In this paper we extend the Shapley-Shubik model to a two period financial economy and essentially address the question of the existence of an equilibrium. More precisely, we show the existence of nice equilibria, i.e. situation in which prices for both assets and commodities are strictly positive. Even if the general lines of the proof are largely influenced by the paper of Dubey-Shubik (1978)...

A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameter p and the agent's behavior x, reacts to perturbations in the first and second moments of p. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash eq...

In this paper, we respecify à la Cournot-Walras the mixed version of a model of noncooperative exchange, originally proposed by Lloyd S. Shapley. We first show that this respecification has a Cournot-Walras equilibrium allocation, which does not correspond to any CournotNash equilibrium of the mixed version of the original Shapley’s model. As this is due to the intrinsic two-stage nature of the...

The exploration of the phase diagram of a minimal model for barchan fields leads to the description of three distinct phases for the system: stationary, percolable, and unstable. In the stationary phase the system always reaches an out-of-equilibrium, fluctuating, stationary state, independent of its initial conditions. This state has a large and continuous range of dynamics, from dilute-where ...

‎in a real hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎in this paper‎, ‎we give a procedure which results‎ ‎in developing shehu's result to solve equilibrium prob...

In 1964 Shapley observed that a matrix has a saddle point in pure strategies whenever every its 2 × 2 submatrix has one. In contrast, a bimatrix game may have no pure strategy Nash equilibrium (NE) even when every 2 × 2 subgame has one. Nevertheless, Shapley’s claim can be extended to bimatrix games as follows. We partition all 2×2 bimatrix games into fifteen classes C = {c1, . . . , c15} depen...

A class of cooperative games arising from shortest path problems is deened. These shortest path games are shown to be totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; rst, by relating to the allocation rules in taxation and bankruptcy problems, second, by constructing an explicit rule that takes opportunity costs in...

This paper deals with the problem of existence of Berge and Berge–Nash equilibria. Abalo and Kostreva have proved existence theorems of Berge and Berge–Nash equilibria for S-equi-well-posed and (S, σ)equi-well-posed games, namely, Theorems 3.2–3.3 [Abalo, K.Y., Kostreva, M.M., 1996. Fixed Points, Nash Games and their Organization. Topological Methods in Nonlinear Analysis 8, 205–215.]. In this ...

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depen...