Simultaneous versus sequential all-pay auctions: an experimental study

While both simultaneous and sequential contests are mechanisms used in practice such as crowdsourcing, job interviews and sports contests, few studies have directly compared their performance. By modeling contests as incomplete information all-pay auctions with linear costs, we analytically and experimentally show that the expected maximum effort is higher in simultaneous contests, in which contestants choose their effort levels independently and simultaneously, than in sequential contests, in which late entrants make their effort choices after observing all prior participants’ choices. Our experimental results also show that efficiency is higher in simultaneous contests than in sequential ones. Sequential contests’ efficiency drops significantly as the number of contestants increases. We also discover that when participants’ ability follows a power distribution, high ability players facing multiple opponents in simultaneous contests tend to under-exert effort, compared to theoretical predictions. We explain this observation using a simple model of overconfidence.     

Passing the Buck On the acceptance of responsibility

In the Passing the Buck game, the n members of a group decide in a given order whether or not to incur costs so that they can fix a certain problem for the benefit of the group. Passing the Buck means that one relies on the service of a successor. The decision is influenced by social preferences and by strategic considerations. We derive three main conclusions from experiments with n=3 and n=4. (i) The unique perfect Baysian equilibrium of the Passing the Buck game with incomplete information about the preferences of other players generally fits the data, however with two interesting exceptions. (ii) Backward induction breaks down if it requires more than two steps, i.e., for the first player in the game with n=4. (iii) Making one of the members of the group an “expert” who alone is competent to fix the problem is connected with a change of social preferences.     

Co-ordination, Spillovers, and Cheap Talk

We analyze the role of cheap-talk in two player games with one-sided incomplete information. We identify conditions under which (1) players can fully communicate and coordinate on efficient Nash equilibria of the underlying complete information game; and (2) players cannot communicate so cheap-talk does not alter the equilibrium set of the Bayesian game. We present examples that illustrate several issues that arise when there is two-sided incomplete information. Journal of Economic Literature Classification Numbers: C72, D82.     

Group efforts when performance is determined by the “best shot”

We investigate the private provision of a public good whose level is determined by the maximum effort made by a group member. Costs of effort are either commonly known or privately known. For symmetric perfect-information games, any number of players may be active and we characterize the unique (mixed-strategy) equilibrium in which active contributors use the same strategy. Increasing the number of active players leads to stochastically lower individual efforts and level of the public good. When information is private, the symmetric equilibrium is in pure strategies. Increasing the number of players yields a pointwise reduction in the equilibrium contribution strategy but an increase in equilibrium payoffs. Comparative statics with respect to costs and levels of risk aversion are derived. Finally, whether information is public or private, equilibria are inefficient—we provide mechanisms that improve efficiency.     

Experimental tests of Tullock’s contest with and without winner refunds

We examined experimentally the two-agent, complete-information Tullock’s contest, with and without refund for the winner. We find that the average bids in the refund group are higher than the average bids in the group without a refund, consistent with the theory. However, the auctioneer does not increase his profit if he changes the design of the contest by reimbursing the winner’s cost of effort. We also find underbidding for the low-valuation players and overbidding for the high-valuation player in a contest with a refund. Some players chose the corner solution of staying out of the game by biding zero.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

Personalized pricing and advertising: An asymmetric equilibrium analysis

We study personalized price competition with costly advertising among n quality-cost differentiated firms. Strategies involve mixing over both prices and whether to advertise. In equilibrium, only the top two firms advertise, earning “Bertrand-like” profits. Welfare losses initially rise then fall with the ad cost, with losses due to excessive advertising and sales by the “wrong” firm. When firms are symmetric, the symmetric equilibrium yields perverse comparative statics and is unstable. Our key results apply when demand is elastic, when ad costs are heterogeneous, and with noise in consumer tastes.     

Learning, teaching, and turn taking in the repeated assignment game

History-dependent strategies are often used to support cooperation in repeated game models. Using the indefinitely repeated common-pool resource assignment game and a perfect stranger experimental design, this paper reports novel evidence that players who have successfully used an efficiency-enhancing turn taking strategy will teach other players in subsequent supergames to adopt this strategy. We find that subjects engage in turn taking frequently in both the Low Conflict and the High Conflict treatments. Prior experience with turn taking significantly increases turn taking in both treatments. Moreover, successful turn taking often involves fast learning, and individuals with turn taking experience are more likely to be teachers than inexperienced individuals. The comparative statics results show that teaching in such an environment also responds to incentives, since teaching is empirically more frequent in the Low Conflict treatment with higher benefits and lower costs.     

Incomplete information in rent-seeking contests

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.     

Mixed-Strategy Nash Equilibrium Based upon Expected Utility and Quadratic Utility

The notion of a mixed-strategy Nash equilibrium suffers from three inherent difficulties. First, given the equilibrium strategies of other players, there are many best replies. Second, the equilibrium is unstable. Third, comparative statics results are counterintuitive. We demonstrate that these difficulties all have their origin in von Neumann and Morgenstern′s expected utility. In contrast, players with "quadratic utility" have unique best replies and the Nash equilibrium appears to yield intuitive comparative statics results. Journal of Economic Literature Classification Number: C72.     

Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.     

The symmetric multiple prize all-pay auction with complete information

This paper extends the analysis of the n-player all-pay auction with complete information to cover the case of m≤n prizes, valued in weakly decreasing order, but symmetrically across players. We provide a complete characterization of the Nash equilibrium distributions for this class of auctions and provide an exact expression for the expected revenue generated.     

Similar bidders in takeover contests

When bidders in a corporate takeover have related resources and post-acquisition strategies, their valuations of a target are likely to be interdependent. This paper analyzes sequential-entry takeover contests in which similar bidders have correlated private valuations. The level of similarity affects information content of bids and bidding competition. Our model predicts that expected acquisition prices and the probability of multiple-bidder contests are the highest for intermediately similar bidders. We test these predictions in laboratory experiments in which we control the similarity between bidders. The experimental data confirm the non-monotonic effects of similarity on prices and on the frequency of multiple-bidder contents.     

Repeated games with present-biased preferences

We study infinitely repeated games with perfect monitoring, where players have β-δ preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in β or δ. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor.     

Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games

Most learning models assume players are adaptive (i.e., they respond only to their own previous experience and ignore others' payoff information) and behavior is not sensitive to the way in which players are matched. Empirical evidence suggests otherwise. In this paper, we extend our adaptive experience-weighted attraction (EWA) learning model to capture sophisticated learning and strategic teaching in repeated games. The generalized model assumes there is a mixture of adaptive learners and sophisticated players. An adaptive learner adjusts his behavior the EWA way. A sophisticated player rationally best-responds to her forecasts of all other behaviors. A sophisticated player can be either myopic or farsighted. A farsighted player develops multiple-period rather than single-period forecasts of others' behaviors and chooses to “teach” the other players by choosing a strategy scenario that gives her the highest discounted net present value. We estimate the model using data from p-beauty contests and repeated trust games with incomplete information. The generalized model is better than the adaptive EWA model in describing and predicting behavior. Including teaching also allows an empirical learning-based approach to reputation formation which predicts better than a quantal-response extension of the standard type-based approach. Journal of Economic Literature Classification Numbers: C72, C91.     

The impact of public information on bidding in highway procurement auctions

A number of papers in the theoretical auction literature show that the release of information regarding the seller's valuation of an item can cause bidders to bid more aggressively. This widely accepted result in auction theory remains largely untested in the empirical literature. Recent theoretical work has also shown that this effect can be more pronounced in auctions with larger common cost uncertainty. We examine the impact of a policy change by the Oklahoma Department of Transportation that led to the release of the state's internal estimate of the costs to complete highway construction projects. We perform a differences-in-differences analysis comparing bidding in Texas, a state that had a uniform policy of revealing the same information all throughout the period of analysis, to bidding in Oklahoma. Our results show that, in comparison to Texas auctions, the average bid in Oklahoma fell after the change in engineers’ cost estimate (ECE) policy. This decline in bids was even larger for projects where the common uncertainty in costs is greater. Moreover, the within-auction standard deviation of bids fell after the change in ECE policy with the most significant decline observed again in projects with greater common cost uncertainty.     

Auctioning Risky Conservation Contracts

Conservation auctions have the potential to increase the efficiency of payments to farmers to adopt conservation-friendly management practices by fostering competition among them. The literature considers bidders that have complete information about the costs of adoption and optimal bidding behavior reflects this information advantage. Farmers seek information rents and bids decrease when risk aversion increases because farmers are more averse to losing the auction. We contribute to the literature by allowing for cost risk. Our paper shows that farmers must balance the risk of losing the auction (thus foregoing information rent) with the risk of submitting a bid that is not high enough to pay the costs of adopting conservation practices (thus incurring losses). We design an experiment to trade off these two risks and examine how risk aversion affects bidding behavior when participants face different sources and levels of risk. Our experiment contributes to a small literature on experimental auctions with risky product valuations. We find that participants decrease their bids as risk aversion increases, even in auctions with cost risk, suggesting that the risk of losing the auction dominates. These findings uncover new challenges for the practical implementation of conservation auctions as an efficient policy instrument.     

Garbling of signals and outcome equivalence

In a game with incomplete information players receive stochastic signals about the state of nature. The distribution of the signals given the state of nature is determined by the information structure. Different information structures may induce different equilibria.Two information structures are equivalent from the perspective of a modeler, if they induce the same equilibrium outcomes. We characterize the situations in which two information structures are equivalent in terms of natural transformations, called garblings, from one structure to another. We study the notion of ‘being equivalent to’ in relation with three equilibrium concepts: Nash equilibrium, agent normal-form correlated equilibrium and the belief invariant Bayesian solution.     

Are ‘true’ preferences revealed in repeated markets? An experimental demonstration of context-dependent valuations

This paper reports a new and significant experimental demonstration that market participants adjust their bids towards the price observed in previous market periods when—by design—individuals’ values should not be affiliated with the market price. This demonstration implies that market prices may not adjust as standard comparative statics predicts and emphasizes the significance of social aspects even in market contexts. Hence, the present study shows that market behaviour is not anomaly-free. Indeed, market behaviour does not reveal the underlying true preferences but rather context-dependent preferences.     

The all-pay auction with complete information

Summary In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium.We are grateful to Jacques Crémer, Chuangyin Dang, Jürgen Dennert, Chaim Fershtman, Martin Hellwig, Arthur Robson, Heinrich Ursprung, Eric van Damme, Ton Vorst, and the referees for helpful comments. We benefitted from presentations at the World Congress of the Econometric Society in Barcelona, the European Meeting on the Economics of Information at Tilburg University, the Midwest Mathematical Economics Meetings at the University of Illinois, and seminars at Texas A&M University, The Pennsylvania State University, Tilburg University and the University of Montreal. Baye is grateful for support from the CentER for Economic Research at Tilburg University and the Tinbergen Institute where earlier versions of this paper were completed. Kovenock acknowledges support from Erasmus Universiteit Rotterdam, the Tinbergen Institute, the Center for Economic Studies at the University of Munich, the Institut d'Analisi Economica CSIC at the Universitat Autonoma de Barcelona, the Krannert School of Management, and the Jay N. Ross Young Faculty Scholar Award.