# Weight of fitness deviation governs strict physical chaos in replicator dynamics.

@article{Pandit2017WeightOF, title={Weight of fitness deviation governs strict physical chaos in replicator dynamics.}, author={Varun Pandit and Archan Mukhopadhyay and Sagar Chakraborty}, journal={Chaos}, year={2017}, volume={28 3}, pages={ 033104 } }

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal…

## 13 Citations

### Periodic Orbit can be Evolutionarily Stable: Case Study of Discrete Replicator Dynamics.

- EconomicsJournal of theoretical biology
- 2020

### Deciphering chaos in evolutionary games.

- EconomicsChaos
- 2020

This work constructs a game-theoretic solution that is realized as the chaotic outcomes in the selection monotone game dynamic that is optimized over the generations of the evolutionary process.

### Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation.

- MathematicsPhysical review. E
- 2020

It is found that while mutation alone can never lead to oscillatory cooperation state in two-player-two-strategy games, the delay can change the scenario and there are situations when delay alone cannot lead to the Hopf bifurcation in the absence of mutation in the selection dynamics.

### Amplitude death in coupled replicator map lattice: Averting migration dilemma.

- EconomicsPhysical review. E
- 2021

A theoretical model consisting of a coupled map lattice of replicator maps based on two-player-two-strategy games is set up, intrigued by the effectiveness of the random migration in sustaining a uniform cooperator fraction across a population irrespective of the details of the replicator dynamics and the interaction among the demes.

### Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective

- Mathematics
- 2022

Even though existence of non-convergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such…

### Chaos and coexisting attractors in replicator-mutator maps

- BiologyJournal of Physics: Complexity
- 2021

It is shown that mutation in a generation-wise nonoverlapping population with two-player-two-strategy symmetric game gives rise to coexisting stable population states, one of which can even be chaotic; the chaotic state prevents the cooperators in the population from going extinct.

### Periodic orbits in evolutionary game dynamics: An information-theoretic perspective

- MathematicsArXiv
- 2022

Even though existence of non-convergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such…

### Game-environment feedback dynamics in growing population: Effect of finite carrying capacity.

- MathematicsPhysical review. E
- 2021

A mathematical framework that incorporates the density dependent payoffs and the logistic growth of the population in the eco-evolutionary dynamics modeling the game-resource feedback is presented and a bistability in the dynamics is discovered: a finite carrying capacity can either avert or cause the TOC depending on the initial states of the resource and the initial fraction of cooperators.

### Effect of chaotic agent dynamics on coevolution of cooperation and synchronization.

- PhysicsChaos
- 2020

A coupled map lattice of the paradigmatic chaotic logistic map of the agent's chaotic state dynamics is constructed by adopting the Watts-Strogatz network algorithm and it is observed that the population does not desynchronize completely-and hence, a finite level of cooperation is sustained-even when the average degree of the coupledMap lattice is very high.

### Cooperators overcome migration dilemma through synchronization

- Economics
- 2021

It is demonstrated that the cooperators—evolving in synchrony—overcome the migration dilemma to proliferate across the population when altruism is mildly incentivized making few of the demes play the leader game.

## 52 References

### Local Replicator Dynamics: A Simple Link Between Deterministic and Stochastic Models of Evolutionary Game Theory

- MathematicsBulletin of mathematical biology
- 2011

The deterministic replicator equation in an infinite population can be used to study the Moran process in a finite population and vice versa, and a one-third law that holds for any population size is derived.

### Stochastic dynamics of invasion and fixation.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

A simple closed formula is derived that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game, and is valid at all intensities of selection and for any initial condition.

### Chaos and unpredictability in evolution of cooperation in continuous time.

- BiologyPhysical review. E
- 2017

This work investigates the infinitely repeated prisoner's dilemma for various values of c with four of the representative memory-one strategies, i.e., unconditional cooperation, unconditional defection, tit-for-tat, and win-stay-lose-shift and demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics.

### Evolutionary Games and Population Dynamics

- Psychology
- 1998

In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.

### Chaos and the evolution of cooperation.

- BiologyProceedings of the National Academy of Sciences of the United States of America
- 1993

Here it is shown that a heterogeneous population consisting of simple strategies, whose behavior is totally specified by the outcome of the previous round, can lead to persistent periodic or highly irregular oscillations in the frequencies of the strategies and the overall level of cooperation.

### Pairwise comparison and selection temperature in evolutionary game dynamics.

- PhysicsJournal of theoretical biology
- 2007

### Chaos and unpredictability in evolutionary dynamics in discrete time.

- PhysicsPhysical review letters
- 2011

A discrete-time version of the replicator equation for two-strategy games is studied, where periodic and chaotic behavior replace the usual fixed-point population solutions.

### Evolutionary dynamics of populations with conflicting interactions: classification and analytical treatment considering asymmetry and power.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is pointed out that norms have a similar function in social systems that forces have in physics, as they allow one to understand conditions for the breakdown of cooperation and the occurrence of polarization or conflict.

### Evolutionary dynamics of collective action in N-person stag hunt dilemmas

- EconomicsProceedings of the Royal Society B: Biological Sciences
- 2008

A model in which a threshold less than the total group is required to produce benefits, with increasing participation leading to increasing productivity is introduced, which constitutes a generalization of the two- person stag hunt game to an N-person game.