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Coevolutionary games - a mini review
Matjaz Perc, Attila Szolnoki
TL;DR
Cooperation is difficult to sustain because selection favors defectors in social dilemmas, and strategy evolution alone may not capture the role of changing environments. This mini review synthesizes coevolutionary evolutionary-game models, finding that evolving networks and player properties can promote cooperation while identifying underexplored game types and research questions.
Problem
Cooperation among selfish individuals conflicts with selection favoring higher fitness, while strategy evolution alone may be insufficient to explain cooperative behavior.
Method
The paper reviews evolutionary games with coevolutionary rules affecting interaction networks, player reproduction capability, reputation, mobility, or age.
Results
Coevolutionary rules can promote cooperation, including through partner searching, interaction-network dynamics, and evolving teaching activity.
Takeaways & Limitations
Coevolution is presented as a promising extension because evolving environments and player properties can continuously or indirectly affect cooperation.
Takeaways & Limitations
Coevolutionary rules have largely focused on social dilemmas, while many other game types remain unconsidered.
Abstract
from arXiv · showhide
Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.
1. Introduction
Social dilemmas pit individually costly cooperation against defection, while spatial structure, network heterogeneity, and coevolutionary rules provide routes for sustaining cooperation. This review focuses on rules that allow strategies and interaction environments or player properties to evolve together.
- Cooperators contribute to collective welfare at personal cost, so selection favors defectors and makes cooperation itself an evolutionary dilemma.
- In well-mixed prisoner’s dilemma games, defectors dominate, whereas snowdrift games permit stable coexistence of cooperators and defectors.
- Spatial structure can let cooperators form clusters that protect them from exploitation by defectors.
- Heterogeneous scale-free networks sustain cooperation across the prisoner’s dilemma, snowdrift, and stag-hunt games.The review attributes this result predominantly to heterogeneity in degree distributions.
- Coevolutionary rules extend evolutionary games by allowing interaction links, reproduction capability, reputation, mobility, or age to evolve alongside strategies.The review treats this as a natural upgrade because evolving environments and other factors feed back on strategy evolution.
- The review distinguishes coevolutionary rules from earlier studies of changing networks and surveys recent work on multiple evolving player and environmental properties.
2. Evolutionary games
Evolutionary games model cooperation and defection through payoff orderings and strategy-adoption rules. This section defines the three principal pairwise social dilemmas, describes network-based update procedures, and highlights how network heterogeneity affects adoption dynamics.
- The prisoner’s dilemma, snowdrift, and stag-hunt games are classified by the payoff orderings T > R > P > S, T > R > S > P, and R > T > P > S.The standard parametrization fixes R = 1 and P = 0, with -1 ≤ S ≤ 1 and 0 ≤ T ≤ 2.
- The reviewed setup commonly begins with equal-probability cooperation and defection on network nodes, although initial conditions and update definitions may vary.
- Players initially receive cooperative or defective strategies, accumulate payoffs from neighbors, and attempt strategy transmission under a specified adoption probability.Random sequential updating selects a player and neighbor, with one full Monte Carlo step comprising N elementary selections.
- The Fermi rule allows payoff-superior strategies to spread deterministically as K → 0, while positive K permits adoption of worse-performing strategies.K represents noise, or equivalently 1/K represents selection intensity.
- For heterogeneous degree distributions, the normalized adoption rule uses the larger degree kq and game-specific payoff differences to reduce degree-related effects.Its trade-off is that it cannot adjust uncertainty in strategy adoption.
- The richest-following rule makes a player imitate its most successful neighbor and therefore imposes deterministic, strongest selection.
3. Coevolutionary rules
Coevolutionary rules jointly alter strategy evolution and another evolving property, such as interaction links, teaching activity, or player heterogeneity. Their effects depend strongly on dynamical timing and network structure, with several rules promoting cooperation under specific conditions.
- Scope: The review organizes coevolutionary rules by their effects on interactions, population growth, teaching activity, mobility, aging, and related individual or global characteristics.These rules extend evolutionary games beyond strategy evolution alone.
- Dynamical interactions: Network adaptation can produce cooperative Nash equilibria when players preferentially replace low-payoff links, while defector-defector rewiring can promote near-complete cooperation even at p = 0.01.The former also yields a network Nash equilibrium; the latter can generate hierarchical and small-world interaction structures.
- Dynamical interactions: A critical strategy-to-rewiring time-scale ratio can cause cooperators to eliminate defectors, whereas another rewiring rule yields an optimal rather than critical separation.The critical ratio is associated with maximal network heterogeneity, while partner choice from local neighborhoods can outperform random population-wide search.
- Dynamical interactions: Deleting an invaded player's links except to the strategy donor, followed by random link additions every τ steps, promotes multilevel selection when strategy adoption is sufficiently frequent between link additions.The mechanism depends on quasi-homogeneous groups and can ultimately disintegrate defector clusters.
- Heterogeneity and dynamics: Coevolutionary heterogeneity includes differences in reputation or influence, and the review identifies time-scale separation as a major determinant of final evolutionary outcomes.The review also notes that coevolutionary network-growth findings may be less robust than those on static scale-free networks because of extreme star-like heterogeneity.
4. Conclusions and outlook
Coevolutionary rules extend evolutionary games by allowing strategies and environments or other influencing factors to evolve together. The review highlights broad applications and identifies unexplored game types and mechanisms as priorities for future research.
- Coevolution is presented as an upgrade to evolutionary games because strategies and environments can evolve simultaneously, influencing strategy outcomes.
- Coevolutionary processes may be finite or lasting, with some affecting cooperation indirectly through the resulting environment and others continuously altering its evolution.
- The review frames the interplay between coevolutionary dynamics and their final outcomes as an open question in explaining cooperation.
- Evolutionary games apply across social and natural sciences, including biochemical systems, traffic congestion, and climate change.
- Coevolutionary rules have primarily addressed social dilemmas, leaving games such as public goods, ultimatum, and rock-scissors-paper comparatively unexplored.