽  
Prisoner’S Dilemma Game ◽  
Scale Free ◽  
Prisoner's Dilemma Game ◽  
Control Degree

The evolutionary game on graphs provides a natural framework to investigate the cooperation behavior existing in natural and social society. In this paper, degree-based pinning control and random pinning control are introduced into the evolutionary prisoner's dilemma game on scale-free networks, and the effects of control mechanism and control cost on the evolution are studied. Numerical simulation shows that forcing some nodes to cooperate (defect) will increase (decrease) the frequency of cooperators. Compared with random pinning control, degree-based pinning control is more efficient, and degree-based pinning control costs less than random pinning control to achieve the same goal. Numerical results also reveal that the evolutionary time series is more stable under pinning control mechanisms, especially under the degree-based pinning control.

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