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Title of Journal: Econ Theory

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Abbravation: Economic Theory

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Springer-Verlag

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10.1007/978-3-662-09877-6_2

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1432-0479

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On the nonlattice structure of the equilibrium

Authors: Sunanda Roy Tarun Sabarwal
Publish Date: 2007/09/28
Volume: 37, Issue: 1, Pages: 161-169
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Abstract

This paper studies models where the optimal response functions under consideration are not increasing in endogenous variables and weakly increasing in exogenous parameters Such models include games with strategic substitutes and include cases where additionally some variables may be strategic complements The main result here is that the equilibrium set in such models is a nonempty complete lattice if and only if there is a unique equilibrium Indeed for a given parameter value a pair of distinct equilibria are never comparable Therefore with multiple equilibria some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium or that use the lattice structure of the equilibrium set do not apply to such models Moreover there are no ranked equilibria in such models Additionally the analysis here implies a new proof and a slight generalization of some existing results It is shown that when a parameter increases no new equilibrium is smaller than any old equilibrium In particular in nplayer games of strategic substitutes with realvalued action spaces symmetric equilibria increase with the parameter

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  2. Weighted approval voting
  3. A note on values for Markovian coalition processes
  4. Fixed-prize tournaments versus first-price auctions in innovation contests
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  15. Passive learning: a critique by example
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  23. Capital growth in a global warming model: will China and India sign a climate treaty?
  24. Noncooperative games, coupling constraints, and partial efficiency
  25. Equilibrium dynamics in discrete-time endogenous growth models with social constant returns
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