<scp>An Example of Nonexistence of Three‐Community Equilibrium</scp>

Gomberg, Andrei

doi:10.1111/j.1467-9779.2005.00204.x

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%

Coalitions

Humphreys

2008

Annu. Rev. Polit. Sci.

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The game theoretic study of coalitions focuses on settings in which commitment technologies are available to allow groups to coordinate their actions. Analyses of such settings focus on two questions. First, what are the implications of the ability to make commitments and form coalitions for how games are played? Second, given that coalitions can form, which coalitions should we expect to see forming? I examine classic cooperative and new noncooperative game theoretic approaches to answering these questions. Classic approaches have focused especially on the first question and have produced powerful results. However, these approaches suffer from a number of weaknesses. New work attempts to address these shortcomings by modeling coalition formation as an explicitly noncooperative process. This new research reintroduces the problem of coalitional instability characteristic of cooperative approaches, but in a dynamic setting. Although in some settings, classic solutions are recovered, in others this new work shows that outcomes are highly sensitive, not only to bargaining protocols, but also to the forms of commitment that can be externally enforced. This point of variation is largely ignored in empirical research on coalition formation. I close by describing new agendas in coalitional analysis that are being opened up by this new approach.

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Section: Simultaneous Gamesmentioning

confidence: 99%

Coalitions

Humphreys

2008

Annu. Rev. Polit. Sci.

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“…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%

Endogenous platforms: the case of many parties

2006

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We analyze existence of equilibrium in a one-dimensional model of endogenous party platforms and more than two parties. The platforms proposed by parties depend on their membership composition. The policy implemented is a function of the different proposals and the vote distribution among such proposals. It is shown that if voters are sincere there is always an equilibrium regardless of the number of parties. In the case of strategic voting behavior, existence of equilibrium can be shown provided a subadditivity condition on the outcome function holds.

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An Example of Nonexistence of Three‐Community Equilibrium

Cited by 2 publications

References 3 publications

Coalitions

Coalitions

Endogenous platforms: the case of many parties

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