Alvin E. Roth

Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term*

We use simple learning models to track the behavior observed in experiments concerning three extensive form games with similar perfect equilibria. In only two of the games does observed behavior approach the perfect equilibrium as players gain experience. We examine a family of learning models which possess some of the robust properties of learning noted in the psychology literature. The intermediate term predictions of these models track well the observed behavior in all three games, even though the models considered differ in their very long term predictions. We argue that for predicting observed behavior the intermediate term predictions of dynamic learning models may be even more important than their asymptotic properties. Journal of Economic Literature Classification Numbers: C7, C92.

The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory

The organization of the labor market for medical interns and residents underwent a number of changes before taking its present form in 1951. The record of these changes and the problems that prompted them provides an unusual opportunity to study the forces at work in markets of this kind. The present paper begins with a brief history and then presents a game-theoretic analysis to explain the orderly operation and longevity of the current market, in contrast to the turmoil that characterized various earlier short-lived attempts to organize the market. An analysis is also given of some contemporary problems facing the market. A subsidiary theme of the paper concerns the history of ideas: the problems encountered in the organization of this market, and some of the solutions arrived at, anticipated the discussion of such issues in the literature of economics and game theory.

The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics

Economists have lately been called upon not only to analyze markets, but to design them. Market design involves a responsibility for detail, a need to deal with all of a markets complications, not just its principle features. Designers therefore cannot work only with the simple conceptual models used for theoretical insights into the general working of markets. Instead, market design calls for an engineering approach. Drawing primarily on the design of the entry level labor market for American doctors (the National Resident Matching Program), and of the auctions of radio spectrum conducted by the Federal Communications Commission, this paper makes the case that experimental and computational economics are natural complements to game theory in the work of design. The paper also argues that some of the challenges facing both markets involve dealing with related kinds of complementarities, and that this suggests an agenda for future theoretical research. Copyright The Econometric Society 2002.

The Economics of Matching: Stability and Incentives

This paper considers some game-theoretic aspects of matching problems and procedures, of the sort which involve matching the members of one group of agents with one or more members of a second, disjoint group of agents, ail of whom have preferences over the possible resulting matches. The main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences, and which produce stable matches.Two principal results are demonstrated. The first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences, even though procedures exist which accomplish either of these goals separately. The second result is that matching procedures do exist, however, which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences.

Learning in High Stakes Ultimatum Games: An Experiment in the Slovak Republic

In an ultimatum game experiment, financial incentives were varied by a factor of twenty-five. Consistent with prior results, changes in stakes had only a small effect on play for inexperienced players. However, rejections were less frequent the higher the stakes and proposals in the high stakes declined slowly as proposers gained experience. The lower rejection frequency when stakes were higher can be explained by the added power of multiple observations per subject in this experiment. A model of learning suggests that the lower rejection frequency is the reason proposers in higher stakes learn to make lower offers.

The Shapley value : essays in honor of Lloyd S. Shapley

Preface 1. Introduction to the Shapley value Alvin E. Roth Part I. Ancestral Papers: 2. A value for n-person games Lloyd S. Shapley 3. A method for evaluating the distribution of power in a committee system Lloyd S. Shapley and Martin Shubik Part II. Reformulation and Generalizations: 4. The expected utility of playing a game Alvin E. Roth 5. The Shapley-Shubik and Banzhaf power indices as probabilities Philip D. Straffin, Jr. 6. Weighted Shapley values Ehud Kalai and Dov Samet 7. Probabilistic values for games Robert James Weber 8. Combinatorial representations of the Shapley value based on average relative payoffs Uriel G. Rothblum 9. The potential of the Shapley value Sergiu Hart and Andreu Mas-Colell 10. Multilinear extensions of games Guillermo Owen Part III. Coalitions: 11. Coalitional value Mordecai Kurz 12. Endogenous formation of links between players and the coalitions: an application of the Shapley value Robert J. Aumann and Roger B. Myerson Part IV. Large Games: 13. Values of large finite games Myrna Holtz Wooders and William R. Zame 14. Payoffs in nonatomic economics: an axiomatic approach Pradeep Dubley and Abraham Neyman 15. Values of smooth nonatomic games: the method of multilinear approximation Dov Monderer and Abraham Neyman 16. Nondifferentiable TU markets: the value Jean-Francois Mertens Part V. Cost Allocation and Fair Division: 17. Individual contribution and just compensation H. P. Young 18. The Aumann-Shapley prices: a survey Yair Tauman Part VI. NTU Games: 19. Utility comparison and the theory of games Lloyd S. Shapley 20. Paths leading to the Nash set Michael Maschler, Guillermo Owen and Bezalel Peleg.

The New York City High School Match

We assisted the New York City Department of Education (NYCDOE) in designing a mechanism to match over 90,000 entering students to public high schools each year. This paper makes a very preliminary report on the design process and the first year of operation, in academic year 2003–2004, for students entering high school in fall 2004. In the first year, only about 3,000 students had to be assigned to a school for which they had not indicated a preference, which is only 10 percent of the number of such assignments the previous year. New York City has the largest public school system in the country, with over a million students. In 1969 the system was decentralized into over 30 community school districts. In the 1990s, the city began to take more centralized control (Mark Schneider et al., 2000), and in 2002, a newly reorganized NYCDOE began to reform many aspects of the school system. In May 2003, Jeremy Lack, then the NYCDOE Director of Strategic Planning, contacted one of us for advice on designing a new high-school matching process. The NYCDOE was aware of the matching process for American physicians, the National Resident Matching Program (Roth, 1984; Roth and E. Peranson, 1999). They wanted to know if it could be appropriately adapted to the city’s schools. The three authors of the present paper (and, at several crucial junctures, also Tayfun Sonmez) advised (and often convinced) Lack, his colleagues (particularly Elizabeth Sciabarra and Neil Dorosin), and the DOE’s software vendor, about the design of the match. I. The Prior (2002–2003) New York City Matching Procedure

The Shapley Value

Preface 1. Introduction to the Shapley value Alvin E. Roth Part I. Ancestral Papers: 2. A value for n-person games Lloyd S. Shapley 3. A method for evaluating the distribution of power in a committee system Lloyd S. Shapley and Martin Shubik Part II. Reformulation and Generalizations: 4. The expected utility of playing a game Alvin E. Roth 5. The Shapley-Shubik and Banzhaf power indices as probabilities Philip D. Straffin, Jr. 6. Weighted Shapley values Ehud Kalai and Dov Samet 7. Probabilistic values for games Robert James Weber 8. Combinatorial representations of the Shapley value based on average relative payoffs Uriel G. Rothblum 9. The potential of the Shapley value Sergiu Hart and Andreu Mas-Colell 10. Multilinear extensions of games Guillermo Owen Part III. Coalitions: 11. Coalitional value Mordecai Kurz 12. Endogenous formation of links between players and the coalitions: an application of the Shapley value Robert J. Aumann and Roger B. Myerson Part IV. Large Games: 13. Values of large finite games Myrna Holtz Wooders and William R. Zame 14. Payoffs in nonatomic economics: an axiomatic approach Pradeep Dubley and Abraham Neyman 15. Values of smooth nonatomic games: the method of multilinear approximation Dov Monderer and Abraham Neyman 16. Nondifferentiable TU markets: the value Jean-Francois Mertens Part V. Cost Allocation and Fair Division: 17. Individual contribution and just compensation H. P. Young 18. The Aumann-Shapley prices: a survey Yair Tauman Part VI. NTU Games: 19. Utility comparison and the theory of games Lloyd S. Shapley 20. Paths leading to the Nash set Michael Maschler, Guillermo Owen and Bezalel Peleg.

The Boston Public School Match

After the publication of “School Choice: A Mechanism Design Approach” by Abdulkadiroglu and Sonmez (2003), a Boston Globe reporter contacted us about the Boston Public Schools (BPS) system for assigning students to schools. The Globe article highlighted the difficulties that Boston’s system may give parents in strategizing about applying to schools. Briefly, Boston tries to give students their firstchoice school. But a student who fails to get her first choice may find her later choices filled by students who chose them first. So there is a risk in ranking a school first if there is a chance of not being admitted; other schools that would have been possible had they been listed first may also be filled. Valerie Edwards, then Strategic Planning Manager at BPS, and her colleague Carleton Jones invited us to a meeting in October 2003. BPS agreed to a study of their assignment system and provided us with micro-level data sets on choices and characteristics of students in the grades at which school choices are made (K, 1, 6, and 9), and school characteristics. Based on the pending results of this study, the Superintendent has asked for our advice on the design of a new assignment mechanism. This paper describes some of the difficulties with the current mechanism and some elements of the design and evaluation of possible replacement mechanisms. School choice in Boston has been partly shaped by desegregation. In 1974, Judge W. Arthur Garrity ordered busing for racial balance. In 1987, the U.S. Court of Appeals freed BPS to adopt a new, choice-based assignment plan. In 1999 BPS eliminated racial preferences in assignment and adopted the current mechanism.

Late and Multiple Bidding in Second Price Internet Auctions: Theory and Evidence Concerning Different Rules for Ending an Auction

In second price Internet auctions with a fixed end time, such as those on eBay, many bidders submit their bids in the closing minutes or seconds of an auction. We propose an internet auction model, in which very late bids have a positive probability of not being successfully submitted, and show that late bidding in a fixed deadline auction can occur at equilibrium in auctions both with private values and with uncertain, dependent values. Late bidding may also arise out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of late bidding are severely attenuated in auctions that apply an automatic extension rule such as auctions conducted on Amazon. Field data show that there is more late bidding on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding.