Robert B. Wilson


Robert Wilson

1. Overview at age 83

After rocky early years, I had a happy youth in a small town, and then stumbled through eight years at Harvard, emerging with little sense of what to do next, until I moved to Stanford where my research thrived. A minor project on adverse selection in auctions led me to join in the nascent reconstruction of economic theory using game-theoretic models, and then later, foundational topics in game theory, all focused on the role of agents’ information and their effect on incentives. I’ve enjoyed working with PhD students and been fortunate to have superb co-authors with better skills.

2. Youth: 1937–1955

I was born in Geneva Nebraska on 16 May 1937 to Robert Butler Wilson Sr. and Naoma Luella Norgren, the first of three sons, with my brother Charles following 13 months later in 1938, and then Timothy 4 years later.

My father Robert was born 5 May 1917 in Moore Montana, the youngest of three children of Clarence Wilson and Elizabeth Butler. Clarence was an unschooled mule trader from Missouri, descended from one of two brothers from Virginia who crossed the Appalachian Mountains circa 1820 to start farms in a stretch of fertile land along the Ohio River across from Tennessee, later called Wilson’s Bottoms. Elizabeth, the daughter of a prominent landowner in the small town of Geneva Nebraska, graduated summa cum laude from the University of Nebraska in 1902. They began their mismatched marriage by emigrating to Montana to homestead near Moore, starting from a sod hut to build a house and farm using her inheritance. They were ill-equipped to till rocky soil, and the farm was barely sustainable. When funds ran out, they moved back to Geneva circa 1929 to run a paint mill that Elizabeth inherited, but Clarence died a few days after I was born, and amid the great depression the paint mill went bankrupt in 1939.

My mother Naoma was born 25 December 1916 in York Nebraska, twenty miles from Geneva, the second of three daughters of Leonard Norgren and Grace May Muse. Grace descended from English stock with little trace of their origins. Leonard was the son of John Stahl Norgren and his wife Katherine, who married the same day in 1880 that he left the army as a medic and they emigrated from Kristianstad in Skåne County to settle in the Swedish-speaking small town of Ong Nebraska, ten miles from Geneva. They were successful farmers and all their ten children survived into adulthood. Later, my beloved ‘grandpa’ Leonard could still recite the Lord’s Prayer in Swedish. Leonard and Grace lived in York in near poverty through the great depression, sustained by a poultry supply business. Grace died early, cared for my mother Naoma.

Robert and Naoma married 23 August 1935, and settled in Geneva, where I was born two years later. My father clerked at the paint mill until it closed, and then we moved to the Montana farm, sharing the farmhouse for a year with his sister’s family, and then two years in Billings Montana, where my father was a salesclerk until the war started in 1941. With most men away at war, he got a good job in Lincoln Nebraska. We were mildly comfortable until he was drafted on Christmas day 1943. To cope with renewed penury, we moved to the farmhouse of Naoma’s younger sister near Ogallala Nebraska. I attended first grade in a one-room schoolhouse, and one day gleefully rode there on a horse. To ease our predicament, grandpa Leonard bought for us in 1944 a tiny house in York, where we lived for nine years until I was 16 and then moved to Lincoln in 1953. After his release from the Navy in 1946, my father was a candy salesman and then an insurance salesman, and later adamant that I become an insurance actuary rather than ‘waste’ my life in a university.

Bob and Chuck Wilson on bikes

Figure 1. Bob and Chuck Wilson on bikes, 1940s.

My childhood in York was wonderfully happy, usually playing with my brother Chuck, who was so close in age that we were like twins. We loved exploring the creeks, fields, and farms around York. Our mother was very loving, but she didn’t know how to handle boys and let us run wild. Chuck and I rode our bikes into the countryside to hunt, fish for bullheads and catfish, trap furry animals, and camp along Beaver Creek and the Blue River, all with minimal supervision. In the summers, we swam every day at York’s pool. In the evenings after the clouds broke on hot humid nights, we caught nightcrawler worms that we nurtured in dirt-filled boxes in the garage and sold as bait. My grandmother Elizabeth Wilson lived with us in the late 1940s and instilled a love of reading by often taking us to the library. We went to three double-bill movies each week, read hundreds of comic books, and played poker with pals. Chuck and I had been sneaking out with Dad’s rifle since I was 9 to hunt varmints like pigeons, crows, rabbits and squirrels, but by 12 I had bought my own rifle and shotgun and moved up to doves, pheasants, ducks, and geese. In a neighbor’s unused garage, we kept birds and animals we trapped for wildlife study. We mail-ordered pigeons (white kings, Russian trumpeters, pygmy pouters) that we raised with pride, and won prizes at the York County Fair. I raised angora rabbits to shear for wool, a ferret that eventually bit our mother, and families of orphaned opossums and owlets; and once I brought home a skunk that I mistakenly trapped while trying to catch mink, but alas it sprayed me thoroughly. We lived a carefree existence, rather like Tom Sawyer and Huck Finn.

I always had a job. From age 7, I delivered newspapers (even in blizzards), mowed grass, shoveled snow, bagged groceries, swept businesses’ walkways, and for two summers toiled in a bottling plant. One summer I managed the golfers’ clubhouse for my grandpa Leonard who had the concession. I excelled in football, basketball, and track until my right leg broke in a football game, but I continued basketball and golf to win a letter. The local schools were good, and I was always at the top of my class.

We were innocent of the economic struggles of our peers, except to know that some had less than we, and a few had more. An exception was my deep concern as a young boy for a kindly old lady with a broken hip who, before Medicare, suffered with little help until her death. After a severe concussion at age 14 in a playful melee I had vision and mood problems, retreated from social interactions, and became the school nerd with no steady girlfriend. Later I began anti-convulsive medication that cleared it away and I regained my old self.

In 1953 my father got a better job in Lincoln Nebraska and bought a nicer house. For two years I attended Lincoln High School, which was ten times the size of York’s, with better teachers and diverse courses, and was much more interesting and challenging. I was an exchange student in Giessen Germany for the summer of 1954, which was deeply stimulating after a childhood in insular small towns. In 1955 I graduated as salutatorian, and senior class president.

3. Education: 1955–1964

Urged by my mother, I applied for and won a prestigious General Motors National Scholarship to attend Harvard, but the stipend (set by Harvard, but GM would approve twice that amount) was so meager that at considerable risk I hitchhiked to and from Nebraska, and for four years I worked as library page, sold milk and donuts in the residence halls, and entered data at the computer center; and in summers, I sold ice cream and then insurance before real jobs as engineer on the Regulus missile and then actuarial trainee. At the end of my third year in 1958 I married my girlfriend Barbara Ferne Saylors, born 29 October 1937 in Hobart Oklahoma and then a student at Radcliff College from Albuquerque New Mexico, whose scholarship was so paltry that she had a board-and-room job, and then had to drop out after her second year. With her job at a local insurance company, we were more comfortable, but Harvard threatened discipline for marrying and living off-campus. We were in one of the first cohorts in Harvard and Radcliffe’s programs of ‘national distribution’ to diversify their students, but often the privilege of being there was outweighed by snobbery towards naive midwesterners who had not attended elite preparatory schools, and Barbara hated the sexism. I tried various majors (engineering, math, philosophy) but they were all unsatisfying, and some of the teaching was abysmal. Other than basic skills, little of it served me later.

Still, I thought I was lucky to be at the ‘the center of the universe’ (in the smug view that prevailed) and I had met Howard Raiffa, then in the statistics department but moving to the business school, so I applied to the doctoral program there, knowing that I had to meet their bizarre prerequisite of first completing the two-year MBA program. I borrowed funds, diligently pursued the program, got a citation for my high-grade average, and worked one summer as financial officer of a small insurance company in St. Paul Minnesota. But other than elective courses with John Lintner and Howard Raiffa it was a waste because the case method of teaching and insistence on an ‘administrative point of view’ were accompanied by abhorrence of theory and science generally. I was dismayed that most professors were ignorant and dismissive of the technical literatures of their fields. I came to view case studies as useful inputs to what should continue with deeper consideration of their implications and the construction of explanatory theory.

Undaunted, I entered the doctoral program in 1961 with a Ford Foundation Fellowship. I made the required field trips to companies, wrote the requisite number of cases, and eked through the mandatory ‘administrative point of view’ exam by faking it. Studies of decision theory with Howard Raiffa were superb. I took some courses in the economics department and studied applied math on my own to produce a dissertation about a new algorithm for constrained optimization. It would not have been finished without Howard’s intensive efforts to help me complete an acceptable version. At the end, I had a pregnant wife and two-year-old daughter Jennifer, born 14 May 1961, but no money, no car, and losing our apartment, so Howard gave me $1000 dollars to get us to UCLA for my first teaching job in June 1963. I always liked and admired Howard and remained deeply grateful that he mentored me and set me onto the path of my career.

At UCLA, Jacob Marshak was kind and supportive, and he loaned me another $1000 to tide me over the transition, but when, contrary to the letter of appointment, UCLA docked my pay for what they had previously paid to reimburse my moving expenses (eventually reversed by the president of the university), I was suddenly destitute, with Barbara about to deliver our second daughter Holly, born 10 December 1963, and the doctor requiring prepayment. So, I began consulting on reliability analysis at the RAND Corporation. It was wonderfully interesting due to discussions with Albert Madansky, and especially with Lloyd Shapley about game theory. I stayed at UCLA only one year because I learned that Howard Raiffa was visiting next year at Stanford’s business school, so I pleaded for and got a visiting appointment beginning July 1964 that was then continued with a regular appointment.

4. Early Career: 1964–1980

We lived in Palo Alto for 6 years and then moved to a house on campus that we built on a parcel leased from the university. I have happily stayed at Stanford for 56 years, always encouraged in my research. The travails to get to Stanford were worth it because Stanford is a perfect place. Palo Alto and the faculty housing on campus are pleasant communities with excellent schools for Jen and Holly, and dear friends. I liked biking, later walking, still later running to and from the university. There was endless joy in hiking in nearby parks, plus frequent backpacking and cross-country skiing in the Sierras with Barbara, Jen, and Holly. I had stimulating colleagues at the business school and elsewhere in the university, began lifelong friendships with Michael Harrison and David Kreps whom I esteemed, and had a nice lunch routine of Ping-Pong with students or chess with Mike. Barbara and Jennifer finished college at Stanford and loved it, including the absence of sexism. Tenure came effortlessly after only 4 years because it was awarded to counter an offer from Harvard initiated by Howard Raiffa. I was set for my life’s work as a scholar, which I relished, though I did serve 5 years as administrative director of the PhD program.

I was a passable teacher in basic MBA courses, but students’ evaluations often had 10% saying I was terrible and 10% saying I was excellent. Essentially, I taught to the segment having what I deemed intellectual curiosity, and this rankled some others. I had no regrets when I retired in 2004 from MBA teaching after 40 years, precipitated by a class where my style was disastrous. The elective courses I offered were more successful, and in later years a few former students, presumably in the 10%, said they were the best they took. Those courses (Multiperson Decision Theory, Competitive Strategies, and later one on Market Design) were my way of introducing strategic analysis into the MBA curriculum.

I loved PhD teaching. I regularly taught a first-year PhD course, and the advanced course Multiperson Decision Theory in which I presented current research in game theory and its applications; I’ve now taught it for 52 years. I liked working with talented young scholars, and we were blessed with many. Moreover, a series of fine students came to me from engineering and the economics department because I was doing research on what their departments were ignoring. My life feels fulfilled by their accomplishments and I am very proud that I had a role encouraging their early work. ‘Encouraging’ is the right word because my style was simply to help them pursue their interests. A great delight is that Alvin Roth, Bengt Holmström, and Paul Milgrom were awarded Nobel Prizes, but I am also elated by the success of three dozen others, including Robert Rosenthal, Jean-Pierre Ponssard, Claude d’Aspremont, Peter Cramton, Christopher Avery, Marciano Siniscalchi, Muhamet Yildiz, David Ahn, David McAdams, Jozsef Sakovics, Qingmin Liu, Yuval Salant, Ron Siegel, Yuliy Sannikov, …

At UCLA I had wasted the year working on sequential sampling and developing and distributing computer code for my optimization algorithm, which came to be called the quasi- Newton method or the Chen-Wilson algorithm, neither of which I published. At Stanford I made a slow start on a vague agenda to develop multiperson decision theory. My first work was about efficient risk sharing, and the second was about vote trading in legislatures, which led me to work on social choice theory in the style of Kenneth Arrow, with whom I often had stimulating conversations. My main contribution characterized social choice without one of Arrow’s assumptions. But I moved on because social choice theory in that style seemed to lead nowhere. I was much more interested in using the more promising tools of game theory, and indeed I had sustained an interest since my conversations with Lloyd Shapley at RAND and UCLA. A first contribution (never published but cited by Shapley and reproduced by von Stengel and others) was a simple example of a two-player game for which a pair of Nash equilibria cannot be found by the Lemke-Howson algorithm unless it starts with one of them, and then a second was a generalization of that algorithm to many-player games, published in the same issue of the SIAM journal as an alternative generalization by another author. In the meantime, I was also studying auctions, motivated by a case at HBS about bidding for offshore exploration leases. First, I took seriously the case situation that one bidder with an adjoining tract had superior information and made a poorly crafted attempt to characterize the mixed strategy of the bidder with inferior information, later solved in a better article by Milgrom and Weber. But a second article showed the effects of adverse selection in a symmetric game with both parties having imperfect information, later called the winner’s curse by Capen, that anticipated the later simulation results of Capen, Clapp, and Campbell that revolutionized how firms bid in such auctions. I then advised the brilliant PhD student Armando Ortega-Reichert on his excellent dissertation, which was never published but the working paper version affected subsequent research by many others.

My work on auctions led Bobby Abraham at Weyerhaeuser timber company to have me present a series of lectures, for which I also devised a set of short hypothetical cases to exemplify how game theory could be used. This work attracted the interest of Darius Gaskins at the U.S. Department of Interior who hired me as a consultant for studies of bidding for exploration leases that continued for several years. After 1978 I also consulted with oil companies on bidding strategies and in the process developed explicit models with practical applications to bidding. The culmination was an article that showed how with many bidders in a symmetric auction with bidders having imperfect information about a common value the winning bid could converge to the true value, which is the classic problem of ‘rational expectations’ or alternatively the ‘efficient markets hypothesis’ that the market-clearing price summarizes all participants’ information. My analysis was awkward because with my limited skills I had to assume that the support of bidders’ estimates moved monotonically with the unobserved true value – later results by Paul Milgrom were more general, and his work with Robert Weber established rigorous foundations for much of what is known about auctions. I also published a model of auctions of shares of a fixed supply that led to later models of double auctions with both buyers and sellers bidding. I showed that, when traders have unit demands or supplies and independent value distributions, a double auction is an incentive efficient mechanism if the number of traders is sufficiently large, but I was frustrated that I needed that proviso. I was especially interested in Chris Avery’s dissertation showing that an auction that allows jump bids has many equilibria with revenue outcomes spanning a wide range. Over the next decade I occasionally did other theoretical work on auctions, and related markets run via posted ask and bid prices, wrote several chapters published in books, and started but never finished my own book. In the 1990s I was absorbed by practical design of spectrum auctions with Milgrom and then consulting on the design of restructured wholesale markets for electric power. Besides rational expectations, which even now I work on with Paulo Barelli and Srihari Govindan, another continuing interest is showing that a double auction is an optimal mechanism.

During the 1970s and 1980s there were other influences. One began in 1978 with consulting at EPRI with Hung-po Chao and Shmuel Oren on retail pricing of electric power, especially priority service contracts to implement demand-side curtailment in periods of short supplies, and then EPRI’s support for preparation of a book on the general theory of nonlinear pricing. In 1967 I spent a term at CORE in Belgium where I got more involved in standard economics. I had learned little from the few economics courses I took, all of which assumed some version of general equilibrium theory’s focus on existence of prices that cleared markets, so I began to learn it for myself, and in my own way focused on strategic behavior and the role of agents’ private information. In 1971 I used a sabbatical to reside in the Stanford economics department (and kept an office there for 8 years) with very interesting colleagues such as Joseph Stiglitz and Michael Spence, and thereafter each summer to attend the series of IMSSS seminar series on economic theory organized by Mordecai Kurz. The attendees and their seminars were wonderfully stimulating, and I was greatly influenced by several fine scholars, especially Leonid Hurwicz who was developing his mechanism design approach to economic theory, and Robert Aumann and his colleagues from Israel who were doing the best work on game theory. It was a delightful way to get involved in the nascent reconstruction of economic theory by infusing it with models and methods drawn from game theory. I won a Guggenheim Fellowship and spent 1977–78 at the local behavioral sciences center but wasted it working fruitlessly on an integer programming algorithm, motivated by Herbert Scarf’s contemporaneous year-long visit to Stanford.

5. Late Career: 1980–2004

In 1978 my beloved associate dean Robert Jaedicke asked me to create a new economics group within the business school. This entailed hiring new faculty and our first hires were Ben Bernanke, Jeremy Bulow, Margaret Bray, and John Roberts, and later Anat Admati and Faruk Gül. It also meant creating new PhD courses and specifying requirements imposed on PhD students. We started right off with superb students and the new program was very successful and imitated elsewhere. Dave Kreps, Faruk Gül, and I did not actually join the new economics group until 5 years later when we were unanimously expelled from our old group, which then reverted to operations research and management.

In 1980 Dave Kreps returned from a sabbatical year in England eager to work on Reinhard Selten’s ‘Chain Store Game’. This led to our work on reputation effects in dynamic games with applications to entry deterrence and to the finitely repeated ‘prisoners dilemma’, the latter with Paul Milgrom and John Roberts; and then to our refinement of Nash equilibrium called sequential equilibrium, intended as a generalization of backward induction and easier to apply than Selten’s refinement called perfect equilibrium. This work was influential, and we were pleased with ourselves until a summer day in 1984 when Elon Kohlberg visited to tell us his and Jean-François Mertens’ criticism of our refinement on the grounds that it violated basic principles like invariance and forward induction. Kreps remained unmoved (and argued why in an article with In-Koo Cho) but I was deeply affected and spent much of later decades working with Srihari Govindan to remedy the defects, resulting ultimately in our axiomization of Mertens’ definition of stability. In the meantime, I had fun working with Faruk Gül and Hugo Sonnenschein, who were visiting for a year, on the Coase conjecture. This led to heightened interest in Peter Cramton’s dissertation that constructed a model of bargaining based on parties’ signaling their own values rather than screening through the other’s possible values; his model does not have the Coase property but better describes situations like a firm and union bargaining over wages. I did considerable work on bargaining without great success, except for a survey article written with John Kennan and a lecture published as one of the Schwartz Lectures at Northwestern.

6. Retirement: 2004–2021

After retiring in 2004 I continued teaching the two PhD courses and advising PhD students. But five years later the university banned emeritus faculty from being principal advisors on dissertations, which to my dismay diminished my student contacts.

I started working with Srihari Govindan on foundational game theory in 1995 and continue still in our search for the full implications of rationality in multi-person contexts. In one article we show that invariant sequential equilibria satisfy forward induction. A series of articles culminated in three axioms that characterize Mertens’ stable sets of Nash equilibria. That article was confined to extensive games with generic payoffs and two players, but recently it is extended to any number of players by strengthening the key axiom that excludes ‘framing effects’, and a slightly stronger axiom that characterizes essential sets of equilibria. Another recent result shows conditions for convergence, as the number of traders increases, of equilibria of asymmetric auctions and double auctions to a Walrasian ‘rational expectations’ equilibrium in which the clearing price identifies a hidden state. We also identify Walrasian equilibria that cannot be obtained as limits of equilibria of auctions.

We’ve also studied the infinitely repeated prisoner’s dilemma with alternating moves when the players have bounded recall. Our computational results show that the unique subgame-perfect outcome is perpetual cooperation when players’ recalls are no more than 4, but many attempts to prove that this is true for longer recalls has not yet succeeded.

7. Retrospective

My research in economics can be summarized by saying that I studied the effects of private information in markets, especially auctions, at a time when this was novel. My lasting contributions, neither about auctions, were co-authored with David Kreps and Srihari Govindan, on whom I relied for their superior skills and deep insights.

In 2020 the Sveriges Riksbank Prize in Economics Sciences in Memory of Alfred Nobel was awarded to Paul Milgrom and me. The diploma cites “improvements in auction theory and inventions of new auction formats”. In fact, the superbly talented Paul Milgrom, and his co-authors and descendants, proved the basic theorems that were the improvements in auction theory, and his genius produced the innovative features of the new designs of spectrum auctions. Earlier, I had provided formulations of various auction formats and studied examples, but I never proved a real theorem. I’ve been aware that my exploratory studies of auctions were influential among other researchers because they offered a new perspective that fit the growing interest in game theory as a tool for re-examining economic theory. So apparently, I shared the prize in my old age because my work as a youngster was influential (but never definitive) in the early stages of a process that has now matured.

I deeply value friendships with my colleagues Srihari Govindan and David Kreps, my former students Claude d’Aspremont, Peter Cramton, Bengt Holmstrom, Paul Milgrom, Jean-Pierre Ponssard, and Alvin Roth, and others I get to visit with less often. The plain fact is that I like and admire my students – including several I work with now.

Sadly, my wife Barbara died 6 March 2010 after 52 years of marriage. Since 23 March 2013 I am married to Mary Riemann, born 19 January 1957 in Sioux Falls, South Dakota. We are soulmates and supremely happy together. We share our love of nature, often hiking nearby and in the mountains.

I’ve had a wonderful life as a husband and father, and as a scholar and teacher. I was lucky to have it come to me accidentally.

Robert and Mary Wilson

Figure 2. Robert and Mary Wilson at the 2015 Frontiers of Knowledge Awards ceremony in 2016.

Copyright © The Nobel Foundation 2021

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