We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we model as a mathematical program with equilibrium constraints, MPEC. The corresponding game is an example of an equilibrium problem with equilibrium constraints, EPEC. We establish sufficient conditions ...

We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any co...

We survey recent joint work with Christos Papadimitriou and Paul Goldberg on the computational complexity of Nash equilibria. We show that finding a Nash equilibrium in normal form games is computationally intractable, but in an unusual way. It does belong to the class NP; but Nash’s theorem, showing that a Nash equilibrium always exists, makes the possibility that it is also NP-complete rather...

in this paper, a new approach based on game theory has been proposed to multi responses problem optimization. game theory is a useful tool for decision making in the conflict of interests between intelligent players in order to select the best joint strategy for them through selecting the best joint desirability. present research uses the game theory approach via definition of each response as ...

Reinhard Selten and Thorsten Chmura (2008) recently reported laboratory results for completely mixed 2 × 2 games used to compare Nash equilibrium with four other stationary concepts: quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium. We reanalyze their data, correct some errors, and find that Nash clearly fits worst while the...

We study a spatial model of party formation in which the set of agendas is the unit circle. We characterize the sets of pure-strategy Nash equilibria under the plurality and proportional rules. In both rules, multiple configurations of parties are possible in Nash equilibrium. We refine our predictions using a new notion called “defection-proof” Nash equilibrium. Under the plurality rule, only ...

Because players whose preferences violate the von Neumann-Morgenstern independence axiom may be unwilling to randomize as mixed-strategy Nash equilibrium would require, a Nash equilibrium may not exist without independence. This paper generalizes Nash’s definition of equilibrium, retaining its rationalexpectations spirit but relaxing its requirement that a player must bear as much uncertainty a...

It is known that a Lindahl equilibrium is not necessarily Pareto-superior to the non-cooperative Cournot-Nash outcome. This paper derives conditions under which the Lindahl Paretodominates the Cournot-Nash solution. We show that all are better off in the Lindahl equilibrium as compared to the Cournot-Nash equilibrium when the exogenously given income distribution is not skewed too much or the n...

We study the structure of the set of equilibrium payoffs in finite games, both for Nash equilibrium and correlated equilibrium. A nonempty subset of R is shown to be the set of Nash equilibrium payoffs of a bimatrix game if and only if it is a finite union of rectangles. Furthermore, we show that for any nonempty finite union of rectangles U and any polytope P ⊂ R containing U , there exists a ...

A Nash equilibrium of a routing network represents a stable state of the network where no user finds it beneficial to unilaterally deviate from its routing strategy. In this work, we investigate the structure of such equilibria within the context of a certain game that models selfish routing for a set of n users each shipping its traffic over a network consisting of m parallel links. In particu...