Variations on the Theme of Conning in Mathematical Economics

The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard xed point theorems in orthodox mathematical economics

Economic system dynamics

We provide the reader with a qualitative summary of the main ideas from econophysics and finance theory, starting with a thorough criticism of the standard ideas taught in typical economics textbooks. The emphasis is on the Galilean or physicists' approach to market synamics, as opposed to the standard nonempirical postulatory one.Utility; equilibrium; supply and demand curves; business cycles; market dynamics

Mean Field Equilibrium in Dynamic Games with Complementarities

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical distribution of the states of other players. Such games can be used to model a diverse set of applications, including network security models, recommender systems, and dynamic search in markets. Stochastic games are generally difficult to analyze, and these difficulties are only exacerbated when the number of players is large (as might be the case in the preceding examples). We consider an approximation methodology called mean field equilibrium to study these games. In such an equilibrium, each player reacts to only the long run average state of other players. We find necessary conditions for the existence of a mean field equilibrium in such games. Furthermore, as a simple consequence of this existence theorem, we obtain several natural monotonicity properties. We show that there exist a "largest" and a "smallest" equilibrium among all those where the equilibrium strategy used by a player is nondecreasing, and we also show that players converge to each of these equilibria via natural myopic learning dynamics; as we argue, these dynamics are more reasonable than the standard best response dynamics. We also provide sensitivity results, where we quantify how the equilibria of such games move in response to changes in parameters of the game (e.g., the introduction of incentives to players).Comment: 56 pages, 5 figure

Response to worrying trends in econophysics

This article is a response to the recent “Worrying Trends in Econophysics” critique written by four respected theoretical economists [1]. Two of the four have written books and papers that provide very useful critical analyses of the shortcomings of the standard textbook economic model, neo-classical economic theory [2,3] and have even endorsed my book [4]. Largely, their new paper reflects criticism that I have long made [4,5,6,7,] and that our group as a whole has more recently made [8]. But I differ with the authors on some of their criticism, and partly with their proposed remedy.General equilibrium; uncertainty; conservation laws; money nonconservation; nonintegrability of dynamical systems; financial markets; stochastic processes