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Games 2013, 4(4), 561-583; doi:10.3390/g4040561

Population Games, Stable Games, and Passivity

School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA 30332, USA
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Received: 4 April 2013 / Revised: 3 September 2013 / Accepted: 26 September 2013 / Published: 7 October 2013
(This article belongs to the Special Issue Advances in Evolutionary Game Theory and Applications)
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Abstract

The class of “stable games”, introduced by Hofbauer and Sandholm in 2009, has the attractive property of admitting global convergence to equilibria under many evolutionary dynamics. We show that stable games can be identified as a special case of the feedback-system-theoretic notion of a “passive” dynamical system. Motivated by this observation, we develop a notion of passivity for evolutionary dynamics that complements the definition of the class of stable games. Since interconnections of passive dynamical systems exhibit stable behavior, we can make conclusions about passive evolutionary dynamics coupled with stable games. We show how established evolutionary dynamics qualify as passive dynamical systems. Moreover, we exploit the flexibility of the definition of passive dynamical systems to analyze generalizations of stable games and evolutionary dynamics that include forecasting heuristics as well as certain games with memory.
Keywords: population games; evolutionary games; passivity theory population games; evolutionary games; passivity theory
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Fox, M.J.; Shamma, J.S. Population Games, Stable Games, and Passivity. Games 2013, 4, 561-583.

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