On the Role of Non-equilibrium Focal Points as Coordination Devices

Considering a pure coordination game with a large number of equivalent equilibria, we argue, first, that a focal point that is itself not a Nash equilibrium and is Pareto dominated by all Nash equilibria, may attract the players' choices. Second, we argue that such a non-equilibrium focal point may act as an equilibrium selection device that the players use to coordinate on a closely related small subset of Nash equilibria. We present theoretical as well as experimental support for these two new roles of focal points as coordination devices.Coordination game, Focal point, Nash equilibrium, Equilibrium selection, Coordination device

On the role of non-equilibrium focal points as coordination devices

Considering a pure coordination game with a large number of equivalent equilibria, we argue, first, that a focal point that is itself not a Nash equilibrium and is Pareto dominated by all Nash equilibria, may attract the players' choices. Second, we argue that such a non-equilibrium focal point may act as an equilibrium selection device that the players use to coordinate on a closely related small subset of Nash equilibria. We present theoretical as well as experimental support for these two new roles of focal points as coordination devices.Coordination game, Focal point, Nash equilibrium, Equilibrium selection, Coordination device, LeeX

Some preliminary remarks on the relevance of topological essentiality in general equilibrium theory and game theory

We define an algebro-topological concept of essential map and we use it to prove several results in the theory of general equilibrium and nash equilibrium refinement.fixed point theory, game theory, equilibrium theory, stability of Nash equilibrium, multiplicity of equilibria

Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints

An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation

Competitive Spectrum Management with Incomplete Information

This paper studies an interference interaction (game) between selfish and independent wireless communication systems in the same frequency band. Each system (player) has incomplete information about the other player's channel conditions. A trivial Nash equilibrium point in this game is where players mutually full spread (FS) their transmit spectrum and interfere with each other. This point may lead to poor spectrum utilization from a global network point of view and even for each user individually. In this paper, we provide a closed form expression for a non pure-FS epsilon-Nash equilibrium point; i.e., an equilibrium point where players choose FDM for some channel realizations and FS for the others. We show that operating in this non pure-FS epsilon-Nash equilibrium point increases each user's throughput and therefore improves the spectrum utilization, and demonstrate that this performance gain can be substantial. Finally, important insights are provided into the behaviour of selfish and rational wireless users as a function of the channel parameters such as fading probabilities, the interference-to-signal ratio

An answer to a question of herings et al

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium existence in discontinuous games.fixed point theorem; discontinuity; nash equilibrium

Approximate social nash equilibria and applications

In this paper, a concept of approximate social Nash equilibria is considered and an existence result is given when the strategic spaces of the players are not compact. These have been obtained using an approximate fixed point theorem. As an application of the existence of such approximate social Nash equilibria, sufficient conditions for the existence of a suitable approximate walrasian equilibrium in finite economies are obtained. Among others things, it is shown that the approximate walrasian equilibrium here considered is approximatively weakly efficient.Abstract economy, approximate social Nash equilibrium, finite economy, approximate walrasian equilibrium, approximate fixed point theorems.

Partial Information Differential Games for Mean-Field SDEs

This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum principle for Nash equilibrium points. Subsequently, under additional assumptions, verification theorem for Nash equilibrium points is also derived. Finally, as an application, a linear quadratic example is discussed. The unique Nash equilibrium point is represented in a feedback form of not only the optimal filtering but also expected value of the system state, throughout the solutions of the Riccati equations.Comment: 7 page