2005
DOI: 10.1111/j.1467-9779.2005.00204.x
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An Example of Nonexistence of Three‐Community Equilibrium

Abstract: In this paper I provide an example of sorting equilibrium nonexistence in a three-community model of the type introduced in Caplin and Nalebuff (1997; Journal of Economic Theory 72, 306-342). With two communities, such an example has been shown to exist only when the dimension of the policy space is even. It turns out, however, that with three communities existence may fail regardless of whether the policy space dimension is odd or even. This suggests that the original odd/even dichotomy can, at least in part,… Show more

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Cited by 2 publications
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“…Gomberg (2004) has also found sufficient conditions for existence for an arbitrary number of dimensions. However, Gomberg (2005) shows that without further constraints on P j or u i , an equilibrium can fail to exist in any number of dimensions if there are just three communities.…”
Section: Simultaneous Gamesmentioning
confidence: 99%
“…Gomberg (2004) has also found sufficient conditions for existence for an arbitrary number of dimensions. However, Gomberg (2005) shows that without further constraints on P j or u i , an equilibrium can fail to exist in any number of dimensions if there are just three communities.…”
Section: Simultaneous Gamesmentioning
confidence: 99%
“…This result follows from the theoretical development of Caplin and Nalebuff (1997) and Gomberg (2004), which showed that conditions necessary to ensure existence of pluralistic equilibria in twojurisdiction (including two-party) models are sensitive to the parity of policy space dimension. The apparently paradoxical result is somewhat clarified by the example in Gomberg (2005), which suggests a more complex interaction between the number of parties and the dimensionality of the policy space.…”
Section: Introductionmentioning
confidence: 99%