Bid Caps Research Articles

Invariant Equilibrium in Discontinuous Bayesian Games

We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is better-reply secure. The invariance property then provides an existence result for all Bayesian games in the class. Results are shown for both pure strategy and behavioral strategy equilibrium. We illustrate the application of the results with an example of a class of contests with bid caps.

Bid Caps in Noisy Contests

This paper studies optimal bid caps in a multiplayer noisy contest in which a higher bid does not guarantee a sure win. The bid cap can be either rigid or flexible. The former imposes outright bidding restrictions on players’ bids, while the latter taxes bids. A designer structures the bid cap to maximize a weighted sum between aggregate bid and tax revenue. Our analysis characterizes the optimum. A rigid bid is always outperformed by flexible ones, and a laissez-faire policy—i.e., no cap—is optimal when the designer maximizes the aggregate bid. The results also generate novel practical implications. (JEL C72, D44, D82)

Disclosure policies in all‐pay auctions with bid caps and stochastic entry: The impact of risk aversion

AbstractWe investigate how risk aversion affects the organizer's disclosing the actual number of bidders in an all‐pay auction with an exogenous bid cap and stochastic entry. With an exogenous probability of participation, the organizer prefers fully concealing the number of participating bidders when bidders are risk neutral. However, this result does not hold with risk aversion. Specifically, whether the organizer prefers fully concealing or fully revealing information depends on the number of potential bidders, the probability of participation, and the size of bid caps. A special case of endogenous entry shows that the organizer's preference is similar to the risk‐neutral case.

Disclosure Policies in All-Pay Auctions with Bid Caps

In this paper, we study the optimal disclosure of bidders’ types in a two-bidder all-pay auction in the presence of a common and exogenously given bid cap. We focus on the set of disclosure policies that are contingent on realizations of bidders’ types and fully characterize the unique symmetric equilibrium under each of them. We find that, allowing only for full disclosure and full concealment, the ex ante expected revenue is higher under full disclosure only for intermediate levels of the bid cap. Allowing also for partial disclosure policies: (i) the ex ante expected revenue under full disclosure is higher than under partial disclosure to low-type bidders but lower than under partial disclosure to high-type bidders, regardless of the bid cap; (ii) full concealment could rank from the highest to the third highest, depending on the bid cap, the prior type distribution, and the type values. These results are due to the different sensitivities of bidders’ bids across bidders’ types and disclosure policies.

Equilibrium existence in contests with bid caps

We prove equilibrium existence in distributional strategies for a general class of multiprize contests, including contests with bid caps. Contests with bid caps violate the assumptions of Reny’s (1999) equilibrium existence results as well as those of many other existence results. The equilibrium existence proof we provide for contests with bid caps refers to a special property of such contests, whereas the proof is much more straightforward for contests without a bid cap.

Demand response potential: An economic analysis for MIBEL and EEX

Day-ahead electricity markets were established based on the premise that short run price elasticity of demand is small, due to electricity importance, convenience and low cost. If demand respond to price signals through curtailing or shifting loads, spot prices are expected to decrease due to a more efficient market operation.This research aims to identify if there is a market design structure more suitable for Demand Response, specifically, regarding electricity markets either with or without bid caps or floor mechanisms. Results indicate that load flexibility in MIBEL would result in a larger number of hours in which is economically viable to perform demand response when comparing to EEX. Increasing flexible loads do not necessarily correspond to spot prices decrease and lower flexibility levels would produce a similar price variation. Moreover, years dominated by non-fossil technologies, negative prices, peak hours, week days and months with lower temperatures were found to decrease the economic potential. Results indicate that in during peak consumption hours the price volatility is lower, which may indicate a lower concurrency level among the generation companies. The research results contribute to improve the debate on policies, providing indications for the development of future energy market design structures.

Improving the cost-effectiveness of the Conservation Reserve Program: A laboratory study

The Conservation Reserve Program (CRP) is arguably the world's largest payments-for-ecosystem services program, with $1.8 billion paid to farmers in 2017 for practices on 23.4 million acres. The CRP uses a pay-as-bid, reverse auction with field-specific price caps to enroll most of the land in the program. Economic theory and empirical studies from other domains suggest that the restrictive price-cap auction format used in the current design of the CRP exhibits issues in terms of efficiency and cost-effectiveness. Using a laboratory experiment, we study the impact of varying the tightness of the price-cap auctions. We also examine two alternative auction formats based on reference prices. We find that excessively tight bid caps reduce efficiency and cost effectiveness by discouraging participation. Conversely, bid caps set too high also reduce cost-effectiveness by allowing higher rents. An exogenous reference price ranking format, which makes medium-cost sellers more competitive against low-cost sellers, reduces both efficiency and cost-effectiveness. An endogenous reference price format increases cost-effectiveness by increasing participation and reducing rents.

The cost-effectiveness of conservation auctions in the presence of asset specificity: An agent-based model

Payments for Environmental Services are a financial incentive for land users to conserve and restore ecosystems. One of the challenges in their implementation is to maximize their cost-effectiveness, or put in other words, to maximize the provision of environmental services for a given budget. This study focuses on two aspects that endanger the cost-effectiveness of such schemes: asymmetric information and asset specificity. If land users are better informed about their own provision costs, compared to the agency, they can increase their rents by demanding higher payments. The presence of asset specificity makes land users vulnerable to being harmed by opportunism. To compensate this risk, they could require higher payments or an exante compensation, likely to compromise compliance. Auctions are claimed to reduce informational rents by revealing land users’ true provision costs. However, their costeffectiveness has been shown to deteriorate if they are repeated over time because bidders can learn and adapt their strategies. Social interaction is particularly important in this context, as it allows land users to gather information on the bid cap; and it allows for trust building, which can substitute the costly formulation and enforcement of contracts, and thus reduce contracting costs. So far, there are only few studies analyzing the effect of asset specificity on the cost-effectiveness of auctions. Our study fills this gap using an agent-based model to analyze the cost-effectiveness of uniform and discriminatory one-shot and repeated auctions. In our model, land users are assumed to be embedded in a social network through which they can interact and learn. Our results suggest that repeated auctions can increase the cost-effectiveness of payments schemes in the presence of asset specificity despite of learning effects over time if land users face liquidity constraints and high time preferences.

Bid Caps and Disclosure Policies

We examine the effect of publicly disclosing or concealing bidders' types in an all-pay auction with a common bid cap. We call partial (full) disclosure policy the setup where the contest designer's disclosure policy is (not) contingent on type realization. Despite a bid cap possibly increasing the expected expenditures under a partial disclosure policy and the expected expenditures of low-types under a policy of full disclosure, the bid cap unambiguously decreases the expected total expenditures, regardless of the disclosure policy. For any given bid cap and allowing for full and partial disclosure policies, we find that expenditures are minimized with the policy in which a designer discloses bidders' types only if both players have a low valuation of the prize. The expenditures are maximized with the full concealment policy or with the policy in which a designer discloses the information only if both players have a high valuation. All in all, when the designer can choose both the disclosure policy and the bid cap, revenue is maximized employing full concealment with no bid cap.

Evaluating the Potential Contribution of Multi-Attribute Auctions to Achieve Agri-Environmental Targets and Efficient Payment Design

This paper analyses the performance of a multi-attribute auction for securing agri-environmental outcomes and cost-effective agri-environmental payments (AEPs). We set up a discriminatory price auction model in which farmers make an offer based on two attributes (i.e. the AEP and a proxy of environmental outcome). We provide a numerical simulation for a hypothetical agri-environmental scheme (AES) in Italy using FADN data 2011 for the Emilia-Romagna region (E-R). In three implementation scenarios, we compare the Budgetary cost-effectiveness (BCE), the Economic cost-effectiveness (ECE) and Information rent (IR) of the auction with that of two alternative policy instruments (i.e. uniform payment and marginal flat rate payment). Due to the heterogeneity in bidders' opportunity costs, the auction is more cost-effective than a uniform payment in delivering the target outcome. The performance indicators are sensitive to the farmers' expectations about the bid caps, revealing the opportunity of using both competition effect and information leverage associated with the implementation mechanism to increase the auction outcome when the budget is limited.

Disclosure policies in all-pay auctions with bid caps and stochastic entry

This paper examines the effects of disclosing the actual number of bidders in contests with stochastic entry and with resource constraint. We study an all-pay auction with complete information. The auction entails one prize and n potential bidders. Each potential bidder has an exogenous probability of participation and faces an exogenous bid cap. It is shown that the contest organizer prefers fully concealing the information about the number of participating bidders. We extend the result to a case with endogenous entry.

Disclosure Policies in All-pay Auctions with Bid Caps and Stochastic Entry

This paper contributes to the literature that examines the effects of disclosing the actual number of bidders in contests with stochastic entry by considering resource constraint. We study an all-pay auction with complete information. The auction entails one prize and $n$ potential bidders. Each potential bidder has an exogenous probability of participation and faces an exogenous bid cap. It is shown that the contest organizer prefers fully concealing the information about the number of participating bidders. We extend the result to a case with endogenous entry.

Revenue-Capped Efficient Auctions

Abstract We study an auction that maximizes the expected social surplus under an upper-bound constraint on the seller’s expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when (i) the auction designer is “pro-buyer”, that is, he maximizes the weighted sum of the buyers’ and seller’s auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multiunit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, “bunching” is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least “at the top,” that is, “no distortion at the top” fails.

Bid caps in large contests

We study the effect of rigid and flexible bid caps on contestants' aggregate costs and aggregate bids in all-pay contests with a large number of heterogeneous contestants and prizes.We show that rigid caps always decrease aggregate costs, whereas flexible caps have essentially no effect on aggregate costs. Rigid caps decrease aggregate bids when costs are linear or concave, but increase aggregate bids under some conditions when costs are convex. Flexible caps always decrease aggregate bids.

On the effects of bid caps in all-pay auctions

This paper analyzes the effects of a bid cap in an all-pay auction with incomplete information. I find that a non-trivial bid cap affects an agent’s expected payment in three ways: An “anti-competition effect” which is associated with this agent’s own signal, a pro-competitive “good news effect” which is associated with her opponents’ signals and which alleviates the winner’s curse, and an “inference effect” caused by affiliation of signals. Unlike the former two effects, the “inference effect” is a double-edged sword. It is anti-competitive when the cap is relatively low and pro-competitive when a cap is relatively high.

On The Effects of Bid Caps in All-Pay Auctions

This note analyzes the effects of a bid cap in an all-pay auction with incomplete information. I find that a non-trivial bid cap affects an agent's expected payment in three ways: An anti-competition effect which is associated with this agent's own signal, a pro-competition good news effect which is associated with her opponents' signals and which alleviates the winner's curse, and an inference effect caused by affiliation of signals. Unlike the former two effects, the inference effect'' is a double-edged sword. It is anti-competitive when the cap is relatively low and pro-competitive when a cap is relatively high.

Credit auctions and bid caps

In this paper we offer two contributions to the field of credit auctions. First, we compare first- and second-price credit auctions and provide solvency-dependent conditions such that one mechanism dominates the other in terms of expected payoffs of all the parties involved. In addition, we present a new possibility of using bid caps in credit auctions. We study the equilibria in the capped mechanisms and show that bid caps can increase the seller's expected payoff and, in some cases, the expected payoffs of all sides (a win–win situation).

Testbed Experiments for Improving the Cost-Effectiveness of the Conservation Reserve Program

The Conservation Reserve Program (CRP) is arguably the world’s largest payments-for-ecosystem services program, with $1.8 billion paid to farmers in 2017 for practices on23.4 million acres. The CRP uses a pay-as-bid, reverse auction with field-specific price caps to enroll most of the land in the program. Economic theory and empirical studies from other domains suggest that the restrictive price-cap auction format used in the cur-rent design of the CRP exhibits issues in terms of efficiency and cost-effectiveness. Using a laboratory experiment, we study the impact of varying the tightness of the price-cap auctions. We also examine two alternative auction formats based on reference prices.We find that excessively tight bid caps reduce efficiency and cost effectiveness by discouraging participation. Conversely, bid caps set too high also reduce cost-effectiveness by allowing higher rents. An exogenous reference price ranking format, which makes medium-cost sellers more competitive against low-cost sellers, reduces both efficiency and cost-effectiveness. An endogenous reference price format increases cost-effectiveness by increasing participation and reducing rents.

The US Conservation Reserve Program: The evolution of an enrollment mechanism

The United States Department of Agriculture’s Conservation Reserve Program (CRP) has evolved from near open enrollment, to competitive enrollment, and now to a mixture of competitive and targeted enrollment. This paper reviews the history of the CRP and the evolution of its enrollment mechanism. I discuss the use of bid caps and the Environmental Benefits Index bid ranking mechanism in the “general” CRP; and the use of highly targeted, but non-competitive, “continuous” CRP. Possible challenges of these designs are discussed, and alternative auction mechanisms are considered that could be more cost effective.

Common-value all-pay auctions with asymmetric information and bid caps

We study a class of two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent and both players are budget-constrained. We extend the results for all-pay auctions with complete information, and show that in our class of all-pay auctions with asymmetric information, sufficiently high (but still binding) bid caps do not change the players’ expected total effort compared to the benchmark auction without any bid cap. Furthermore, we show that there are bid caps that increase the players’ expected total effort compared to the benchmark. Finally, we demonstrate that there are bid caps which may have an unanticipated effect on the players’ expected payoffs—one player’s information advantage may turn into a disadvantage as far as his equilibrium payoff is concerned.