### Abstract

This paper introduces epsilon-stability as a generalization of the

concept of stochastic stability in learning and evolutionary game

dynamics. An outcome of a model of stochastic evolutionary dynamics is

said to be epsilon-stable in the long-run if for a given model of

mistakes it maximizes its invariant distribution. We construct an

efficient algorithm for computing epsilon-stable outcomes and provide

conditions under which epsilon-stability can be approximated by

stochastic stability. We also define and provide tighter bounds for

contagion rate and metastability as measures for characterizing the

short-run and medium-run behaviour of a typical stochastic evolutionary

model.

Keywords: Stochastic evolution, network games, epsilon-stable sets, expected

waiting time, metastability, contagion rate.

concept of stochastic stability in learning and evolutionary game

dynamics. An outcome of a model of stochastic evolutionary dynamics is

said to be epsilon-stable in the long-run if for a given model of

mistakes it maximizes its invariant distribution. We construct an

efficient algorithm for computing epsilon-stable outcomes and provide

conditions under which epsilon-stability can be approximated by

stochastic stability. We also define and provide tighter bounds for

contagion rate and metastability as measures for characterizing the

short-run and medium-run behaviour of a typical stochastic evolutionary

model.

Keywords: Stochastic evolution, network games, epsilon-stable sets, expected

waiting time, metastability, contagion rate.

Original language | English |
---|---|

Place of Publication | Maastricht |

Publisher | UNU-MERIT |

Publication status | Published - 1 Jan 2014 |

### Publication series

Series | UNU-MERIT Working Papers |
---|---|

Number | 036 |

## Cite this

Azomahou, T. T., & Opolot, D. (2014).

*Epsilon-stability and the speed of learning in network games*. UNU-MERIT. UNU-MERIT Working Papers, No. 036 http://www.merit.unu.edu/publications/wppdf/2014/wp2014-036.pdf