Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.     

Simultaneous ascending auctions with complementarities and known budget constraints

We study simultaneous ascending auctions of two identical objects when bidders are financially constrained and their valuations exhibit complementarities. We assume the budget constraints are known but the values for individual objects are private information, and characterize noncollusive equilibria. Equilibrium behavior is affected by the exposure problem. Bidders with higher budgets are more reluctant to bid, because opponents with lower budgets may end up pursuing a single object, thus preventing the realization of complementarities. Therefore poor bidders may win both objects when they do not have the highest valuation. We gratefully acknowledge comments by Marco Battaglini, Benny Moldovanu and participants at seminars held at Montreal, Yale, Texas A&M, Washington St. Louis and at the Workshop on Mechanism Design with Budget Constraints held at SUNY - Stony Brook. Sandro Brusco acknowledges financial support from the Ministerio de Educacion y Ciencias D.G.E.S., proyecto SEC2001-0445.     

Multi-unit auctions with budget limits

We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubel?s “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible.     

On the continuous equilibria of affiliated-value,all-pay auctions with private budget constraints

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.     

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].     

Procurement auctions with ex-ante endogenous bribery

Corruption is a prevalent phenomenon in various procurement auctions. This paper explores a pattern of bribery between an auctioneer and a favored bidder, and also investigates the regulation scheme of buyer. In the model, the favored bidder is allowed to submit two bids simultaneously with the advantageous one to be announced; auctioneer decides the share of the difference between two bids which is the bribe transfer. The analysis shows that, the favored bidder does not participate in the corruption if his cost exceeds a threshold; otherwise he submits two bids whose difference is decreasing in the share. The corruption benefits both the auctioneer and the favored bidder but harms other bidders. The bribery endogenously leads to allocation inefficiency with a probability decreasing in the bribe share. Specifically, with two uniformly distributed bidders, we examine how the auctioneer optimizes the bribe share and how the buyer regulates the corruption. We find that, by driving the auctioneer to charge a higher bribe share that is less attractive for the favored bidder, severer regulation tends to reduce the probability of corruption. A buyer who adopts extremely severe regulation can exclude the corruption and achieve maximum social welfare, while a buyer who aims to maximize his own profit should tolerate some degree of the corruption.     

The government budget constraint with endogenous money

This paper examines the effectiveness and stability of fiscal policy in a model with a budget constraint and an endogenous money stock. This model avoids the need to treat only two polar cases, pure bond and pure money financing-neither of which is appropriate given the structure of the monetary system and the way monetary policy has been conducted historically. Furthermore, the model allows one to differentiate the effects of a money-financed deficit for the different tools of monetary control. We find that neither the long-run effectiveness nor stability of a mixed bond/money financed deficit is invariant to the monetary policy tool used.     

Asymmetric information about rivals' types in standard auctions: An experiment

This paper studies experimentally how information about rivals' types affects bidding behavior in first- and second-price auctions. The comparative static hypotheses associated with information about rivals enables us to test the relevance of such information as well as the general predictions of the auction theory, by providing an effective means to control for risk aversion and other behavioral motives that were difficult to control for in previous experiments. Our experimental evidence provides strong support for the theory, and sheds light on the roles of risk aversion and the spite motive in first- and second-price auctions, respectively.     

A near Pareto optimal auction with budget constraints

In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We also show that ex-post Nash equilibrium of our mechanism is near Pareto optimal in the sense that all full winners? values are above all full losers? values.     

Education and growth with endogenous debt constraints

When future human capital cannot be alienated, households are allowed to borrow up to the point where it is in their own interest not to default. In such a framework, endogenous borrowing limits arise as the outcome of individual rationality constraint. In a model where education is the engine of growth, we show that endogenous borrowing constraints imply global indeterminacy. Comparing outcomes across the various equilibria we show that the relation between growth and yields is hump-shaped. Maximum growth can arise in an equilibrium with binding borrowing constraints, specially if the elasticity of human capital to education spending is large. Deepening financial markets promotes long-run growth in the case of a poverty trap, but not necessarily otherwise. On the methodological side, our approach stresses the importance of studying borrowing limits in general equilibrium, not only in small open economies. Philippe Michel passed away on July 22, 2004. His death is a great loss for his friends and for the overlapping generations and optimal control community.     

Employee types and endogenous organizational design: An experiment

When managers are sufficiently guided by social preferences, incentive provision through an organizational mode based on informal implicit contracts may provide a cost-effective alternative to a more formal mode based on explicit contracts and active monitoring. This paper reports the results from a stylized laboratory experiment designed to test whether subjects in the role of firm owner rely on the social preferences of other (‘employee’) subjects with whom they are matched when choosing which payoff version of a simple trust game these employee subjects should play (‘the organizational mode’). Our main finding is that they do so, albeit in a different way than theory predicts. The importance of the first mover's social preferences for trusting behavior is recognized by the owner subjects, but the significant (first order) impact second movers’ social preferences have on trusting behavior of first movers seems to be overlooked.     

Asymmetric auctions with resale: An experimental study

We study auctions with resale based on Hafalir and Krishna's (2008) [6] model. As predicted, weak bidders bid more with resale than without, so that average auction prices tend to increase. When the equilibrium calls for weak types to bid higher than their values with resale they do, but not nearly as much as the theory predicts. In other treatments outcomes are much closer to the risk neutral Nash model's predictions. Bid distributions for weak and strong types are more similar with resale than without, in line with the theory.     

English auctions with resale: An experimental study

I design and test a simple English auction and two English auctions with resale, but with different informational backgrounds. All three treatments theoretically have the same equilibrium. I find, however, that the possibility of resale alters behavior significantly. In the two treatments with resale, subjects deviated from both the Nash prediction and the common results about bidding behavior in English auctions. Subjects tend to overbid, when they are certain they can reap the whole surplus in the resale market. I employ different models like QRE and levels of reasoning and conclude that overbidding can be explained as a rational response to the noisy environment in markets with human participants, that is, as rational decision making when anticipating others to make errors. When the outcome of the resale market is not certain, there is significant signaling behavior and auction prices tend to be lower than the Nash prediction.     

Intertemporal budget policies in an endogenous growth model with nominal assets

Intertemporal budget policies are assessed in an endogenous growth model with nominal assets. The paper provides relative rankings of policies and policy instruments in terms of the tax liabilities of the private sector necessary to guarantee intertemporal government budget solvency and in terms of the welfare of the representative agent. The role of nominal assets is shown to be of relative importance.     

Asymmetric common-value auctions with applications to private-value auctions with resale

We study a model of common-value auctions with two bidders in which bidders’ private information are independently and asymmetrically distributed. We present sufficient and necessary conditions, respectively, under which the expected revenues from first-price and second-price auctions can be ranked. Using these conditions and a bid-equivalence between common-value auctions and private-value auctions with resale, we extend the revenue-ranking result of Hafalir and Krishna [Am Econ Rev 98, 2008a] and provide necessary conditions for their ranking to hold. In addition, we provide sufficient and necessary conditions for the opposite ranking of revenues, respectively. Our analysis helps clarify the roles of two forms of regularity assumptions (buyer-regularity and seller-regularity) in ranking revenues and illustrates how revenue ranking is linked to submodularity and supermodularity of the common-value function and to a single-crossing property of a function derived from the monopoly or monopsony pricing function in the resale stage.     

Optimal education policies under endogenous borrowing constraints

This paper studies optimal education policies under endogenous borrowing constraints in a standard life-cycle model. In a closed economy, a policy that appropriately bundles an education subsidy with an old-age pension can restore the complete market allocation. Such a policy also removes persistent indeterminacies and endogenous fluctuations that exist in its absence. In a small open economy, a similar policy may restore the complete market allocation for a wide range of parameters, a range much wider than previously believed. These results broaden the rationale for a two-armed welfare state (education and pension) to a large class of economies.     

Scheduling with package auctions

In scientific collaborations, technologies have broadened access to scarce scientific and engineering resources. While broader access is often applauded, little attention has been focused on the problem of efficient and equitable resource allocation. This paper presents laboratory experiments designed to compare different allocation mechanisms for access to joint research facilities. Specifically, we study the Vickrey-Clarke-Groves (VCG) auction, a simultaneous ascending auction (the Resource Allocation Design, RAD), and a mechanism based on submitted rankings (Knapsack). Experimental results show that RAD and VCG are both more efficient than Knapsack, while Knapsack achieves a more equal distribution of resources than RAD or VCG. The findings highlight the need for systematic exploration of allocation mechanisms within collaboratories.     

An incremental budgeting model of local public expenditure setting in the presence of piecewise linear budget constraints

This Paper develops and tests an incremental budgeting model of local government expenditure decisions using data on British local government. The model introduces two distinctive feautures into the incremental budegeting literature. Firstly, it takes explicit account of the availability of an independent source of revenue for jurisdictions (in this example, a local property tax). And secondly it shows how it is possible to develop satisfactory emperical models when budget constraints are only piecewise linear. The model is shown to perform well, both in explaining within-year variability in budgeting decisions, and in predicting subsequent budgets under revised budget constraints.     

Soft budget constraints and the property rights theory of ownership

Modeling the government make-or-buy decision, Hart and colleagues [Hart, O., Shleifer, S. and Vishny, R.W., 1997, The proper scope of government: Theory and an application to prisons, Quarterly Journal of Economics 112, 1127–1161] assume government providers are exogenously more replaceable than private providers. Instead, we posit government managers' soft incentives arise endogenously from their lack of control rights, because of rationally softer budget constraints.