Jacob K. Goeree

A theoretical analysis of altruism and decision error in public goods games

Abstract We formalize an equilibrium model in which altruism and decision-error parameters determine the distribution of contributions for linear and quadratic public goods games. The equilibrium density is exponential for linear games, and normal for quadratic games. Our model implies: (i) contributions increase with the marginal value of the public good, (ii) total contributions increase with the number of participants, (iii) mean contributions lie between the Nash prediction and half the endowment. These predictions, which are not implied by a Nash analysis, are consistent with laboratory data. Maximum likelihood estimates of altruism and error parameters are significant and plausible.

Risk Averse Behavior in Generalized Matching Pennies Games

In experimental studies of behavior in 2×2 games with unique mixed strategy equilibria, observed choice frequencies are systematically different from mixed-strategy Nash predictions. This paper examines experimental results for a variety of such games, and shows that a structural econometric model which incorporates risk aversion into a quantal response equilibrium explains the data very well. Moreover, risk aversion estimates are stable across the different games and are close to those obtained from laboratory and field auction data, as well as from individual lottery choice experiments.

Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction

The winner‐take‐all nature of all‐pay auctions makes the outcome sensitive to decision errors, which we introduce with a logit formulation. The equilibrium bid distribution is a fixed point: the belief distributions that determine expected payoffs equal the choice distributions determined by expected payoffs. We prove existence, uniqueness, and symmetry properties. In contrast to the Nash equilibrium, the comparative statics of the logit equilibrium are intuitive: rent dissipation increases with the number of players and the bid cost. Overdissipation of rents is impossible under full rationality but is observed in laboratory experiments. Our model predicts this property.

How (not) to raise money

We show that standard winner‐pay auctions are inept fund‐raising mechanisms because of the positive externality bidders forgo if they top another’s high bid. Revenues are suppressed as a result and remain finite even when bidders value a dollar donated the same as a dollar kept. This problem does not occur in lotteries and all‐pay auctions, where bidders pay irrespective of whether they win. We introduce a general class of all‐pay auctions, rank their revenues, and illustrate how they dominate lotteries and winner‐pay formats. The optimal fund‐raising mechanism is an all‐pay auction augmented with an entry fee and reserve price.

A model of noisy introspection

We present a theoretical model of noisy introspection designed to explain behavior in games played only once. The model determines layers of beliefs about others’ beliefs about ..., etc., but allows for surprises by relaxing the equilibrium requirement that belief distributions coincide with decision distributions. Noise is injected into iterated conjectures about others’ decisions and beliefs, which causes the predictions to differ from those of deterministic models of iterated thinking, e.g., rationalizability. The paper contains a convergence proof that implies existence and uniqueness of the outcome of the iterated thought process. In addition, estimated introspection and noise parameters for data from 37 one-shot matrix games are reported. The accuracy of the model is compared with that of several alternatives.

An experimental study of costly coordination

This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria nor do they alter the predictions of adjustment theories based on imitation or best response dynamics. As expected, however, increasing the effort cost lowers effort levels. Maximization of a stochastic potential function, a concept that generalizes risk dominance to continuous games, predicts this reduction in efforts. An error parameter estimated from initial two-person, minimum-effort games is used to predict behavior in other three-person coordination games.

Efficiency in Auctions with Private and Common Values: An Experimental Study

This discussion has resulted in a publication in the American Economic Review , 2002, 92(3), 625-43. Auctions are generally not efficient when the objects expected value depends on private and common value information. We report a series of first-price auction experiments to measure the degree of inefficiency that occurs with financially motivated bidders. While some subjects fall prey to the winners curse, they weigh their private and common value information in roughly the same manner as rational bidders, with observed efficiencies close to predicted levels. Increased competition and reduced uncertainty about the common value positively affect revenues and efficiency. The public release of information about the common value also raises efficiency, although less than predicted.

Quantal Response Equilibrium

A quantal response specifies choice probabilities that are smooth, increasing functions of expected payoffs. A quantal response equilibrium has the property that the choice distributions match the belief distributions used to calculate expected payoffs. This stochastic generalization of the Nash equilibrium provides strong empirical restrictions that are generally consistent with data from laboratory experiments with human subjects. We define the concept of regular quantal response equilibrium and discuss several applications from the recent literature.

Bidding for the future: signaling in auctions with an aftermarket

Abstract This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.

An Explanation of Anomalous Behavior in Models of Political Participation

This paper characterizes behavior with “noisy” decision making for models of political interaction characterized by simultaneous binary decisions. Applications include: voting participation games, candidate entry, the volunteers dilemma, and collective action problems with a contribution threshold. A simple graphical device is used to derive comparative statics and other theoretical properties of a “quantal response” equilibrium, and the resulting predictions are compared with Nash equilibria that arise in the limiting case of no noise. Many anomalous data patterns in laboratory experiments based on these games can be explained in this manner.