Paul Robert Milgrom (born April 20, 1948) is an American economist. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at the Stanford University School of Humanities and Sciences, a position he has held since 1987. He is a professor in the Stanford School of Engineering as well and a Senior Fellow at the Stanford Institute for Economic Research. Milgrom is an expert in game theory, specifically auction theory and pricing strategies. He is the winner of the 2020 Nobel Memorial Prize in Economic Sciences, together with Robert B. Wilson, "for improvements to auction theory and inventions of new auction formats".
He is the co-creator of the no-trade theorem with Nancy Stokey. He is the co-founder of several companies, the most recent of which, Auctionomics, provides software and services for commercial auctions and exchanges.
Milgrom and his thesis advisor Wilson designed the auction protocol the FCC uses to determine which phone company gets what cellular frequencies. Milgrom also led the team that designed the broadcast incentive auction between 2016 and 2017, which was a two-sided auction to reallocate radio frequencies from TV broadcast to wireless broadband uses.Incentive Auction Rules Option and Discussion September 12, 2012.
In 2024, Milgrom's firm, Auctionomics, won a technical Emmy Award for their contributions to spectrum auction design.
Early life and education Paul Milgrom was born in Detroit, Michigan, April 20, 1948, the second of four sons to Jewish parents Abraham Isaac Milgrom and Anne Lillian Finkelstein. His family moved to Oak Park, Michigan, and Milgrom attended the Dewey Elementary School and then Oak Park High School. Milgrom had a strong interest in math from a young age, which was fostered by his teachers. He attended the Ross summer math camp at Ohio State University in 1965, where he finished number one in his class.
Milgrom graduated from the University of Michigan in 1970 with a B.A. in mathematics. He worked as an actuary for several years in San Francisco at the Metropolitan Insurance Company and then at the Nelson and Warren consultancy in Columbus, Ohio. Milgrom became a Fellow of the Society of Actuaries in 1974. In 1975, Milgrom enrolled for graduate studies at Stanford University and earned an M.S. in statistics in 1978 and a Ph.D. in business in 1979.
Academic career Milgrom assumed a teaching position at the Kellogg School of Management at Northwestern University where he served from 1979 to 1983. At Northwestern, Milgrom was part of a group of professors including future Nobel laureates Roger Myerson and Bengt Holmstrom, along with Nancy Stokey, Robert J. Weber, John Roberts and Mark Satterthwaite that helped to bring game theory and information economics to bear on a wide range of problems in economics such as pricing, auctions, financial markets, and industrial organization.
Weber recounted his collaboration with Milgrom. During what was supposed to be a brief meeting to ponder a problem faced by Weber, Milgrom had a key insight. Weber wrote, "And there, in a matter of a few minutes, was the heart of our first two joint papers."
From 1982 to 1987, Milgrom was a professor of economics and management at Yale University. In 1987, Milgrom returned as an economics professor to his alma mater, Stanford University, where he is currently the Shirley and Leonard Ely Professor of Humanities and Sciences in the Department of Economics.
Milgrom held editorial positions at the American Economic Review, Econometrica and the Journal of Economic Theory. He became a Fellow of the Econometric Society in 1984, and the American Academy of Arts and Sciences in 1992. In 1996, he gave the Nobel memorial lectureProcuring Universal Service: Putting Auction Theory to Work, in Le Prix Nobel: The Nobel Prizes, 1996, Nobel Foundation, 1997, 382-392. honoring the laureate William Vickrey, who had died three days after the Nobel prize announcement. In 2006, Milgrom was elected to the National Academy of Sciences.
Awards and honors Milgrom received the Erwin Plein Nemmers Prize in Economics in 2008 "for contributions dramatically expanding the understanding of the role of information and incentives in a variety of settings, including auctions, the theory of the firm, and oligopolistic markets."
He won the 2012 BBVA Foundation Frontiers of Knowledge Award in Economy, Finance and Management category "for his seminal contributions to an unusually wide range of fields of economics including auctions, market design, contracts and incentives, industrial economics, economics of organizations, finance, and game theory."
In 2013, Milgrom was elected as Vice President of the American Economic Association. In 2014, he won a Golden Goose Award for his work involving auction design. In 2017, he won the CME Group-MSRI Prize in Innovative Quantitative Applications for his work in auction design. In 2020, he was appointed a Distinguished Fellow of the American Economic Association.
In October 2020, Milgrom was the co-recipient of the 2020 Nobel Memorial Prize in Economic Sciences with Robert B. Wilson. The Royal Swedish Academy of Sciences stated that it awarded the Nobel Memorial Prize jointly to Milgrom and Wilson because they "used their insights to design new auction formats for goods and services that are difficult to sell in a traditional way, such as radio frequencies. Their discoveries have benefitted sellers, buyers and taxpayers around the world." The citation went on to say:
Game theory Milgrom made several fundamental contributions to game theory in the 1980s and 1990s on topics including the game-theoretic analysis of reputation formation, repeated games, supermodular games and learning in games.
Reputation formation In an influential 1982 paper with David M. Kreps, John Roberts, and Robert B. Wilson (Kreps et.al., 1982), Milgrom showed that if one or both players have even a very small probability of being committed to playing tit-for-tat, then in equilibrium both players cooperate until the last few periods. This is because even an uncommitted player has an incentive to "build a reputation" for being committed to tit-for-tat, as doing so makes the other player want to cooperate. The Kreps-Milgrom-Roberts-Wilson "Gang of Four" paper launched an entire branch of the game theory literature on such "reputation effects."
Distributional strategies Milgrom's 1985 paper with Robert J. Weber on distributional strategies showed the general existence of equilibria for a Bayesian game with finitely many players, if the players' sets of types and actions are compact metric spaces, the players' payoffs are continuous functions of the types and actions, and the joint distribution of the players' types is absolutely continuous with respect to the product of their marginal distributions. These basic assumptions are always satisfied if the sets of types and actions are finite.
Repeated games Milgrom made a fundamental contribution to the theory of repeated games. When players' actions are hidden and noisy signals about their actions are observable (i.e., in the case of imperfect monitoring), there are two general ways to achieve efficiency. One way is to transfer future payoffs from one player to others. This is a way to punish a potential deviator without reducing the total future payoffs. The classical folk theorem result under imperfect monitoring is built on this idea. The second general method is to delay the release of information. Under the second method, the outcomes of the noisy signals are released in every T periods, and upon the release of information players "review" the signals in the last T periods and decide to punish or reward each other. This is now widely known as the "review strategy", and Milgrom's paper with D. Abreu and D. Pearce (Abreu, Milgrom and Pearce, 1991) was the first to show the efficiency of review strategy equilibrium in discounted repeated games. The review strategy turns out to be useful when players receive private signals about each other's actions (the case of private monitoring), and the folk theorem for the private monitoring caseSugaya, T. (2013), "The Folk Theorem in Repeated Games with Private Monitoring," mimeo, Stanford GSB. is built on the idea of the review strategy.
Supermodular games The theory of supermodular games is an important recent developments in economic theory. Key contributions to this theory include seminal work Topkis's Theorem, Vives (1990), and the Milgrom and Roberts (1990c).
The impact and importance of the theory of supermodular games came from its breadth of application, including search, technology adoption, bank runs, arms races, pretrial negotiations, two-player Cournot competition, N-player Bertrand competition, and oil exploration, and the economics of organizations (Milgrom and Roberts, 1990b).
Learning in games Milgrom and Roberts build on their work in supermodular games to understand the processes by which strategic agents reach equilibrium in a normal-form game. In Milgrom and Roberts (1991), they proposed two learning processes each with a degree of generality so as to not model learning but learning processes. They considered a sequence of plays over time which, for a player n, is denoted {xn(t)} where for each possible time, t, xn(t) is a pure strategy. Given this, an observed sequence, {xn(t)}, is consistent with adaptive learning if a player n eventually chooses only strategies that are nearly best-replies to some probability distribution over the joint strategies of other players (with near zero probability being assigned to strategies that have not been played for a sufficiently long time). By contrast, {xn(t)}, is consistent with sophisticated learning if the player eventually chooses only nearly best-replies to their probabilistic forecast of the choices of other players, where the support of that probability distribution may include not only past plays but also strategies that the players might choose if they themselves were adaptive or sophisticated learners. Thus, a sequence consistent with adaptive learning is also consistent with sophisticated learning. Sophisticated learning allows players to make use of payoff information that is used in equilibrium analysis but does not impose the fulfilled expectations requirement of equilibrium analysis.
With these definitions in place, Milgrom and Roberts showed that if a sequence converges to a Nash equilibrium or correlated equilibrium then it is consistent with adaptive learning. This gave a certain generality to those processes. They then showed how these processes related to the elimination of dominated strategies. This was shown to have implications for convergence in Cournot and Bertrand games.See also Gans, J.S. "Best Replies and Adaptive Learning," Mathematical Social Sciences, Vol.30, No.3, 1995, pp.221-234.Milgrom, P. and Roberts, J. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Vol.3, No.3, 1991, pp.82-100.
Comparative statics Milgrom's research has often highlighted the restrictiveness (and often superfluity) of these assumptions in economic applications. For example, in the study of modern manufacturing (Milgrom and Roberts, 1990b), one would like to focus on the complementarity or substitutability across production inputs, without making assumptions on scale economies or divisibility (through a concavity condition on the production function).