The All Pay. Common Value Auction as a Model of Contests

An all pay, common value auction is proposed as a model of contests. The common value of the prize is ex-ante unknown, but each contestant has private information about its true value. These private information are affiliated. Unlike in the symmetric winner pay auction model of Milgrom and Weber (1982). The affiliation assumption is not sufficient to ensure the existence of an increasing equilibrium bid. The all pay auction is shown to require a stronger condition; a joint restriction on the expected valuation of the prize and the beliefs bidders have of each other’s estimates of the prize. Equilibrium bids are increasing if there is not too strong a degree of affiliation and the expected value of the prize is increasing sufficiently rapidly in each bidder’s type. When there exists an increasing equilibrium, the equilibrium is unique even in the asymmetric bidder case. The results extend to the all pay private values auction which is obtained as a special case. The all pay and winner pay auctions are then compared at the symmetric equilibrium. With increasing equilibrium bids, it is possible to order the expected revenues from the two auctions. This was first proposed by Amann and Leininger (1994). It is shown by way of an example that although sufficient, monotonicity of equilibrium bids is not a necessary condition for the ordering. Without monotonicity, however comparing the two auctions can lead to conclusions which are not robust. Two examples are provided to compare the role of affiliation and the effects of nonmonotonicity in the all pay and winner pay auctions

Asymmetric Information in Common-Value Auctions and Contests: Theory and Experiments

In common-value auctions and contests economic agents often have varying levels of information regarding the value of the good to be allocated. Using theoretical and experimental analysis, I examine the effect of such information asymmetry on behavior. Chapter II considers a model in which players compete in two sequential contests. The winner of the first contest (the incumbent) privately observes the value of the prize, which provides private information if the prizes are related. Relative to the case where the prizes are independent, the incumbent is strictly better off, and the other contestants (the challengers) are strictly worse off. This increases the incentive to win the first contest such that the sum of expected effort over both contests increases relative to the case of independent prizes. Chapter III experimentally considers the role of asymmetric information in first-price, sealed-bid, common-value auctions. Bidders who observe a private signal tend to overbid relative to Nash equilibrium predictions. Uninformed bidders, however, tend to underbid relative to the Nash equilibrium. Chapter IV examines asymmetric information in one-shot common-value all-pay auctions and lottery contests from both experimental and theoretical perspectives As predicted by theory, asymmetric information yields information rents for the informed bidder in both all-pay auctions and lottery contests

Auctions with private entry costs

We study auctions where bidders have private information about their entry costs and the seller does not benefit from these entry costs. We consider a symmetric environment where all bidders have the same value for the object being sold, and also an asymmetric environment where bidders may have different valuations for the object. In these environments, the seller's pay-off as well as the social surplus may either increase or decrease in the number of bidders though not necessarily in the same direction. The auction designs that maximize the social surplus or the seller's pay-off are analysed

Characterizing the interplay between information and strength in Blotto games

In this paper, we investigate informational asymmetries in the Colonel Blotto game, a game-theoretic model of competitive resource allocation between two players over a set of battlefields. The battlefield valuations are subject to randomness. One of the two players knows the valuations with certainty. The other knows only a distribution on the battlefield realizations. However, the informed player has fewer resources to allocate. We characterize unique equilibrium payoffs in a two battlefield setup of the Colonel Blotto game. We then focus on a three battlefield setup in the General Lotto game, a popular variant of the Colonel Blotto game. We characterize the unique equilibrium payoffs and mixed equilibrium strategies. We quantify the value of information - the difference in equilibrium payoff between the asymmetric information game and complete information game. We find information strictly improves the informed player's performance guarantee. However, the magnitude of improvement varies with the informed player's strength as well as the game parameters. Our analysis highlights the interplay between strength and information in adversarial environments.Comment: 8 pages, 2 figures. Accepted for presentation at 58th Conference on Decision and Control (CDC), 201

Auctions with Severely Bounded Communication

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g., that in optimal mechanisms bidders simply report the interval in which their valuation lies in, as well as some surprising properties, e.g., that asymmetric auctions are better than symmetric ones and that multi-round auctions reduce the communication complexity only by a linear factor

Charitable asymmetric bidders

Recent papers show that all-pay auctions are better at raising money for charity than first-price auctions with symmetric bidders and under incomplete information. Yet, this result is lost with sufficiently asymmetric bidders and under complete information. In this paper, we consider a framework on charity auctions with asymmetric bidders under some incomplete information. We find that all-pay auctions still earn more money than first-price auction. Thus, all-pay auctions should be seriously considered when one wants to organize a charity auction.All-pay auctions, Charity, Externalities

Market Experience and willingness to trade: evidence from repeated markets with symmetric and asymmetric information

Many studies have found a gap between willingness-to-pay and willingness-to-accept that is inconsistent with standard theory. There is also evidence that the gap is eroded by experience gained in the laboratory and naturally occurring markets. This paper argues that the gap and the effects of experience are explained by a caution heuristic. This conjecture is tested in a repeated market experiment with symmetric and asymmetric information. The results support the conjecture: people do seem to use heuristics rather than reacting optimally and their behavior adjusts slowly when the environment changes.WTA/WTP disparity, endowment effect, market experience, bounded rationality, asymmetric information