We present explicit examples to show that the ‘compatibility criterion’ [recently obtained by us towards providing equilibrium configurations compatible with the structure of general relativity] which states that: for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), whereM is the total mass andR is the radius of the config...

In this paper, we study necessary optimality conditions for nonsmooth mathematical programs with equilibrium constraints. We first show that, unlike the smooth case, the Mathematical Program with Equilibrium Constraints Linear Independent Constraint Qualification is not a constraint qualification for the strong stationary condition when the objective function is nonsmooth. We argue that the str...

This paper presents a location–price equilibrium problem on a tree. A sufficient condition for having a Nash equilibrium in a spatial competition model that incorporates price, transport, and externality costs is given. This condition implies both competitors are located at the same point, a vertex that is the unique median of the tree. However, this is not an equilibrium necessary condition. S...

In this paper, we present a contest success function (CSF), which is homogeneous of degree zero and in which the probability of winning the prize depends on the relative difference of efforts. In a simultaneous game with two players, we present a necessary and sufficient condition for the existence of a pure strategy Nash equilibrium. This equilibrium is unique and interior. This condition does...

The paper explores a model of equilibrium selection in coordination games, where agents from an infinite population stochastically adjust their strategies to changes in their local environment. Instead of playing perturbed best-response, it is assumed that agents follow a rule of `switching to better strategies with higher probability'. This behavioral rule is related to bounded-rationality mod...

In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equili...