This paper demonstrates the Vickrey auction has a Nash equilibrium in the core. Generally, the dominant-strategy-equilibrium outcome of the Vickrey auction is not located in the core. However, a particular profile of truncation strategies is a Nash equilibrium, and it implements an outcome in the bidderoptimal core. The specified strategy profile is identical to that in core-selecting auctions ...

A game-theoretic model is presented to study the management of transmission power in a wireless data network. We propose a power game for a multiuser multicarrier setting where all the users are assumed to transmit at equal rate. At equilibrium, each user is shown to transmit over a single carrier, as in [Mehskati et al., 2006]. We derive the necessary conditions on the path gains when the Nash...

The main contribution of this thesis is a new solution concept for symmetric games (of complete information in strategic form), the exchangeable equilibrium. This is an intermediate notion between symmetric Nash and symmetric correlated equilibrium. While a variety of weaker solution concepts than correlated equilibrium and a variety of refinements of Nash equilibrium are known, there is little...

This paper addresses the problem of learning a Nash equilibrium in γ-discounted multiplayer general-sum Markov Games (MGs) in a batch setting. As the number of players increases in MG, the agents may either collaborate or team apart to increase their final rewards. One solution to address this problem is to look for a Nash equilibrium. Although, several techniques were found for the subcase of ...

We show that in zero-sum polymatrix games, a multiplayer generalization of two-person zerosum games, Nash equilibria can be found efficiently with linear programming. We also show that the set of coarse correlated equilibria collapses to the set of Nash equilibria. In contrast, other important properties of two-person zero-sum games are not preserved: Nash equilibrium payoffs need not be unique...

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals’ preferences over A, where the subset is interpreted as the set of ‘‘welfare optima’’. A game form (or ‘‘mechanism’’) implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game for...

Non-cooperative game theory has been tightly combined with Computational Methods, in which the Nash Equilibrium (NE) is undoubtedly the most important solution concept. While players face several Nash Equilibriums, their most pragmatic strategy may not be the most optimal one, but one they prefer for other reasons. Players may choose a sub-optimal strategy instead of a more optimal but more com...

The concept of Nash equilibriumhas become central to the theory and practice of economics. In these remarks I would like to reflect a bit on why this has come to happen. Interestingly enough the founding treatise of the theory of games (The Theory of Games and Economic Behaviour, published in 1944 and authored by a mathematician J. von Neumann and an economist O. Morgernstern) had, for practica...

A crime has been committed for which two prisoners are held incommunicado. The district attorney is assigned to question the prisoners. He designs the following incentive structure to induce the prisoners to talk. If neither prisoner talks, both prisoners automatically receive mild sentences (payoff 4). But if exactly one prisoner squeals on the other, the squealer is let off scot free (payoff ...

We study extreme Nash equilibria in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel identical links, to control the routing of its own assigned traffic. In a Nash equilibrium, each user selfishly routes its traffic on those links that minimize its expected latency cost. T...