Setting Cournot Versus Lyapunov Games Stability Conditions and Equilibrium Point Properties

Julio B. Clempner ()
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Julio B. Clempner: Center for Economics, Management and Social Research, National Polytechnic Institute, Lauro Aguirre 120, Col. Agricultura, Del. Miguel Hidalgo, Mexico City, 11360, Mexico

International Game Theory Review (IGTR), 2015, vol. 17, issue 04, 1-10

Abstract: In potential games, the best-reply dynamics results in the existence of a cost function such that each player's best-reply set equals the set of minimizers of the potential given by the opponents' strategies. The study of sequential best-reply dynamics dates back to Cournot and, an equilibrium point which is stable under the game's best-reply dynamics is commonly said to be Cournot stable. However, it is exactly the best-reply behavior that we obtain using the Lyapunov notion of stability in game theory. In addition, Lyapunov theory presents several advantages. In this paper, we show that the stability conditions and the equilibrium point properties of Cournot and Lyapunov meet in potential games.

Keywords: Cournot; Lyapunov; potential games; dominance-solvable games; routing games; shortest-path; best-reply; 22E46; 53C35; 57S20 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219198915500115

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