Indefinitely repeated contests: An experimental study

Experimental Economics - We experimentally explore indefinitely repeated contests. Theory predicts more cooperation, in the form of lower expenditures, in indefinitely repeated contests with a...     

An experimental study of precautionary bidding

Auctions often involve goods exhibiting a common-knowledge ex-post risk. In such auctions, precautionary bidding predicts that under expected utility, DARA bidders reduce their bids by more than the appropriate risk premium. Because the degree of riskiness of an auctioned good and bidders׳ levels of risk aversion are difficult to observe in field settings, we conduct experimental auctions that allow us to identify the precautionary premium directly. We find strong evidence for precautionary bidding. The effect is robust to changes in experimental design features. Our experiment provides the first empirical demonstration of precautionary motives in a strategic setting.     

Entry in contests with incomplete information: Theory and experiments

This paper studies entry decisions in contests with private values. Potential contestants observe their value and the common opportunity cost of entry, and make entry decisions simultaneously. Theory predicts that whether or not contestants are informed of the number of entrants prior to choosing their expenditures has no effect on entry or aggregate expenditures. We test these assertions in our experiments. We find substantial over-entry in both information structures. However, entry is higher when contestants are informed. Since expenditures do not, on average, differ across information structures, aggregate expenditure is also higher when contestants are informed. Contestants earn on average less than the opportunity cost of entry.     

Entry into winner-take-all and proportional-prize contests: An experimental study

This experiment compares the performance of two contest designs: a standard winner-take-all tournament with a single fixed prize, and a novel proportional-payment design in which that same prize is divided among contestants by their share of total achievement. We find that proportional prizes elicit more entry and more total achievement than the winner-take-all tournament. The proportional-prize contest performs better by limiting the degree to which heterogeneity among contestants discourages weaker entrants, without altering the performance of stronger entrants. These findings could inform the design of contests for technological and other improvements, which are widely used by governments and philanthropic donors to elicit more effort on targeted economic and technological development activities.     

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

Asymmetric information contests

We consider how asymmetries in information affect contest behavior. We find two effects drive behavior-risk and perceptions of an opponent's value. Our results also suggest that the more tractable one-sided asymmetric information contest might be sufficient to capture contest behavior under uncertainty. However, the efficiency of a contest is sensitive to asymmetric information and the distribution a players' values because players with relatively low values can have an increased probability of success. Thus, it is important (a) to account for information asymmetries to avoid biasing predicted efficiency, and (b) to recognize that this bias is unsystematic.     

Indicative bidding: An experimental analysis

Indicative bidding is a practice commonly used in sales of complex and very expensive assets. Theoretical analysis shows that efficient entry is not guaranteed under indicative bidding, since there is no equilibrium in which more qualified bidders are more likely to be selected for the final sale. Furthermore, there exist alternative bid procedures that, in theory at least, guarantee 100% efficiency and higher revenue for the seller. We employ experiments to compare actual performance between indicative bidding and one of these alternative procedures. The data shows that indicative bidding performs as well as the alternative procedure in terms of entry efficiency, while having other characteristics that favor it over the alternative procedure. Our results provide an explanation for the widespread use of indicative bidding despite the potential problem identified in the equilibrium analysis.     

An experimental study of strategic information transmission

Summary We examine strategic information transmission in an experiment. Senders are privately informed about a state. They send messages to Receivers, who choose actions resulting in payoffs to Senders and Receivers. The payoffs depend on the action and the state. We vary the degree to which the Receivers' and the Senders' preferences diverge. We examine the relationship between the Senders' messages and the true state as well as that between actions and the true state and contrast the ability of different equilibrium message sets to explain the data.When preferences are closely aligned Senders disclose more. We assess two comparative statics: (i) as preferences diverge, state and action are less frequently matched, and (ii) messages tend to become less informative as preferences diverge. The first result is weakly confirmed for adjacent treatments but is considerably stronger when non-adjacent treatments are compared. We find that as preferences diverge messages become less informative. While the ex-ante Pareto-optimal Bayesian Nash Equilibrium does not explain our conditions, the equilibrium message sets supported by the data are similar to the ex-ante Pareto Optimal message sets.We would like to thank seminar participants at the Economic Science Association meetings, the University of Iowa, the University of Minnesota, Northwestern University and the Society for the Advancement of Economic Theory meetings for their comments. We would like to thank Beth Allen, Joyce Berg, Robert Forsythe, Yong-Gwan Kim, Antonio Merlo, Leonard Mirman, In-Uck Park, Charles Plott, Jennifer Reinganum and an anonymous referee for their suggestions. Financial support from the Accounting Research Center at the University of Minnesota is also acknowledge.     

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.     

Entry decisions and bidding behavior in sequential first-price procurement auctions: An experimental study

Though many real life auctions are run independently of each other, from the bidders' point of view they often form sequences of auctions. We investigate how behavior responds to the additional incentives that are present in such auction sequences. Comparing subjects' decisions in single first-price procurement auctions with their decisions in a game consisting of two subsequent first-price procurement auctions, we find that, in line with the theoretical prediction, entry and bidding behavior is crucially affected by the opportunity cost of early bid submission. Though, entry decisions and average bids in the auction sequence systematically deviate from the perfect Bayesian equilibrium prediction. While the nature of the opponent (human being or computer) has no significant effect on these findings, giving subjects additional feedback on winners and prices seems to reduce the deviations from the equilibrium prediction.     

On the effects of joint bidding in independent private value auctions: An experimental study

This article explores the effect of a subset of symmetric bidders joining to bid together. Possible applications include mergers, collusion and joint-bidding arrangements. The change produces a “strong” party with a more advantageous value distribution than the remaining “weak” bidder(s). The predicted effects include inefficiency, a decrease in the sellerʼs revenue, and higher biddersʼ payoffs. Under risk neutrality, the members of the strong party benefit less than the weak bidders. The prediction is reversed when the bidders are sufficiently risk-averse. These hypotheses are tested experimentally. Contrary to the theory, joint bidding increases efficiency and the sellerʼs revenue decreases by less than expected. Strong bidders benefit more than weak bidders indicating that incentives to bid jointly may be greater than hypothesized. Additionally, the experiment assesses the effect of group decision-making. A Nash equilibrium prediction for individual–group differences based on differences in risk attitudes is not supported by the data.     

Endogenous group formation in experimental contests

We experimentally study endogenous alliance formation and contest effort choices in a generic three-player contest. Differences in intrinsic or extrinsic incentives to expend effort cause self-selection. Weakly motivated players have an incentive to enter into an alliance and to free-ride on strongly motivated players; hence, strong players prefer to stand alone. Self-selection has direct consequences for effort in endogenously formed alliances. But we also find evidence of an effort stimulating effect if players endogenously form an alliance, which is in line with theories of in-group favoritism. The experimental evidence on self-selection is in conformity with a theory analysis of the game.     

Multi-player contests with asymmetric information

We consider imperfectly discriminating, common-value, all-pay auctions (or contests) in which some players know the value of the prize, others do not. We show that if the prize is always of positive value, then all players are active in equilibrium. If the prize is of value zero with positive probability, then there is some threshold number of informed players such that if there are less, all uninformed players are active, and otherwise all uninformed players are inactive.     

An experimental study of information and mixed-strategy play in the three-person matching-pennies game

Summary. Recent experiments on mixed-strategy play in experimental games reject the hypothesis that subjects play a mixed strategy even when that strategy is the unique Nash equilibrium prediction. However, in a three-person matching-pennies game played with perfect monitoring and complete payoff information, we cannot reject the hypothesis that subjects play the mixed-strategy Nash equilibrium. Given this support for mixed-strategy play, we then consider two qualitatively different learning theories (sophisticated Bayesian and naive Bayesian) which predict that the amount of information given to subjects will determine whether they can learn to play the predicted mixed strategies. We reject the hypothesis that subjects play the symmetric mixed-strategy Nash equilibrium when they do not have complete payoff information. This finding suggests that players did not use sophisticated Bayesian learning to reach the mixed-strategy Nash equilibrium. Received: August 9, 1996; revised version: October 21, 1998     

Incentives and incomplete information

The problem of incentives for correct revelation in a collective decision model is presented as a game with incomplete information. Two approaches to incomplete information are used, a first where the individual beliefs are not introduced and a second where they are. In the first approach it is recalled that the mechanisms for which the solution to the incentive problem is in dominant strategies lead in general to a budgetary problem for the central agency. For these mechanisms a uniqueness property is demonstrated. In the second approach it is shown that if a compatibility condition is imposed on the individual beliefs and if a Bayesian solution is given to the incentive problem, then it is possible to avoid the budgetary problem.     

Reporting bias in incomplete information model

Company financial reports are likely to be systematically biased. In this paper, we extend the Duffie and Lando (2001) model with a skewness correction which can account for both random and directional components of reporting noise.     

Coarse matching with incomplete information

We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), an intermediary’s revenue, and the agents’ welfare (defined as the total surplus minus payments to the intermediary). Following Chao and Wilson (Am Econ Rev 77: 899–916, 1987) and McAfee (Econometrica 70:2025–2034, 2002), our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than random matching, while still requiring only a minimal amount of information.     

Representation of constitutions under incomplete information

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizens are private information. We investigate whether there exist decision schemes (i.e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: (i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and (ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties.