This paper provides an elementary, non-technical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthcoming.); We begin with the most fundamental concepts, and then introduce the basic analysis of optimal auctions, the revenue equivalence theorem, and marginal revenues. Subsequent sections address risk-aversion, affiliation, asymmetries, entry, collusion, multi-unit auctions, double auctions, royalties, incentive contracts, and other topics. Appendices contain technical details, some simple worked examples, and a bibliography for each section.

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Auction Theory: A Guide to the Literature

We examine who the winners are in science problem-solving contests characterized by open broadcast of problem information, self-selection of external solvers to discrete problems from the laboratories of large research and development intensive companies, and blind review of solution submissions. Analyzing a unique data set of 166 science challenges involving over 12,000 scientists revealed that technical and social marginality, being a source of different perspectives and heuristics, plays an important role in explaining individual success in problem solving. The provision of a winning solution was positively related to increasing distance between the solver's field of technical expertise and the focal field of the problem. Female solvers---known to be in the “outer circle” of the scientific establishment---performed significantly better than men in developing successful solutions. Our findings contribute to the emerging literature on open and distributed innovation by demonstrating the value of openness, at least narrowly defined by disclosing problems, in removing barriers to entry to nonobvious individuals. We also contribute to the knowledge-based theory of the firm by showing the effectiveness of a market mechanism to draw out knowledge from diverse external sources to solve internal problems.

http://www.eecs.harvard.edu/cs286r/courses/fall10/papers/JL09.pdf

Marginality and Problem-Solving Effectiveness in Broadcast Search

In an innovation contest, a firm (the seeker) facing an innovation-related problem (e.g., a technical R&D problem) posts this problem to a population of independent agents (the solvers) and then provides an award to the agent that generated the best solution. In this paper, we analyze the interaction between a seeker and a set of solvers. Prior research in economics suggests that having many solvers work on an innovation problem will lead to a lower equilibrium effort for each solver, which is undesirable from the perspective of the seeker. In contrast, we establish that the seeker can benefit from a larger solver population because he obtains a more diverse set of solutions, which mitigates and sometimes outweighs the effect of the solvers' underinvestment in effort. We demonstrate that the inefficiency of the innovation contest resulting from the solvers' underinvestment can further be reduced by changing the award structure from a fixed-price award to a performance-contingent award. Finally, we compare the quality of the solutions and seeker profits with the case of an internal innovation process. This allows us to predict which types of products and which cost structures will be the most likely to benefit from the contest approach to innovation.

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Innovation Contests, Open Innovation, and Multiagent Problem Solving

What is the optimal number of entrants in a race, or the optimal number of teams in a baseball league? What is the optimal structure of prizes for a golf tournament, or degree of revenue sharing for a football championship? How evenly balanced should the competing teams be in the NASCAR or Formula One championships? What is the maximum number of entrants per nation to the Olympic Games that should be permitted? What quota of qualifying teams to the soccer World Cup should be allocated to the developing nations?

https://pennstatelaw.psu.edu/_file/Sports%20Law%20Policy%20and%20Research%20Institute/Szymanski%20Economic%20Design%20of%20Sports%20Contests_JEL%20published%20version.pdf

The Economic Design of Sporting Contests

This chapter summarizes the recent literature on peer effects in student outcomes at the elementary, secondary, and post-secondary levels. Linear-in-means models find modest sized and statistically significant peer effects in test scores. But the linear-in-means model masks considerable heterogeneity in the effects experienced by different types of students. Using nonlinear models, one prevalent finding is larger peer effects in which high ability students benefit from the presence of other high ability students. Studies that stratify students by race and ability often find that students are affected both by the racial composition of their peers and by the achievement of their same-race peers. At the university level, several studies find modest sized effects from dormmate and roommate background on own academic performance. For both university and high school students, the measured peer effects on “social” outcomes such as drinking are larger than the effects on academic outcomes. Many authors find substantial peer effects in drinking, drug use, and criminal behavior. This chapter suggest areas for future investigation and data collection.

Peer Effects in Education: How Might They Work, How Big Are They and How Much Do We Know Thus Far?

We estimate peer effects in college achievement using a data set in which individuals are exogenously assigned to peer groups of about 30 students with whom they are required to spend the majority of their time interacting. This feature enables us to estimate peer effects that are more comparable to changing the entire cohort of peers. Using this broad peer group, we measure academic peer effects of much larger magnitude than found in previous studies. The effects persist at a diminished rate into follow‐on years, and we find evidence of nonlinearities in the magnitude of the effects across student academic ability.

/pdf/does-your-cohort-matter-measuring-peer-effects-in-college-1gt4diw9yd.pdf

Does Your Cohort Matter? Measuring Peer Effects in College Achievement

A research tournament model with heterogeneous contestants is presented. For a large class of contests the optimal number of competitors is two. This insight makes designing the tournament easier and highlights the importance of selecting highly qualified contestants. While customary uniform‐price and discriminatory‐price auctions are intuitively appealing mechanisms for solving this adverse selection problem, in practice they generally will not be efficient mechanism for selecting contestants. Instead, we propose an alternative auction format that is equally simple to implement and efficiently selects the most qualified contestants to compete, regardless of the form of contestant heterogeneity.

/pdf/auctionin-entry-into-tournaments-5cdnurijmf.pdf

Auctionin Entry into Tournaments

To estimate peer effects in college achievement we exploit a unique dataset in which individuals have been exogenously assigned to peer groups of about 30 students with whom they are required to spend the majority of their time interacting. This feature enables us to estimate peer effects that are more comparable to changing the entire cohort of peers. Using this broad peer group, we find academic peer effects of much larger magnitude than found in previous studies that have measured peer effects among roommates alone. We find the peer effects persist at a diminishing rate into the sophomore, junior, and senior years, indicating social network peer effects may have long lasting effects on academic achievement. Our findings also suggest that peer effects may be working through study partnerships versus operating through establishment of a social norm of effort.

A research tournament model with heterogeneous contestants is presented. For a large class of contests the optimal number of contestants is two. This insight makes designing the tournament easier and highlights the importance of selecting highly qualified contestants. While customary uniform-price and discriminatory-price auctions are intuitively appealing mechanisms for solving this adverse selection problem, in practice they generally will not be efficient mechanisms for selecting contestants. Instead, we propose an alternative auction format that is equally simple to implement and efficiently selects the most qualified contestants to compete, regardless of the form of contestant heterogeneity.

Auctioning Entry into Tournaments

This article explores theoretical and experimental implications of using auctions to reward winners of research tournaments. This process is a hybrid of the research tournament for a prize and a first-price auction held after the research is complete. The bids in the auction consist of a vector of both quality of the innovation and price. The experimental evidence supports the hypothesis that conducting auctions at the end of research tournaments will generally reduce the sponsor's prize expenditure relative to fixed-prize research tournaments. The potential importance of these results to the U.S. Department of Defense acquisition process is emphasized.

Richard L. Fullerton

Papers

Does Your Cohort Matter? Measuring Peer Effects in College Achievement

Auctionin Entry into Tournaments

Does Your Cohort Matter? Measuring Peer Effects in College Achievement

Auctioning Entry into Tournaments

Using Auctions To Reward Tournament Winners: Theory and Experimental Investigations