Source-linked AI summary
Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game
Zhen Wang, Matjaz Perc
TL;DR
The paper asks how changing the selection of strategy donors affects cooperation in the prisoner’s dilemma. It introduces a payoff-biased neighbor-selection rule and tests it across networks and adoption-uncertainty levels. Positive w promotes cooperation, with the effect attributed to negative feedback and changes in the effective interaction network.
Problem
The paper examines how strategy-donor selection influences cooperation in the prisoner’s dilemma, where defection typically dominates despite the prevalence of cooperation in social groups.
Method
The study introduces parameter w to bias neighbor selection toward higher- or lower-payoff players and evaluates it through simulations across multiple interaction networks and uncertainty levels.
Results
Positive w promotes cooperation, increasing the critical cost-to-benefit threshold by a full order of magnitude at w = 4.0 versus w = 0 and producing qualitatively similar effects across tested networks.
Takeaways & Limitations
The findings attribute cooperation’s promotion to negative feedback that increases defectors’ vulnerability and to w altering the effective interaction network and uncertainty’s impact.
Abstract
from arXiv · showhide
Strategy changes are an essential part of evolutionary games. Here we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new strategy. For positive $w$ players with high payoffs will be considered more likely, while for negative $w$ the opposite holds. Setting $w$ equal to zero returns the frequently adopted random selection of the opponent. We find that increasing the probability of adopting the strategy from the fittest player within reach, i.e. setting $w$ positive, promotes the evolution of cooperation. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction network. Since the evolution to widespread defection is tightly associated with cooperators having a lower fitness than defectors, the fact that positive values of $w$ facilitate cooperation is quite surprising. We show that the results can be explained by means of a negative feedback effect that increases the vulnerability of defectors although initially increasing their survivability. Moreover, we demonstrate that the introduction of $w$ effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the evolution of cooperation.
I. INTRODUCTION
The paper studies how selecting strategy donors by payoff affects cooperation in the prisoner’s dilemma across spatial and complex interaction networks. It introduces a fittest-neighbor mechanism and tests its effects under different network structures and adoption uncertainty.
- I. INTRODUCTION: The prisoner’s dilemma models conflict between individually optimal defection and the socially beneficial outcome of mutual cooperation.Its payoff ranking T>R>P>S makes defection the individually maximizing choice regardless of the opponent’s decision.
- I. INTRODUCTION: Spatial structure can promote cooperation by allowing cooperators to form clusters that protect them from exploitation.This result motivated extensive investigation of mechanisms and interaction topologies that sustain cooperation.
- I. INTRODUCTION: Complex networks, including scale-free networks, can substantially improve cooperator survivability compared with the classical square lattice.Prior studies identified complex interaction topologies as important for maintaining cooperation across broad parameter ranges.
- I. INTRODUCTION: The paper introduces payoff-based donor selection, making the most successful neighbor more likely to serve as a role model than under uniform random selection.It examines this mechanism on square lattices, scale-free networks, and random regular graphs under different levels of strategy-adoption uncertainty.
II. EVOLUTIONARY GAME
The evolutionary game uses a rescaled prisoner’s dilemma and a sequential strategy-update process in which parameter w controls which neighbor can donate a strategy. Simulations vary interaction networks, uncertainty, and selection preferences to study cooperation thresholds.
- II. EVOLUTIONARY GAME: The rescaled payoff parameters are R = 1, T = 1 + r, S = −r, and P = 0, with r = c/(b −c) as the cost-to-benefit ratio.The original payoffs are T = b, R = b −c, P = 0, and S = −c, satisfying T>R>P>S for b>c.
- II. EVOLUTIONARY GAME: Players interact on square lattices, random regular graphs, or scale-free networks and begin as cooperators or defectors with equal probability.The scale-free network has L2 nodes, average degree four, and is generated with the Barabási-Albert algorithm.
- II. EVOLUTIONARY GAME: Each update first calculates a player’s payoff from all neighbors, then selects a potential donor and adopts that donor’s strategy probabilistically.The process is performed sequentially, with every player receiving one chance to adopt a neighboring strategy per full iteration.
- II. EVOLUTIONARY GAME: For w = 0, a neighbor is selected uniformly; w > 0 favors higher-payoff donors, while w < 0 favors lower-payoff donors.The parameter w therefore tunes the preference for potential strategy sources.
- II. EVOLUTIONARY GAME: Finite K controls uncertainty in strategy adoption, while simulations measure the cooperator fraction after 10^5 full iterations and average results across independent runs.Populations range from 100 × 100 to 400 × 400 individuals, with up to 40 runs used for accuracy.
III. RESULTS
Positive selection parameter values promote cooperation across interaction networks, despite an initial defector advantage, through a recovery mechanism linked to altered effective interactions and uncertainty effects.
- At w = 4.0, the critical cost-to-benefit threshold r = rc increases by a full order of magnitude relative to w = 0.
- Positive w promotes cooperation, whereas negative w impairs it on the square lattice, random regular graph, and scale-free network.
- Positive w initially deepens cooperator decline because higher-payoff defectors are more likely to be chosen as strategy donors, but cooperation later recovers.
- The recovery reflects negative feedback: early defector exploitation leaves few cooperators to exploit, weakening defectors and enabling resilient cooperator clusters to expand.
- For w = 0, intermediate uncertainty optimizes cooperator survivability, whereas for w = 2.0 an intermediate K minimizes rc and larger K eventually increases it.
- Preference for fittest neighbors effectively alters the interaction network, changing how uncertainty affects cooperation.
IV. SUMMARY
The paper concludes that aspiring to the fittest promotes cooperation across interaction networks and uncertainty levels through a negative feedback effect. The selection parameter also alters how uncertainty affects cooperation and offers interpretations linked to information processing and moral-based role-model choice.
- IV. SUMMARY: Aspiring to the fittest promotes cooperation irrespective of the interaction network and uncertainty in strategy adoption.The mechanism involves robust cooperative clusters or groups that resist defector attacks, even under high temptation to defect.
- IV. SUMMARY: Defectors may initially appear dominant, but exploiting cooperators reduces their strength and allows remaining cooperators to overtake them.This negative feedback effect increases defectors’ vulnerability after their initial success.
- IV. SUMMARY: The selection parameter effectively alters the interaction network and changes the role of uncertainty in strategy adoption.Without this parameter, an intermediate uncertainty can maximize cooperative survival; with it, that optimum disappears.
- IV. SUMMARY: Positive selection toward successful role models is presented as applicable to studying how successful leaders emerge through coevolutionary processes.The paper frames this as a direction for future studies rather than a demonstrated leadership mechanism.
- IV. SUMMARY: Negative selection can represent role-model choices based on moral values when highly successful individuals are viewed as unethical.The paper also associates greater randomness with limited information-processing capability.