The Edgeworth exchange formulation of bargaining models and market experiments

We construct Edgeworth exchange economies equivalent to demand and supply environments typically used in bargaining models and market experiments. This formulation clearly delineates environment, institution, and behavior for these models and experiments. To illustrate, we examine results by Gode and Sunder, who simulate random behavior in a double auction and argue that this institution leads to an efficient allocation, even in the absence of rationality. We use the Edgeworth exchange representation of their economic environment to demonstrate that they model individually rational behavior, and show that their model is a special case of theoretical results by Hurwicz, Radner, and Reiter.Double auction, Market experiment, Edgeworth exchange, Bounded rationality

Information Aggregation in a Catastrophe Futures Markets

We experimentally examine a reinsurance market in which participants have differing information regarding the probability distribution over losses. The key question is whether the market equilibrium reflects traders maximizing value with respect to their different priors, or whether the equilibrium is one based on a common belief incorporating all participants’ information. When assuming subjects are expected value maximizers, we reject both full information aggregation and no information aggregation equilibria. We discover, as in past individual choice insurance experiments, that buyers under-assess the probabilities of large loss states, or alternatively, subjects assign larger utility values to losses than to comparable gains. After accounting for these decision theoretic concerns, the non-aggregation of information hypothesis explains the data better than full information aggregation.

Individual Rationality and Market Efficiency

The demonstration by Smith [1962] that prices and allocations quickly converge to the competitive equilibrium in the continuous double auction (CDA) was one of the first – and remains one of the most important results in experimental economics. His initial experiment, subsequent market experiments, and models of price adjustment and exchange have added considerably to our knowledge of how markets reach equilibrium, and how they respond to disruptions. Perhaps the best known model of exchange in CDA market experiments is the random behavior in the “zero-intelligence” (ZI) model by Gode and Sunder [1993]. They conclude that even without trader rationality the CDA generates efficient allocations and “convergence of transaction prices to the proximity of the theoretical equilibrium price,” provided only that agents meet their budget constraints. We demonstrate that – by any reasonable measure – prices don’t converge in their simulations. Their budget constraint requires that a buyer’s currency never exceeds her value for the commodity, which is an unnatural restriction. Their conclusion that market efficiency results from the structure of the CDA independent of traders’ profit seeking behavior rests on their claim that the constraints that they impose are a part of the market institution, but this is not so. We show that they in effect impose individual rationality, which is an aspect of agents' behavior. Researchers on learning in markets have been misled by their interpretation of the ZI simulations, with deleterious effects on the debate on market adjustment processes.Bounded rationality; double auction; exchange economy; experimental economics; market experiment; "zero intelligence" model

Learning about Learning in Games through Experimental Control of Strategic Interdependence

We conduct experiments in which humans repeatedly play one of two games against a computer decision maker that follows either Roth and Erev's reinforcement learning algorithm or Camerer and Ho's EWA algorithm. The human/algorithm interaction provides results that can't be obtained from the analysis of pure human interactions or model simulations. The learning algorithms are more sensitive than humans in calculating exploitable opponent play. Learning algorithms respond to these calculated opportunities systematically; however, the magnitude of these responses are too weak to improve the algorithm's payoffs. Human play against various decision maker types does not significantly vary. These results demonstrate that humans and currently proposed models of their behavior differ in that humans do not adjust payoff assessments by smooth transition functions and that when humans detect exploitable play they are more likely to choose the best response to this belief.

The performance of reverse auctions versus request for quotes when procuring goods with quality differences

The use of dynamic auctions is a major component in many enterprises' e-procurement initiatives. In the case where suppliers offer goods and services of inherently different quality the traditional mechanism has been the request for quote. In a request for quote, suppliers submit a sealed bid and the fixed quality of their offering and then the buyer selects the seller who offers the greatest difference between quality and price. The winning seller receives a price equal to his submitted bid. The reverse auction has immerged as the most commonly adopted dynamic auction for this setting. In a reverse auction, suppliers first submit the qualities of their goods and then the suppliers participate in an auction with the same message space as an open outcry English auction (descending because this is a procurement auction.) However, the auction is only used to set each suppliers price. The last price a supplier submits in the auction becomes their actual submitted price. After, the auction the buyer selects the winning seller who offers the greatest difference between quality and actual submitted price. We provide a game theoretic analysis of both mechanisms. We also provide extensive experimental evaluation of the two mechanisms as wellReverse Auction, Request for Quote, procurement

Procurement Auctions for Differentiated Goods

We consider two mechanisms to procure differentiated goods: a request for quote and an English auction with bidding credits. In the request for quote, each seller submits a price and the inherent quality of his good. Then the buyer selects the seller who offers the greatest difference in quality and price. In the English auction with bidding credits, the buyer assigns a bidding credit to each seller conditional upon the quality of the seller’s good. Then the sellers compete in an English auction with the winner receiving the auction price and his bidding credit. Game theoretic models predict the request for quote is socially efficient but the English auction with bidding credits is not. The optimal bidding credit assignment under compensates for quality advantages, creating a market distortion in which the buyer captures surplus at the expense of the seller’s profit and social efficiency. In experiments, the request for quote is less efficient than the English auctions with bidding credits. Moreover, both the buyer and seller receive more surplus in the English auction with bidding credits.

Do We Detect and Exploit Mixed Strategy Play by Opponents?

We conducted an experiment in which each subject repeatedly played a game with a unique Nash equilibrium in mixed strategies against some computer-implemented mixed strategy. The results indicate subjects are successful at detecting and exploiting deviations from Nash equilibrium. However, there is heterogeneity in subject behavior and performance. We present a one variable model of dynamic random belief formation which rationalizes observed heterogeneity and other features of the data.best response correspondence, mixed strategy

Procurement Auctions for Differentiated Goods

We consider two mechanisms to procure differentiated goods: a request for quote and an English auction with bidding credits. In the request for quote, each seller submits a price and the inherent quality of his good. Then the buyer selects the seller who offers the greatest difference in quality and price. In the English auction with bidding credits, the buyer assigns a bidding credit to each seller conditional upon the quality of the seller’s good. Then the sellers compete in an English auction with the winner receiving the auction price and his bidding credit. Game theoretic models predict the request for quote is socially efficient but the English auction with bidding credits is not. The optimal bidding credit assignment under compensates for quality advantages, creating a market distortion in which the buyer captures surplus at the expense of the seller’s profit and social efficiency. In experiments, the request for quote is less efficient than the English auctions with bidding credits. Moreover, both the buyer and seller receive more surplus in the English auction with bidding creditsAuctions, Product Differentiation, Experiment

Auctioning the right to play ultimatum games and the impact on equilibrium selection

We conduct an experiment in which we auction the scarce rights to play the Proposer and Responder positions in subsequent ultimatum games. As a control treatment, we randomly allocate these rights and then charge exogenous participation fees according to the auction price sequences observed in the auction treatment. With endogenous selection into ultimatum games via auctions, we find that play converges to a session-specific Nash equilibrium and auction prices emerge which support this equilibrium by the principle of forward induction. With random assignment and exogenous participation fees, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. The Nash equilibrium observed within a session results in low ultimatum game offers, but the subgame perfect Nash equilibrium is never observed

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.Minimax, mixed strategy, experiment