A game in strategic form does not always have a Nash equilibrium in which each player deterministically chooses one of his strategies. However, players may instead randomly select from among these pure strategies with certain probabilities. Randomizing one’s own choice in this way is called a mixed strategy. A profile of mixed strategies is called a mixed equilibrium if no player can gain on av...

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 ...

Nash [13] introduced the concept of Nash equilibria in non-cooperative games and proved that any game possesses at least one such equilibrium. A well-known algorithm for computing a Nash equilibrium of a 2-player game is the Lemke-Howson algorithm [11], however it has exponential worst-case running time in the number of available pure strategies [15]. Recently, Daskalakis et al [4] showed that ...

In this technical report, we generalize the betweenness definition in Bounded Budget Betweenness Centrality Game (called B3C game) introduced in [1] to only count shortest paths with a length limit `. We denote this game `-B3C game. We prove that the hardness results in [1] about nonuniform game still hold in this generalized version. In Section 2, we provide the detailed definition of the `-B3...

representing the players act as rational players, i.e. they act to maximise their expected utility in each match of a game, and if such agents play k matches of the game they will converge in playing one of the Nash Equilibria of the game. SALENE can be conceived as a heuristic and efficient method to compute at least one Nash Equilibria in a non-cooperative game represented in its normal form.

The comparative dynamics of locally differentiable feedback Nash equilibria are derived for the ubiquitous class of autonomous and exponentially discounted infinite horizon differential games. The resulting refutable implications are intrinsic to the said class of differential games, and thus form their basic, empirically testable, properties. Their relationship with extant results in the optim...

Motivated by the study of linear quadratic differential games, we introduce a new class of nonsymmetric algebraic Riccati equations. It is shown that every equation in this class has a unique stabilizing solution, which is the solution required to find the open-loop Nash equilibrium for the differential game. We show that the doubling algorithm can be used to find this solution efficiently. The...

As far as Integrated Cellular networks are concerned, a significant issue that service providers are faced with is with regard to bandwidth (Resource or Service) allocations for different service classes when it pertains to the balancing profit and service quality simultaneously. The challenge increases when there a dynamic competition emanates between the service provider and its users. This p...

This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the definition of the Nash-stable core and we analyze the conditions for having a non-empty Nash-stable core. More precisely, we prove that using relaxed efficiency in ut...

The dual reduction process, introduced by Myerson, allows to reduce a finite game into a smaller dimensional game such that any equilibrium of the reduced game is an equilibrium of the original game. This holds both for Nash equilibrium and correlated equilibrium. We present examples of applications of dual reduction and argue that this is a useful tool to study Nash equilibria and correlated e...