Population Games, Stable Games, and Passivity

Michael J. Fox and Jeff S. Shamma
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Michael J. Fox: School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA 30332, USA
Jeff S. Shamma: School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA 30332, USA

Games, 2013, vol. 4, issue 4, 1-23

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 (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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