Gains in evolutionary dynamics: a unifying approach to stability for contractive games and ESS

by   Dai Zusai, et al.

In this paper, we investigate gains from strategy revisions in deterministic evolutionary dynamics. To clarify the gain from revision, we propose a framework to reconstruct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) available action set and switching cost. Many of major dynamics can be constructed in this framework. We formally define net gains from revisions and obtain several general properties of the gain function, which leads to Nash stability of contractive games---generalization of concave potential games---and local asymptotic stability of a (regular) evolutionary stable state. The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is observable or unobservable or whether heterogeneity is in payoffs or in revision protocols. This extends the known positive results on evolutionary implementation of social optimum through Pigouvian pricing to the presence of heterogeneity and non-aggregate payoff perturbations. While the analysis here is confined to general strategic-form games, we finally discuss that the idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability is promising for further applications to more complex situations.


page 1

page 2

page 3

page 4


Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamics

In the presence of persistent payoff heterogeneity, the evolution of the...

Heterogeneity and aggregation in evolutionary dynamics: a general framework without aggregability

We consider general evolutionary dynamics under persistent payoff hetero...

Stability of Gradient Learning Dynamics in Continuous Games: Vector Action Spaces

Towards characterizing the optimization landscape of games, this paper a...

Stability and bifurcations in transportation networks with heterogeneous users

A critical aspect in strategic modeling of transportation systems is use...

On logit dynamics in population games

We study the logit evolutionary dynamics in population games. For genera...

Evolutionary dynamics in the public goods games with switching between punishment and exclusion

Pro-social punishment and exclusion are common means to elevate the leve...

Dynamic system optimal traffic assignment with atomic users: Convergence and stability

In this study, we analyse the convergence and stability of dynamic syste...

Please sign up or login with your details

Forgot password? Click here to reset