Strong Monotonicity Condition Research Articles

(s, S) Equilibria in Stochastic Games

We study a class of two-player continuous time stochastic games in which agents can make (costly) discrete or discontinuous changes in the variables that affect their payoffs. It is shown that in these games there are Markov-perfect equilibria of the two-sided (s, S) rule type. In such equilibria at a critical low state (resp. high state), player 1 (resp. 2) effects a discrete change in the environment. In some of these equilibria either or both players may be passive. On account of the presence of fixed costs (to discrete changes), the payoffs are non-convex and hence standard existence arguments fail. We prove that the best response map satisfies a strong monotonicity condition and use this to establish the existence of Markov-perfect equilibria. The first-best solution is also a two-sided (s, S) rule but the symmetric first-best solution has a wider (s, S) band than the symmetric Markov equilibrium. Journal of Economic Literature Classification Numbers: C73, D4.

What Strong Monotonicity Condition on Fourier Coefficients can make the Ratio || f - S n (f) || /E n (f) Bounded?

What Strong Monotonicity Condition on Fourier Coefficients can make the Ratio || f - S n (f) || /E n (f) Bounded?

What strong monotonicity condition on Fourier coefficients can make the ratio ‖𝑓-𝑆_{𝑛}(𝑓)‖/𝐸_{𝑛}(𝑓) be bounded?

Let { ϕ n } n = 1 ∞ \{ {\phi _n}\} _{n = 1}^\infty be a positive increasing sequence and ϕ n f ^ ( n ) {\phi _n}\hat f(n) decrease. We ask what exact conditions on { ϕ n } \{ {\phi _n}\} make ‖ f − S n ( f ) ‖ / E n ( f ) \left \| {f - {S_n}(f)} \right \|/{E_n}(f) bounded? The present paper will give a complete answer to it.

Strongly order preserving semiflows generated by functional differential equations

The aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems, due to the authors [ 12, 13 J, to certain systems of functional differential equations (FDE’s) which do not enjoy the quasimonotone property considered by one of us in [9]. The present work extends our previous results in this direction for scalar equations in [ 111 to systems. In the fundamental paper [S], M. W. Hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space X tend to the set E of equilibria. Employing ideas of Hirsch and of H. Matano [7], the authors have extended the theory to obtain some improvements in the results of Hirsch and Matano under Matano’s weaker assumption that the semiflow is strongly order preserving. Recently, in [13], we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium. These conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium. P. PoliCik [S] has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties. In this paper, WC apply the convergence results developed in [ 131 to nonquasimonotone FDE’s. In this Introduction, WC briefly review the application of monotone dynamical systems theory to FDE’s enjoying the quasimonotone property. This research appeared in [9, 133. Then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property (M,) holds. Some simple examples are given which

Measuring Welfare, Poverty and Inequality

A class of poverty measures is identified, the members of which satisfy strong monotonicity and transfer conditions. These measures are closely related to indices of income inequality based on the notion of a mean-equivalent income. A restriction on the class of admissible measures allows poverty to be interpreted in terms of the loss in mean-equivalent income resulting from the fact that some people are poor. Copyright 1987 by Royal Economic Society.

Continuity of monotone functions

Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. Any monotone pointwise continuous function is uniformly continuous. Continuous inverse functions are also obtained. The methods used are in accord with the principles of Bishop's Foundations of Constructive Analysis, 1967.