Mark Walker

The free rider problem: Experimental evidence

Concluding remarksWe have described a number of ‘invalidating factors,’ any one of which, if present, could account for the weakness or absence of the free rider problem in the voluntary provision of a public good. When any of these factors is present, the free rider phenomenon is not necessarily an implication of economic theory. These invalidatingg factors have been used as a guide in the construction of an experiment which, by avoiding all such factors, should exhibit the free rider phenomenon. The results of performing the experiment indicate that the free rider hypothesis should not be rejected. The contrast between this result and previous experimental results indicates that some of the factors we have identified will be important in attempting to explain the presence or absence of the free rider phenomenon in any particular situation in which a public good is to be financed by voluntary means.

On the Generic Nonoptimality of Dominant-Strategy Allocation Mechanisms: A General Theorem That Includes Pure Exchange Economies

It is shown that if an economys participants cannot be separated into groups across which there are no potentially conflicting interests--i.e., if the economy is indecomposable--then every continuous truth-dominant allocation mechanism will attain nonoptimal allocations on an open dense set of preference profiles. Classical Edgeworth-box exchange economies (economies with no externalities and no production, but with arbitrary numbers of consumers and goods), as well as economies with public goods and economies with other kinds of externalities, are all shown via simple arguments to be indecomposable. The results are extended to cover nonrevelation mechanisms. Copyright 1990 by The Econometric Society.

Learning to play Cournot duopoly strategies

Abstract The paper reports results from experiments designed to determine whether subjects can learn to play Cournot duopoly strategies and whether their out-of-equilibrium play is consistent with the predictions of learning models. The experiments include duopolies with constant and with decreasing marginal costs, and with theoretically stable and unstable equilibria. After a few periods, subjects do play stable interior equilibria but they do not play stable boundary equilibria nor unstable interior equilibria. Subjects out-of-equilibrium play is inconsistent with the predictions of the learning models.

On the Informational Size of Message Spaces

Abstract In a recent paper, Mount and Reiter established that, in a certain sense, the competitive mechanism is an “informationally most efficient” procedure for allocating resources. This result, of course, depends upon the way in which we characterize the notion of informational efficiency. Several alternative characterizations, and the relationships among them, are given here, and it is shown under which characterizations the above result is true, and under which it is false. It is shown that there is an intuitively appealing “best” characterization for which it is true.

Hide and seek in Arizona

Laboratory subjects repeatedly played one of two variations of a simple two-person zero-sum game of “hide and seek”. Three puzzling departures from the prescriptions of equilibrium theory are found in the data: an asymmetry related to the player’s role in the game; an asymmetry across the game variations; and positive serial correlation in subjects’ play. Possible explanations for these departures are considered.

Maximal elements of weakly continuous relations

Abstract A weaker than usual continuity property is defined for binary relations. Relations that have this property, along with certain transitivity properties, are shown to have maximal elements on compact sets. The results cover “interval orders,” the kind of relations that often characterize choice situations in which similar alternatives are indistinguishable.

An Experiment to Evaluate Bayesian Learning of Nash Equilibrium Play

Some recent theoretical approaches to the question of how players might converge over time to a Nash equilibrium have assumed that the players update their beliefs about other players via Bayes Rule. Jordan has shown in a Bayesian model of this kind that play will (theoretically) always converge to a complete-information Nash equilibrium, even though individual players will not generally attain complete information. We report on an experiment designed to evaluate the empirical implications of Jordans model. A finite version of the model is constructed which generates unique predictions of subjects choices in nearly all periods. The experimental data reveals that the theory does reasonably well at predicting the equilbria that subjects eventually play, even when there are multiple equilibria. The results thus suggest that Jordans Bayesian model can provide an empirically effective solution to the equilibrium selection problem when the players have beliefs with finite support. However, the models predictions about the path of play over time are not consisitent with the experimental data.

A Generalization of the Maximum Theorem

The Maximum Theorem and its generalizations have become one of the most useful tools in economic theory. The theorem first stated and proved, to the best of my knowledge, by Claude Berge [1963, p. 116] gives conditions under which a maximizing correspondence (a correspondence which always picks out the set of maximal elements) will be closed, and hence, in many cases, upper hemicontinuous. A further generalization of Berges theorem is provided here, one which extends the usefulness of the theorem, especially to equilibrium concepts in multi-person decision situations. The generalization is suggested by a natural decomposition of Berges result into two parts, and by the nature of the domination concept in game theory. Several applications are suggested, probably none of which is a new result, but each of which becomes transparent in the light of the theorems general form. Thus, the generalized theorem provides a unified treatment of upper hemicontinuity for the kinds of correspondences which occur frequently in the social sciences. The original form of the Maximum Theorem was essentially as follows:

Equilibrium play in matches: Binary Markov games

We study two-person extensive form games, or matches, in which the only possible outcomes (if the game terminates) are that one player or the other is declared the winner. The winner of the match is determined by the winning of points, in point games. We call these matches binary Markov games. We show that if a simple monotonicity condition is satisfied, then (a) it is a Nash equilibrium of the match for the players, at each point, to play a Nash equilibrium of the point game; (b) it is a minimax behavior strategy in the match for a player to play minimax in each point game; and (c) when the point games all have unique Nash equilibria, the only Nash equilibrium of the binary Markov game consists of minimax play at each point. An application to tennis is provided.

A simple auctioneerless mechanism with Walrasian properties

Abstract A simple mechanism for reallocating holdings is described, in which no auctioneer is required: outcomes are determined solely from traders actions and without any requirement that the mechanism be in equilibrium. The mechanism is shown to exactly duplicate the performance of the Walrasian auctioneer (both in its equilibria and in its disequilibrium path) if individuals are price takers, and, if the number of individuals is large, to approximately duplicate the auctioneers performance even when individuals behave strategically, each taking account of his own influence on prices.