Optimality and Natural Selection in Markets

Evolutionary arguments are often used to justify the fundamental behavioral postulates of competive equilibrium. Economists such as Milton Friedman have argued that natural selection favors profit maximizing firms over firms engaging in other behaviors. Consequently, producer efficiency, and therefore Pareto efficiency, are justified on evolutionary grounds. We examine these claims in an evolutionary general equilibrium model. If the economic environment were held constant, profitable firms would grow and unprofitable firms would shrink. In the general equilibrium model, prices change as factor demands and output supply evolves. Without capital markets, when firms can grow only through retained earnings, our model verifies Friedman's claim that natural selection favors profit maximization. But we show through examples that this does not imply that equilibrium allocations converge over time to efficient allocations. Consequently, Koopmans critique of Friedman is correct. When capital markets are added, and firms grow by attracting investment, Friedman's claim may fail. In either model the long-run outcomes of evolutionary market models are not well described by conventional General Equilibrium analysis with profit maximizing firms.evolution, natural selection, equilibrium, incomplete markets

Lexiocographic Refinements of Nash Equilibrium

The fundamental idea of game theory is that each player in the game acts in his own best interests, given the actions of the other players. Nash equilibrium makes this idea precise by defining each player's best interests as the maximization of his expected utility, where the expectation is taken with respect to the (mixed) strategies played by the other players. New equilibrium concepts and refinements of old equilibrium concepts should adhere to this fundamental idea of self-interested action. This is to say, they must be justified in decision-theoretic terms. A notion of "self-interest" must be defined by specifying the preferences of the players, and equilibrium must be defined with respect to these preferences. This paper characterizes preferences that justify perfect and proper equilibrium as the outcome of rational, self-interested behavior.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100637/1/ECON113.pd

Implementation of Walrasian Expectations Equilibria

In an exchange economy with differentially informed traders, Non-exclusivity of information (NEI) is the condition that each trader's private information be perfectly predictable by an outside observer who has observed the private information of all other traders. NEI is one of a set of conditions which, taken together, are sufficient for the implementability of fully revealing expectations equilibria. Here we show that this condition is in fact necessary for the weak implementation of a much broader class of Walrasian equilibria, herein called expectations equilibria.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100640/1/ECON116.pd

New techniques for the study of stochastic equilibrium processes

This paper develops the notion of transition correspondences; the set-valued analog of transition probabilities. A generalization of the Feller property for transition probabilities is shown to imply the existence of a selection from the transition correspondence having a stationary equilibrium. These techniques are applied to the existence problem for Markov temporary equilibrium processes in place of assumptions about the existence of continuous selections from the equilibrium price correspondence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24087/1/0000343.pd

Poverty traps in Markov models of the evolution of wealth

Poverty trap models are dynamical systems with more than one attractor. Similar dynamical systems arise in optimal growth and macroeconomic models. These systems are often studied empirically by ad hoc methods relying on intuition from deterministic systems, such as looking for multiple peaks in the stationary distribution of states. We develop Markov wealth processes in which parents' investments in children stochastically determine children's wealth, and consequently their own investment choices. We show that, relative to a zero-shock process, some of the multiple attractors are less fragile than are others, and that their presence dominates the stationary behavior of the wealth distribution. Typically, mass accumulates around attractors. An only slightly stochastically perturbed deterministic system will have an invariant distribution which puts close to probability 1 on a single steady state rather than having significant mass distributed among several attractors. We also examine how policy effects the shape of the invariant distribution

Rational expectations equilibrium: An alternative approach

We study a dynamic market process in which traders condition their beliefs about payoff-relevant parameters on past endogenously generated market data and current exogenous data. We say that a market process is informative if the beliefs of traders who receive only endogenously generated market data converge almost surely to the true parameter value. Our main result is that under standard regularity hypotheses, the generic market process is informative. We define an equilibrium as the limit points of the market process.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24673/1/0000092.pd

Learning to be rational

We study the dynamical system of expectations generated by a simple general equilibrium model of an exchange economy in which each agent considers a finite collection of models, each of which specifies a relationship between payoff-relevant information and equilibrium prices. One of the models under consideration is a correct description of the rational expectations equilibrium. We find that under a Bayesian type of learning process the rational expectations equilibrium is locally stable, but that nonrational equilibria may also be locally stable.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24022/1/0000271.pd

Characterization of optimal plans for stochastic dynamic programs

This paper provides general techniques for the characterization of optimal plans resulting from stochastic dynamic programming. We show that under standard assumptions the optimal plans in both finite and infinite horizon problems can be obtained by an application of the Implicit Function Theorem to first order conditions. Further, we show that under certain checkable conditions, optimal plans and value functions are p-times differentiable for any integer p [ges] 0. Finally, we apply our technique to obtain a Cp plan and value function in a one sector infinite horizon growth problem under uncertainty.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23779/1/0000017.pd

Uniqueness of Nash equilibrium in private provision of public goods : An improved proof

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29701/1/0000033.pd