A non-robustness in the order structure of the equilibrium set in lattice games
Andrew Monaco and
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Andrew Monaco: Department of Economics, University of Kansas
No 201004, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics
The order and lattice structure of the equilibrium set in games with strategic complements do not survive a minimal introduction of strategic substitutes: in a lattice game in which all-but-one players exhibit strategic complements (with one player exhibiting strict strategic complements), and the remaining player exhibits strict strategic substitutes, no two equilibria are comparable. More generally, in a lattice game, if either (1) just one player has strict strategic complements and another player has strict strategic substitutes, or (2) just one player has strict strategic substitutes and has singleton-valued best-responses, then without any restrictions on the strategic interaction among the other players, no two equilibria are comparable. In such cases, the equilibrium set is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Moreover, in such cases, with linearly ordered strategy spaces, the game has at most one symmetric equilibrium. Several examples are presented.
Keywords: Lattice games; strategic complements; strategic substitutes; equilibrium set (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2010-08, Revised 2011-08
New Economics Papers: this item is included in nep-gth
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