In this paper, we consider the problem of general equilibrium in a finite-dimensional space on a closed convex set. For solving this problem, we developed an interior proximal point algorithm with φ-divergence. Under reasonable assumptions, we prove that the sequence generated by the algorithm converges to a solution of the Equilibrium Problem, when the regularization parameters are bounded.

and Applied Analysis 3 The Nash equilibrium E is located at the intersection of the two reaction curves which represent the locus of points of vanishingmarginal profits in (5). In the following, we assume that (10) is satisfied, so the Nash equilibrium E exists. The study of the local stability of equilibrium points is based on the eigenvalues of the Jacobian matrix of the (6): J = [ 1 + 11 1 (...

The fundamental question as to whether thin intergranular films can adopt an equilibrium thickness in polycrystalline ceramics is addressed. Two continuum approaches are presented, one based on interfacial energies and the other on the force balance normal to the boundary. These indicate that there will exist a stable thickness for the intergranular film and that it will be of the order of 1 nm...

We investigate a class of reinforcement learning dynamics in which players adjust their strategies based on their actions’ cumulative payoffs over time – specifically, by playing mixed strategies that maximize their expected cumulative payoff minus a strongly convex, regularizing penalty term. In contrast to the class of penalty functions used to define smooth best responses in models of stocha...

In this note we study a class of 2× 2 Pólya-Eggenberger urn models, with ball transition matrix given by M = ( 0 −b c −d ) , for arbitrary parameters b, c ∈ N, assuming the balancing condition d = c+ b. This urn model serves as a stochastic model in biology describing cannibalistic behavior of populations. The special case b = c = 1 and d = 2 was studied by Pittel [16] using asymptotic approxim...

This paper presents a participation game experiment to study the impact of uncertainty and costly political participation on the incidence of reform. Fernandez and Rodrik (1991) show that uncertainty about who will ultimately gain or lose as a result of a reform can prevent its adoption. We introduce intra-group conflict into this framework by incorporating costly political participation, which...

In this paper I show that, just as with Nash Equilibrium, there are sparse conditions, not involving common knowledge of rationality, that lead to (correlated) rationalizability. The basic observation is that, if the actual world belongs to a set of states where the set Z of action pro…les is played, each player knows her own payo¤, everyone is rational and it is mutual knowledge that the actio...

A class of nondegenerate n n bimatrix games is presented that have asymptotically more than 2:414 n = p n Nash equilibria. These are more equilibria than the 2 n ? 1 equilibria of the game where both players have the identity matrix as payoo matrix. This refutes the Quint{Shubik conjecture that the latter number is an upper bound on the number of equilibria of nondegenerate n n games. The rst c...

This chapter is a simple, rigorous, practically-oriented exposition of computable general equilibrium (CGE) modeling. The general algebraic framework of a CGE model is developed from microeconomic fundamentals, and employed to illustrate (i) how a model may be calibrated using the economic data in a social accounting matrix, (ii) how the resulting system of numerical equations may be solved for...

The rapid, degenerate 1,2-hydride shift in 2,3-dimethyl-2-butyl cation in stable solution in SbF5/ S02C1F was perturbed by deuterium and 13C leading to splittings observed by 13C NMR spectros­ copy over a range of temperatures. Accurate values for equilibrium isotope effects were obtained from these data. Theoretical calculations of the equilibrium isotope effects were performed using the Gauss...