Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium

William Sandholm

Games, 2009, vol. 1, issue 1, 1-15

Abstract: We introduce a class of evolutionary game dynamics — pairwise comparison dynamics — under which revising agents choose a candidate strategy at random, switching to it with positive probability if and only if its payoff is higher than the agent’s current strategy. We prove that all such dynamics satisfy Nash stationarity : the set of rest points of these dynamics is always identical to the set of Nash equilibria of the underlying game. We also show how one can modify the replicator dynamic and other imitative dynamics to ensure Nash stationarity without increasing the informational demands placed on the agents. These results provide an interpretation of Nash equilibrium that relies on large numbers arguments and weak requirements on payoff observations rather than on strong equilibrium knowledge assumptions.

Keywords: evolutionary game theory; dynamical systems; Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
https://www.mdpi.com/2073-4336/1/1/3/pdf (application/pdf)
https://www.mdpi.com/2073-4336/1/1/3/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:1:y:2009:i:1:p:3-17:d:6406

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().