On coalition-proof Nash equilibria in common agency games

Article Abstract:

An analysis investigated three issues regarding the structure of the set of coalition-proof Nash equilibria in common agency games. The first concerns the use of varying conceptualizations of a coalitional deviation, namely strict deviation and weak deviation. The second issue focuses on the conditions where some or all the coalition-proof Nash equilibria of a common agency game are strong as discussed by Aumann (1959). Finally, this study examines the link between the set of coalition-proof Nash equilibria and the set of Pareto undominated Nash equilibria.

Analysis, Equilibrium (Economics), Agency (Law)

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Equilibria in a model with partial rivalry

Article Abstract:

Three assumptions are needed to be satisfied by individuals' preferences for a non-cooperative game with a finite set of players and common finite strategy sets to yield a strong Nash equilibrium in pure strategies. The anonymous assumption, the independence of irrelevant choices assumption, and the partial rivalry assumption yield the existence of a pure strategy strong Nash equilibrium and the equivalence of the sets of Nash and strong Nash equilibria in pure strategies.

Models

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A theorem on symmetric two-player zero-sum games

Article Abstract:

There is the existence of an equilibrium in mixed strategies when all off-diagonal entries of the pay-off matrix of finite and symmetric two-player zero-sum games are odd integers. The most extensive form of completeness is the zero-sum game.

Competition (Economics)

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