On Equilibrium Refinement in Supermodular Games
We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategies. We illustrate that, in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games, perfect equilibria may involve play of actions in the interior of the set of weakly dominated actions. We prove that when the set of undominated actions is a sublattice, supermodular games satisfying sequential better-reply security possess pure strategy perfect equilibria that can be obtained as limits of undominated actions.
|Date of creation:||26 Dec 2012|
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- Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, Open Access Journal, vol. 2(3), pages 1-22, July.
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- Oriol Carbonell-Nicolau & Richard McLean, 2013.
"Approximation results for discontinuous games with an application to equilibrium refinement,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 1-26, September.
- Oriol Carbonell-Nicolau & Richard McLean, 2011. "Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement," Departmental Working Papers 201128, Rutgers University, Department of Economics.
- Oriol Carbonell-Nicolau & Richard McLean, 2012. "Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement," Departmental Working Papers 201206, Rutgers University, Department of Economics.
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- Carbonell-Nicolau, Oriol, 2014. "On essential, (strictly) perfect equilibria," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 157-162.
- Oriol Carbonell-Nicolau, 2012. "On Essential, (Strictly) Perfect Equilibria," Departmental Working Papers 201208, Rutgers University, Department of Economics.
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- Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
- Oriol Carbonell-Nicolau, 2011. "On Equilibrium Refinement For Discontinuous Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 269-280.
- Salonen, Hannu, 1996. "On the Existence of Undominated Nash Equilibria in Normal Form Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 208-219, June.
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