# Multiplicative updates in coordination games and the theory of evolution

@inproceedings{Chastain2012MultiplicativeUI, title={Multiplicative updates in coordination games and the theory of evolution}, author={Erick J. Chastain and Adi Livnat and Christos H. Papadimitriou and Umesh V. Vazirani}, booktitle={Information Technology Convergence and Services}, year={2012} }

In this paper we point out a new and unexpected connection between three fields: Evolution Theory, Game Theory, and Algorithms.
In particular, we study the standard equations of population genetics for Evolution, in the presence of recombination (sex), focusing on the important special case of weak selection [1,2] in which all fitness values are assumed to be close to one another. Weak selection is the mathematical regime capturing the widely accepted Neutral Theory proposed by Kimura in the…

## 26 Citations

### Natural Selection as an Inhibitor of Genetic Diversity: Multiplicative Weights Updates Algorithm and a Conjecture of Haploid Genetics [Working Paper Abstract]

- EconomicsITCS
- 2015

It is established that, under specific assumptions, mathematical models of biological evolution can be reduced to studying discrete replicator dynamics, a close variant of MWUA, in coordination games, and it is shown that haploid evolution imply the extinction of genetic diversity in the long term limit.

### Mutation, Sexual Reproduction and Survival in Dynamic Environments

- MathematicsITCS
- 2017

This work provides the first, to the knowledge, polynomial convergence bound for noisy MWU in a coordination game, and shows that in static environments, sexual evolution with mutation converges, for any level of mutation.

### On Sex, Evolution, and the Multiplicative Weights Update Algorithm

- MathematicsAAMAS
- 2015

It is shown that the marginal allele distributions induced by the population dynamics precisely match the marginals induced by a multiplicative weights update algorithm in this general setting, thereby affirming and substantially generalizing these earlier results.

### The game of survival: Sexual evolution in dynamic environments

- Computer ScienceArXiv
- 2015

This work extends classic evolutionary models to allow for a dynamically changing environment, and shows that with mutation, as long as the rate of change of the environment is not too fast, long term survival is possible.

### Making the most of potential: potential games and genotypic convergence

- BiologybioRxiv
- 2020

There is a unified underlying theory underlying genotypic convergence of populations and all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem.

### Approximating the Geometry of Dynamics in Potential Games: Point-wise Convergence, Regions of Attraction, Average Case Performance Analysis and System Invariants

- Mathematics
- 2014

Novel yardsticks and techniques are devised that allow for much more detailed analysis of game dynamics and network computation more generally and open possibilities for a deeper understanding of many settings of networked, decentralized computation.

### Learning Dynamics and the Co-Evolution of Competing Sexual Species

- BiologyITCS
- 2018

A stylized model of co-evolution between any two purely competing species, both sexually reproducing, to establish a novel class of conservative dynamical systems that makes a simple and robust behavioral prediction.

### The multiplicative weight updates method for evolutionary biology

- Biology
- 2017

This thesis presents a novel connection between universal semantic communication and the Rivoire-Leibler model of population genetics, in addition to infinite population asexual selection models... with MWU as the key to proving the latter connection.

### Multiplicative Weights Updates with Constant Step-Size in Graphical Constant-Sum Games

- EconomicsNeurIPS
- 2018

It is shown that Multiplicative Weights updates with any constant step-size eps > 0 converge to the boundary of the state space, and thus do not satisfy the permanence and Poincare recurrence properties, but it is also shown that MW updates have a regret lower bound of Omega.

### The Computational Complexity of Genetic Diversity

- BiologyESA
- 2016

The key contribution is to establish complexity theoretic hardness results implying that even in the textbook case of single locus (gene) diploid models, predicting whether diversity survives or not given its fitness landscape is algorithmically intractable.

## References

SHOWING 1-10 OF 17 REFERENCES

### A mixability theory for the role of sex in evolution

- BiologyProceedings of the National Academy of Sciences
- 2008

It is shown that selection in the presence of sex favors the ability of alleles to perform well across different combinations in a highly robust manner and that the mechanism responsible has been out of the purview of previous theory, because it operates during the evolutionary transient.

### Some Mathematical Models in Evolutionary Genetics

- Biology
- 2011

The basic models and the most fundamental results about the evolutionary dynamics of a population in which selection acts on many gene loci are presented and the selection response and the evolution of (multivariate) quantitative traits is investigated.

### On the formation of interaction networks in social coordination games

- EconomicsGames Econ. Behav.
- 2002

### Evolution in Sexual and Asexual Populations

- BiologyThe American Naturalist
- 1965

The evolution of diploidy from haploidy confers an immediate reduction in the mutation load by concealment of deleterious recessives, but this advantage is lost once a new equilibrium is reached and the development of diPloidy may be because of an immediate advantage rather than because of any permanent benefit.

### Convergence of multilocus systems under weak epistasis or weak selection

- EconomicsJournal of mathematical biology
- 1999

It is proved that if epistasis or selection is sufficiently weak (and satisfies a certain nondegeneracy assumption whose genericity the authors establish), then there is always convergence to some equilibrium point, and cycling cannot occur.

### Efficient algorithms using the multiplicative weights update method

- Computer Science
- 2007

A single meta-algorithm is presented which unifies all known applications of the Multiplicative Weights method in the design of efficient algorithms for various optimization problems and derives the following algorithmic applications: fast algorithms for approximately solving several families of semidefinite programs which beat interior point methods.

### Why sex and recombination?

- BiologyScience
- 1998

The effect of sex and recombination in breaking down negative correlations between favorable variants at different genetic loci, which increases the efficiency of natural selection, is likely to be a major factor favoring their evolution and maintenance.

### An analytical contrast between fitness maximization and selection for mixability.

- BiologyJournal of theoretical biology
- 2011

### The Major Transitions in Evolution

- Biology
- 1995

This book discusses the origins of societies, development and evolution, and the development of spatial patterns in simple organisms.

### How easy is local search?

- Computer Science26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
- 1985