This article is from WeChat official account:Economic Observer Observer (ID: eeoobserver), author: Chen Yongwei, title figure from: vision China
At around 2 am on October 12th, U.S. Western time, a person in Palo Alto, California (Palo Alto) was wearing pajamas The old man hurried across the street and rang his neighbor’s doorbell. While pressing, shout: “Paul, open the door, you won the Nobel Prize! They want to contact you, but they can’t get through your phone!”
The neighbor could hardly believe what the old knocker said, and asked carefully: “Really? I won the Nobel Prize?”
“Yes, Paul, congratulations! You took it!” The old knocker replied affirmatively.
Hearing the old man’s confirmation, the neighbor was suddenly ecstatic. After a while, he suddenly remembered and asked the old man: “Is it only me? Without you?”
After listening to these words, the old knocker smiled, because he was indeed awarded the Nobel Prize just now, with his neighbor.
The old man knocking on the door is Stanford University professor emeritus, Robert Wilson(Robert Wilson) , And the neighbor who was awakened by his knock on the door was His former student and colleague, Stanford University professor Paul Milgrom(Paul Milgrom). Not long before the above scene, they were just announced by the Royal Swedish Academy of Sciences as the winners of the 2020 Nobel Prize in Economics. The reason for the award was “developed auction theory and invented newAuction method”.
Interestingly, although the 83-year-old Professor Wilson kept telling his good student Milgrom turned off his cell phone to sleep at such an important time as the Nobel Prize draw, he actually called him at the Nobel Prize Jury. At home, he also mistaken it for a harassing call and hung up. If Wilson’s wife hadn’t confirmed the news in time, then the pair of masters and apprentices knew that the time for their award might be delayed by several hours.
The so-called “wen has no first and Wu has no second”, since the development of economics, it can be said that there are many branches and factions. For every economist in the subdivisions, they have their own heroes in their hearts. Therefore, it is difficult to reach a broad consensus on who is the most powerful and qualified to win the Nobel Prize. It is for this reason that every year after the Nobel Prize is issued, some disputes arise. This phenomenon has been particularly prominent in recent years. For example, after the Nobel Prize was awarded to Banagher and Diflo last year, many economists directly said that they were not worthy of the Nobel Prize. Unlike previous years, After this year’s Nobel Prize was released, few people expressed dissent. Almost all people in the economics circle believed that this year’s two winners were well deserved.
The famous economist David Kreps(David Kreps) is known for his hot temper and dislikes compliments, but he After this year’s Nobel Prize was issued, he immediately sent a congratulatory letter to Wilson, one of the winners. In the congratulatory letter, he praised the achievements of the two men and called Wilson the founder of “Economics as Engineering”, thinking that his contribution was enough to match Paul Samuelson(Paul Samuelson) and Kenneth Arrow(Kenneth Arrow) and other economic giants, while Milgrom The achievement should be able to “get the Nobel Prize for his achievements in any research field.” In Kreps’ view, if there is anything wrong with this year’s Nobel Prize, it is that it is twenty years late.
Although as a student of Wilson and a fellow of Milgrom, Krepps’ above comments are inevitably mixed with personal likes and dislikes, but overall, his evaluation of the two winners is still very accurate. .
Wilson: a mathematician in business school
Wilson was born on May 16, 1937 in Nebraska in the Midwestern United States. Since childhood, Wilson has worked very hard in his studies. With excellent grades, he was successfully admitted to Harvard University after graduating from high school and won a full scholarship. In 1959, he graduated with a bachelor’s degree and received a bachelor’s degree, but instead of leaving Harvard, he entered Harvard Business School and continued his graduate studies. Since then, he received a Master of Business Administration (MBA) and a Doctor of Business Administration (DBA) degree.
During Wilson’s postgraduate years, his advisor was the famous applied mathematician Howard Raiffa(Howard Raiffa). For people nowadays, the name Leifa may be a bit strange, but at the time, it was a well-known character. Not only is he one of the founders of the decision science field, but he also wrote (Duncan Luce) with the famous mathematical psychologist Duncan Luce “Games and Decisions” (Games and Decisions). Within my knowledge, this book published in the 1950s should be the earliest game theory textbook. Of course, the content introduced in this book is mainly based on the von Neumann tradition, which is very different from the game theory we are now familiar with.
Under Rayfa’s guidance, Wilson received very rigorous mathematics training during graduate school. His doctoral dissertation discussed a very “hard core” problem-solving convex programming under nonlinear constraints by reusing quadratic programming. Although Wilson himself did not continue to engage in relevant research after graduation, the ideas in his doctoral thesis were inherited by people. After some improvements, the “sequential quadratic programming method” was formed.(Sequential Quadratic Programming Methods), which is the SQP often mentioned in operations research. So far, SQP is still the most common method to deal with convex programming problems.
After earning his doctorate, Wilson worked for a short period of time at the University of California, Los Angeles (UCLA). In 1964, he joined the Stanford University School of Business as an assistant professor. In 1971, he was promoted to professor, and then in 1976 he was awarded the “Atholl McBean Professor of Economics” (Atholl McBean Professor of Economics)< /span>, in 2000 he became “Adams Distinguished Professor of Management” (Adams Distinguished Professor of Management). Until his retirement in 2004, except for a few short visits, his research career was basically spent at Stanford.
Interestingly, from study to work, Wilson spent decades in business school. In the impression of many people, the research conducted by business school professors is relatively “soft”, but Professor Wilson has chosen a very “hard-core” research style, and perfectly combines the power of theoretical tools with the practicality of business schools. The needs are combined. This combination, as described by Kreps’s “engineer’s perspective of economics”, is probably the most appropriate.
It is very difficult to fully summarize Wilson’s achievements in economics. In fact, he has made great contributions to game theory, auctions, and competitive strategies. Here, we can only select some of them for introduction:
1. Research on “Syndicate”
Wilson’s first major theoretical contribution came from his paper “Syndicate” published in (Econometrica) in “Econometrics” in 1968. The Theory of “(The Theory of Sydicates)-Although in many introductions expounding Wilson, this contribution is not specifically listed, but in Some of Wilson’s own self-reports, as well as his students’ introduction to it, specifically mentioned it. It can be seen that for Wilson himself, This research has very important significance.
Everyone has seen the word “syndicate” in the political economy textbooks of middle school. There, it refers to a form of monopoly in which peer companies realize a monopoly through contracts. In Wilson’s context, the term “syndicate” has a different meaning, referring to a group of people who make joint decisions, obtain common results, and share under conditions of uncertainty.
In “Syndicate Theory”, Wilson tries to answer the following questions, under what circumstances will a syndicate make decisions like an independent person? When this happens, what will this syndicated utility function look like? How does it relate to the utility function of each person in the syndicate? The questions Wilson wants to ask are very theoretical, but they are very important to economics. We know that many analyses of economics are carried out on the basis of organizations. For example, when analyzing a company or a country, we use an anthropomorphic approach to look at them. This view has aroused criticism from many people. Especially scholars of the Austrian school are extremely opposed to this kind of analytical thinking.
In this context, Wilson’s question becomes very important, because it allows us to understand under what circumstances, this kind of analysis is applicable, and under what circumstances, Analysis ideas have limitations. Through analysis, Wilson pointed out that one condition for the establishment of the syndicate is that the members of the syndicate must judge the probability of the occurrence of the risk in a consistent manner, or in other words, each member must have “consistent alertness” to the risk.(identical cautiousness). Once the syndicate is established, the payment shared by each member will be consistent with the risk shared by it.
It should be pointed out that although the article “Syndicate’s Theory” seems very theoretical, the later development proves that the important conclusions in it have very important practical value. In fact, shortly after the publication of this article, the discipline of financial engineering began to flourish. In the process of designing financial products, people often encounter the problem of syndicates composed of different investors. When financial engineers pondered over these issues, they were surprised to find that Wilson had already pointed out the direction for solving the problems for themselves. In a commemorative article later written for him by several of Wilson’s students, he called the article “Syndicate Theory” “influencing a whole generation of economics, finance, and accounting.”
The article “Syndicate Theory” is also extremely important for the formation of Wilson’s entire research thinking. In this paper, he focused on the differencesThe problem of coordination and performance among judges, and his subsequent game theory research and related applications of the theory, to a certain extent, continue to think about similar issues.
2. Contributions to game theory theory
Since the 1970s, Wilson and his collaborators have made many pioneering contributions to game theory. Due to space limitations, only two are introduced here:
The first is the study of sequential equilibrium.
We know that John Nash(John Nash) is the founder of modern non-cooperative games, and his Nash equilibrium(Nash Equilibrium) is the basis of the entire game analysis. The so-called Nash equilibrium, in short, is an equilibrium in which each participant in the game sets an optimal response to all the strategies of other participants, and then these “optimal response strategies” form an equilibrium.
For example, two friends are going to eat out, but it is difficult for them to decide whether to eat Sichuan food or Cantonese food. Suppose that for two people, the important thing is to be with friends and it doesn’t matter what you eat. In other words, for everyone, if a friend eats Sichuan food, his best choice is to eat Sichuan food, and if a friend eats Cantonese food, his best choice is to eat Cantonese food. In this case, there will be two (pure strategy) Nash equilibriums in this game, that is, both eat Sichuan food, or both eat Lu dish.
From the above analysis, we can see that for a game, its Nash equilibrium may not be single. This is a huge trouble for those who analyze the game and predict the outcome of the game-in fact, when Nash proposed the concept of Nash equilibrium, von Neumann was very disapproving, and the reason may be that. It should be pointed out that what we have considered above is only a very simple and intuitive question.
In reality, the game is much more complicated than this example. It involves dynamic and asymmetric information. In this case, if you simply use the Nash equilibrium to analyze the game, the conclusion may not only be misleading , It may even be ridiculous. In order to deal with this problem, the study of game theoryThe author gives a lot of methods to “refine” the game, remove those unrealistic equilibriums, and leave useful equilibriums. For example, the so-called “perfect Nash equilibrium of subgames” and “trembling hands equilibrium” are all methods to refine the game.
In 1982, Wilson and Kreps proposed the concept of “Sequential Equilibria” (Sequential Equilibria) . Technically speaking, this concept is very complicated, but roughly speaking, it expresses such a meaning: In a game, everyone will have a pre-determined decision about who their opponent is and what strategy they will adopt. “belief”. What kind of strategy each person chooses in the game is essentially determined by this belief. However, as the game deepens, these beliefs will gradually change, so people’s corresponding strategies in subsequent games will also change accordingly. In such a scenario, if the equilibrium of the game is reasonable, then it must satisfy “sequential rationality”, that is, actions must be consistent with beliefs.
For example, when we first deal with a friend and think that he is an honest person, then we have to choose to treat others with sincerity, and if we find that he is actually a big fool as the relationship deepens, then we don’t Pay attention to him again. In this process, our beliefs must first change as his behavior changes. This is the consistency of beliefs with actions. Conversely, our follow-up actions must be adjusted according to changes in beliefs. This is the consistency of actions with beliefs. . If a Nash equilibrium satisfies sequential rationality, then it is a sequential equilibrium.
Although sequential equilibrium is a theoretical concept, it is very valuable in practice. Later, Wilson and his collaborators applied this theory to the analysis of specific problems and successfully solved a series of problems that plagued the economics community, such as the “chain store paradox” and “Coase conjecture”. Due to space limitations, it will not be expanded here.
The second is the so-called “KMRW” theorem.
In the field of economics, there is a famous “Gang of Four” whose members are Wilson, Milgrom, Kreps and Roberts(John Roberts). The reason why these four people are called together is because they often “make gangs” together to do research and write papers. The KMRW theorem, named after the initials of the four people, is the result of the “gang committing crimes” of these four people.
What does the KMRW theorem say? In layman’s terms, it explains why cooperation occurs. We know that when people work with others, they are not so happy. In order to maintain cooperation, they usually need to spend a lot of costs. But why are people willing to cooperate? People usually use repeated games to explain-because they are afraid that their uncooperative behavior will be retaliated in the future, they cooperate honestly. However, the knowledge of game theory tells us that this statement is difficult to establish. Since the game will always come to an end, at the moment of the end, everyone will find that self-interested and uncooperative behavior is more beneficial to them.
Now, let the time go back a bit. At this moment, if all players in the game expect that the game will end in the next moment, and no one will punish themselves for not cooperating, then he will immediately choose not to cooperate. If we use this “reverse induction” approach to push time forward, we will find that in the first second of the game, everyone will not cooperate.
So, how to solve the problem of cooperation? The explanation given by the “Gang of Four” in the game is that people can be disguised. In order to allow others to cooperate with themselves, people must pretend to be irrational. Once they find that the opponent has problems, they must be punished. In this way, all people will not know whether their opponent is a “rational person” who adjusts their strategies according to cost and benefit, or an “irrational person” who only accepts death and does not pay attention to benefits. In this way, at the beginning of the game, even the most “rational” people will maintain a cooperative treatment in order not to be punished and obtain higher returns.
3. Contributions to nonlinear pricing
The so-called non-linear pricing means that merchants do not use a one-to-one linear relationship between price and sales. In reality, our most common nonlinear pricing is the so-called “second type of price discrimination.” For example, in a supermarket, if we only buy one item, the price is often higher; and if we buy several items at once, we can enjoy a discount. Why do businesses want to set prices like this? The reason is that they don’t know the true preferences of consumers, so they discount more consumption and let high-demand consumers expose themselves by selling “information rent”. Nowadays, many people talk about “price discrimination”, especially anti-monopoly people, who hate price discrimination, but in fact they are very common in commercial practice and can effectively improve market operation efficiency .
Since the 1980s, Wilson has beenThe problem of non-linear pricing has been studied for a long time, and a monograph called “Non-linear pricing” was published in 1993, which systematically introduced many contents in this field. For space reasons, I only want to focus on one of the applications, that is, his research on capacity pricing. In reality, many industries are characterized by high fixed investment and low marginal costs. For example, in the information industry, the construction of infrastructure requires a huge investment. Once completed, the follow-up investment will be much lower. Those who operate these industries need to allocate the huge fixed costs of inputs to consumers, but how to allocate them is a problem.
In the 1985 paper “Capacity Pricing” (Capacity Pricing), Wilson and Oren (Shmuel Oren) and Smith (Stephen Smith) analyzed this issue together. They believe that this difficulty can be solved by distinguishing between “capacity asking price” and “service asking price”, where the asking price of production capacity is determined by the largest capacity, and the asking price of services can provide alternative solutions according to the different requirements of consumers for product quality. Price discrimination against them. After this plan was put forward, it was widely used by the industry and became a common plan to solve the problem of capacity pricing.
4. Contributions to the auction field
As early as the 1960s, Wilson began his research on auctions. The first paper he published was “Competitive Bidding under Asymmetric Information” on “Management Science” in 1967(Management Science)< span class="text-remarks" label="Note">(Competitive Bidding with Asymmetric Information). Although the theoretical contribution of this paper is far inferior to its follow-up research, it itself has updated the basic setting of Hessani’s game with incomplete information, thus contributing to the basic theory of game theory.
After entering the 1970s, Wilson conducted a systematic study of auction issues. In terms of contribution, he is leading the auctionThe achievements of the domain are embodied in several aspects: The first aspect is the study of common value auctions. The so-called common value auction is relative to the private value auction. As the name implies, private value means that each bidder’s valuation of the goods being auctioned is different, while common value auction means that each bidder has the same valuation of the lot, but it is limited by information before the auction starts. , They don’t understand the true value of the lot. Before Wilson, people usually only cared about private value auctions, and he was the first to analyze the problem of common value auctions, and compared the results of auctions under information symmetric and information asymmetric environments.
The second aspect is research on competitive auctions. He found that as bidders increase, the final auction price will converge to the true price of the product. This finding is not only a guide for auction theory, but also has a strong guiding significance for our understanding of market competition.
The third aspect is analysis of specific auction formats. Wilson analyzed many specific forms of auctions. For example, he analyzed double auctions, that is, auctions in which both buyers and sellers have a large number of bidders, and they are listed and traded through quotation (The stock market and the futures market use this kind of auction); in addition, he also compared the overall auction (Unit Auction) and Share the proceeds of the auction (Share Auction). We will continue to clarify this point.
Mirgrom: All-rounder in economic theory
Paul Milgrom was born in Detroit, Michigan, USA in 1948. Since childhood, he has been very interested in mathematics. In 1970, he graduated with honors from the University of Michigan and received a bachelor’s degree in mathematics. In 1978, he received a master’s degree in statistics from Stanford University. In 1979, he completed his doctoral thesis “Information Structure of Competitive Bidding” and obtained his PhD. His doctoral thesis later won the Savage Prize (Leonard Savage Prize).
After graduating from his Ph.D., Milgrom taught at the Department of Management Economics and Decision Science at the Kellogg School of Management at Northwestern University, and was promoted from assistant professor to professor. At this stage, he and his colleagues Roger Myerson (Roger Myerson), Bent Holmstrong (Bengt Holmstrom) has studied a lot of game theory and industrial organization issues together, and Myerson and Holmstrom have also been in 2007 and 2015. Won the Nobel Prize. In 1983, Milgrom moved to Yale University. After working there for four years, he returned to his alma mater in 1987 and has continued to this day.
Compared to Wilson, Milgrom’s research scope is broader and he has outstanding contributions in every field. As Kreps said, any of his contributions in these areas is worth a Nobel Prize. In fact, almost everyone in the economics circle believes that he should be at least more qualified than Myerson and Holmstrong to win the Nobel Prize first. But why did his Nobel Prize come so late? I am afraid it can only be explained by his charm. Because there has always been a gossip in the circle, saying that he has robbed his love and robbed a Nobel judge’s girlfriend, so he has been hidden for so long.
Here, I can only choose to introduce some of his contributions:
1. Contributions in the field of game theory
Milgrom’s contribution to game theory is tremendous.
The first is the study of repeated games. Milgrom has done a lot of research on repeated games. One of the achievements is the KMRW model that we mentioned earlier. He and Wilson and others completed the KMRW model. This model explains the establishment of reputation and pretending to be a tough “irrational person.” “The importance of cooperation. In addition to joint research with Wilson and others, Milgrom also worked with Abreu (Dilip Abreu), Pierce(David Pearce) and others have done a lot of cooperation. In a paper in 1991, they pointed out several factors that allow people to maintain lasting cooperation in cooperation, which is not only theoretically importantIt is also very valuable for guiding practice.
The second is game learning theory. In traditional game theory, what people pay attention to is the analysis of existing strategies. In fact, in the course of the game, people can continuously learn based on the opponent’s behavior and external information. Adjust your strategy. Therefore, in a relatively recent period of time, the theory of game learning has become a prominent subject. Before Milgrom, the game learning model only focused on the same game played repeatedly, and ignored a problem: the enlightenment effect of the gains of the previous stage of the game on the gains of the latter stage of the game. Based on this consideration, Milgrom and Roberts, one of the Gang of Four, examined a two-stage learning model and found that in this game, the sequential equilibrium and the adaptive equilibrium of learning reached a consistent result.
The supermodel game again (Supermodular Game). This is one of the issues that interests me the most among all Milgrom’s contributions. In the supermodel game, the participants are “strategy complementary”. In other words, the marginal utility caused by each participant’s increasing strategy increases as the opponent’s strategy increases. For example, we often talk about platform ecology. There are many apps in an ecosystem. How useful each app is depends on the quality of other apps. They are in a symbiotic relationship. In this game, there will be a phenomenon, that is, either everyone develops and the ecology is very prosperous, or everyone does not develop and the ecology is withered.
In fact, behind this phenomenon, it shows different balances, good balances and bad balances. So how do these equilibriums change? Traditional economics tools cannot explain, because traditional economics uses marginal analysis, which relies on the continuity of decision-making, and the changes in the game equilibrium are precisely discontinuous, so this method is invalid. In order to analyze this kind of problem, Milgrom and Roberts jointly developed the mathematician Tobics (Topkis) in 1978 Work and created a set of methods for analyzing supermodel games. Later, this method was introduced into system analysis by Aoki Masahiko and others, and it was widely used to explain system differences between different countries and regions.
2. Contributions to motivation theory and organization theory
Speaking ofMotivation and organization theory, Milgrom is also a figure that cannot fail to mention. His contributions in this area are roughly as follows:
The first is the motivation theory research conducted with Holmstrong. Holmstrong is also a student of Wilson. In fact, Wilson’s analysis of syndicate has taken into account the so-called “principle-agent”( Principal-agent problem), but he didn’t expand much. In his doctoral dissertation, Holmstrong has conducted an in-depth discussion on this issue and studied many methods for the principal to motivate the agent. Generally speaking, people later deal with the principal-agent problem under the framework of Holmstrong. However, the analysis in Holmstrong’s doctoral dissertation is rough. In his framework, the client has only one goal, which is obviously not in line with reality. In reality, the expectations of a leading opponent are often multifaceted.
For example, school leaders hope that teachers can both give lectures and post articles. How should incentives be provided under such “multitasking” conditions? Milgrom and Holmstrong answered this in a collaborative paper. They believe that in order to motivate agents to do better work under multitasking conditions, strong incentives should be used for those tasks that can be clearly measured, while weak incentives should be used for those that are difficult to clearly measure. This theory is of great guiding value to reality. This tells the bosses that KPI can be used to monitor physical work, but for some creative activities, employees should be given better play. In addition, Milgrom and Holmstrong have investigated many incentive issues in other studies, such as incentives using options or options. Due to space limitations, I will not repeat them here.
The second is research on organizational design with Roberts. In a sense, the most important contribution of Milgrom and Roberts on the issue of organizational design can actually be regarded as an application of supermodel game theory. In the process of organizational design, many factors are interdependent and mutually causal. Therefore, Milgrom and others pointed out that the complementarity between these factors must be considered when designing an organization, so that their positive factors Play better. This conclusion seems intuitive, but it is often overlooked in reality.
For example, many entrepreneurs often like to go to other companies to learn experience, and then come back to benchmark. This kind of acquisition seems to be very clever, but the so-called “Oranges born in Huainan are oranges, and those born in Huaibei are oranges.” Every experience of an enterprise is developed in a specific environment. If you ignore its productionThe condition of birth, if brought blindly, will often backfire. Of course, in addition to the above contribution, Milgrom and Roberts also conducted a lot of research on organizational theory. They wrote the textbook “Economics, Organization and Management” together. In my opinion, whether you are an economist or a management scholar, it is necessary to read this in-depth textbook.
3. Contributions to auction theory and practice
Although Milgrom has made outstanding contributions to many areas of economic theory, it is his contribution to auctions that really makes him famous. This is also the main reason why he won the Nobel Prize this time. However, to fully understand his achievements in auctions, we also need to have a relatively preliminary understanding of auctions and their theoretical development, so I will leave the relevant content behind.
Of course, in addition to the above contributions, Milgrom has also made contributions in many other areas. For example, he and Nancy Stokey(Nancy Stokey ) together, put forward the “no-trade theorem” in financial economics (no-trade theorem); with Robert Hall (Robert Hall) to research the labor market together; also with North (Douglas North) and Weingast (Barry Weingast) together investigated economic history. Due to space limitations, I won’t repeat it here.
The past and present of the auction
Etymologically speaking, auction (auction) is derived from the Greek augere, which means “increase”. As the name implies, it is a resource allocation method that allows bidders to continuously increase prices and decides the allocation of items based on the final offer.
ForFor the resource allocation method, auctions appeared very early. According to Herodotus’s “History” records, as early as 700 BC, Babylonians began to use auctions. However, some of the “commodities” they auctioned seem to be contrary to today. For example, they will auction brides, gather women of school age together, and let men bid. By the time of Ancient Rome, auctions had become very common. This commonality was not only reflected in daily life, but also appeared in the decision-making process of some major issues.
In 193 AD, the Forbidden Army of the Roman Empire mutiny and killed the then Emperor Pertinax (Pertinax). But the country cannot be without a king for a day, and who will be the emperor becomes a question. At that time, the Forbidden Army actually thought of determining the ownership of the throne through auction. In the end, a man named Didius Julianus (Didius Julianus) won the throne with a high price. But the good times did not last long. Soon after, the Forbidden Army mutiny again and killed Julianus. Later, someone joked that this may be the earliest “winner’s curse” in history (Winner’s Curse).
After the 17th century, European wealth began to grow rapidly, and the allocation of high-value items such as artworks and ships became a problem that needed to be solved. In this context, auction has gradually developed from a simple resource allocation method to a specialized industry, and many auction houses have emerged. Some of the auction houses we know now were actually born in that era. For example, Sotheby’s auction house was established in 1744, and Christie’s auction house was established in 1766.
It should be pointed out that auctions are by no means exotic. In ancient China, auctions were also widely used. Yang Liansheng, a well-known historian and professor at Harvard University, once inspected the “sing of clothes” from the Tang Dynasty to the Yuan Dynasty, that is, the auction of the relics of the dead monks. From Mr. Yang’s records, it is not difficult to see that the ancients really spent a lot of thought in designing these auctions. For example, in the Song Dynasty, it was necessary to preview in advance before “singing clothes”. The auction host needs to know the normal price of the lot in advance. When the price in the auction deviates from the normal price, he is responsible for reminding. From the perspective of modern auction theory, these practices can actually be understood to eliminate information asymmetry while preventing problems such as the “winner’s curse” from occurring.
In addition to the private sector, our country has also applied auctions to the public domain very early. For example, in the Song Dynasty, a system of “buying” was very popular, in which the ownership or management rights of wine shops, tax fields, river crossings, and salt wells were issued to private individuals through auctions. I once inspected this system with my students, and we were surprised to find that people in the Song Dynasty actually used double auctions in the process of “buying”.
In modern times, auctions have become more prosperous. Many people believe that auctions can only take place in auction houses, and the commodities involved are mainly artworks and cultural relics. This understanding is obviously wrong. In fact, the current auctions can be conducted either in the auction house, outside the auction house, or even online. For example, we can buy a lot of goods on eBay, and on Alibaba’s auction platform, you can even buy houses through auctions.
It should be pointed out that In addition to these explicit auctions, auctions are also used in many scenes that seem to have nothing to do with auctions. For example, in the electricity market, power supply companies will determine the allocation of electricity through auctions. In the stock market, stock trading is essentially a high-frequency auction. In the Internet field, auctions are used more. Whether it is shopping sites that determine the configuration of booths or search engines selling keywords, auctions will be used in this configuration method.
I think it’s most appropriate to use a sentence from the Nobel Prize Jury to evaluate the application of auctions now: Nowadays, auctions are everywhere.
Auction Theory: A Minimalist History
Although the practice of auctions has lasted for thousands of years, it was the 1960s that really used economic theories to study auctions. In 1961, Vickery (William Vicrey) in a classic paper discussed the four most widely used single-item auctions Auction format.
British auction: Bidders bid from low to high, and the highest bidder wins.
Dutch auction: The auction of the lot is from high to low until a bidder expresses its acceptance.
First-order sealed price auction: Bidders write their own quotations in the envelopes, and the highest quotation gets the price and pays the price.
Second-order sealed price auctionSelling: The bidders write their own quotations in the envelopes. The highest quotation is awarded, but only the price quoted by the second highest quotation is paid.
In this paper of less than 30 pages, Vickery came to a landmark conclusion for modern auctions-“Theorem of income equivalence“, that is, in single-item auctions If all the bidders’ ratings for the lot are given independently, then no matter what auction format is used, the auctioneer can get the same expected income. In addition, Vickery also came to an important conclusion: in the second-order sealed price auction, all bidders will quote honestly, that is, how high the evaluation of the lot is, the higher the price will be quoted; and the first-order sealed price auction However, the bidder’s offer may be far below their true evaluation level of the item.
The intuition of this conclusion is very simple. When a first-order sealed price auction is used, if the bidder bids according to his true evaluation of the item, it will not be profitable even if it wins the auction. In order to obtain possible benefits, bidders have incentives to quote prices that are far lower than their true evaluation. This problem can be well overcome in the second-order sealed price auction. This achievement of Vickery won him the Nobel Prize, but unfortunately, he died unexpectedly before receiving the award.
After Vickery, a large number of scholars began to pay attention to auction theory. Among them, Roger Myerson is particularly worth mentioning. He used the newly developed mechanism design theory to study the common value auction proposed by Wilson. Through rigorous mathematical derivation, it is concluded that all possible auction mechanisms will bring the same expectations to the auctioneers under a series of assumptions that the bidders’ evaluations of the items are mutually independent and the bidders only care about their own expected returns. income.
Obviously, this conclusion goes beyond the previous research ideas of scholars such as Vickery on the income of specific auction forms, and can study all possible auctions, which greatly advances auction theory. In addition, Myerson also analyzed the “Winner’s Curse” issue. Since information is continuously disclosed during the auction process, when someone finally wins the auction, he knows that the item he has bought may not be worth his original valuation. As a result, the “curse” is born.
However, Myerson’s research still has problems. In fact, the establishment of the “return equivalence theorem” relies on many assumptions, the most critical of which is that all bidders’ evaluations of the lot are independently given. But in reality, this assumption is difficult to hold. The bidder’s evaluation of the lot depends not only on himself, but also has a major relationship with the evaluation of other bidders. When there is “relevance evaluation”, Myerson’s theory is no longer applicable, andThe auctioneer may increase its expected income through the design of the transaction mechanism.
Professor Milgrom was the first to study the auction mechanism with “relevant evaluation”. In 1982 and Weber (Robert Weber) co-authored thesis “Auction and Competitive Bidding Theory”(A Theory of Auctions and Competitive Bidding), Professor Milgrom constructed an analysis framework that deals with information, prices and auctioneer’s revenue when there is “relevant evaluation”. Based on their observation of auction practice, they suggested that the bidder’s valuation may be related, and a bidder’s higher evaluation of the lot can easily improve the evaluation of other participants.
So, auction can be understood as a display game (Revelation Game), any buyer’s offer will not only show his own evaluation of the item The information will also partially reveal the private information of other buyers. In this way, the amount of interest of the bidder mainly depends on the degree of private information. Once the information in the auction is revealed, bidders can guess each other’s possible bids, and in order to win the auction, they must quote a higher price. Therefore, for the auctioneer, the auctions that can bring him the highest expected return must be those private auctions that can most effectively weaken the bidder’s information.
In the literature of auction theory, this discovery by Milgrom is called the “connection principle“. Applying the “connection principle”, Milgrom analyzed various popular auction formats. In British auctions, the bids of bidders who withdrew from the auction earlier showed their information about the value of the item, and the auction price was linked to the valuation of all unwinning bidders, which could generate higher returns. In the second-order sealed price auction, the auction price is only linked to the bidder who has the second highest valuation of the lot, so the revenue generated is lower. In the Dutch auction and the first-order sealed price auction, since the prices have no connection, they will bring the auctioneer the minimum expected return.
This discovery by Milgrom gives a good explanation for the popularity of British auctions in China. In response to the “winner’s curse” and other issues discovered by Myerson, Milgrom also gave some solutions, such as disclosing information through multiple rounds of bidding, thereby reducing the occurrence of these problems. These ideas have been applied toLater he designed the auction.
Practice what you have learned: an auction designed with theory
It should be pointed out that although Wilson and Milgrom’s theory on auctions is very exciting, auctions are after all practical studies. What really reflects the value of these theories is their design of real auctions. In reality, they are all masters of auction design.
Wilson has helped the US government and many companies design auctions. His most famous design is to help the U.S. Department of the Interior design the auction of development rights for oil and gas plots on the continental shelf. At that time, the Ministry of the Interior had considered two options: overall auction and divided auction. The overall auction is easy to understand, that is, directly auction a plot to the person with the highest bid. In a split auction, a plot is divided into several parts, and then people are allowed to bid. At this time, each bidder can give a share that he is willing to buy at different prices, for example, if he buys all of 1 million, he buys 90% of 1.1 million. In the end, the auctioneer can sell the lot to them based on the quotations of all bidders.
The preferred method of the Ministry of the Interior is divided into auctions. The reason is simple. This seems to be more able to sell these plots. But after studying it, Wilson told the Department of the Interior that the possible price of this method may be much lower than the overall auction. The theory given by Wilson is very complicated, but we understand it intuitively like this: In essence, divided auctions are equivalent to giving each bidder more choices, allowing them to specify each marginal demand separately Willing to bid. In this way, they avoid the auctioneer’s “tying” of additional shares, thereby obtaining higher consumer surplus.
In contrast, in the overall auction, they will get a certain share at the price they want, while the other parts are “tied”, so their consumer surplus is less. Conversely, when the bidder’s income is more, the auctioneer’s income is less, so for the same product, the income from the auction will be less.
Milgrom is more active in the practice of auctions, even opened an auction website called Auctionomics (But it seems to be closed down). However, it is the American radio that he helped the Federal Telecommunications Commission (FCC) design for his most famous name.Spectrum license auction. In 1993, President Clinton signed a decree authorizing the FCC to auction spectrum licenses and requiring the first public auction within a year, while Milgrom participated in the auction design as a consultant.
The plan given by Milgrom for the FCC is a mechanism of “simultaneous up-bid auctions”: in each round of auctions, bidders bid separately for one or more spectrums they want to buy, and the bids are not public. of. At the end of each round of quotation, only the highest quotation of each spectrum is announced, and based on this, the starting price of each spectrum in the next round of auction is determined (for example, in the last round The highest price is based on a predetermined increase, such as 5% or 10% increase). After the start of the next round of auctions, the highest bid of the previous auction will remain until it is replaced by the updated highest bid. If no new higher bids appear, the auction ends.
This new auction mechanism is very suitable for the substitution of auctioned licenses. In the auction process, as the price rises, buyers whose bids for a certain spectrum have been surpassed by others may turn to bidding for other licenses with lower current prices. At this time, alternate licenses will occur. Effective arbitrage between certificates. The more significant the substitution effect, the closer the auction prices of these licenses. These are all things that the traditional auction mechanism cannot achieve.
In the 1994 auction, after 5 days and 47 rounds of bidding, 10 licenses finally sold for a sky-high price of US$617 million, far exceeding the expectations of the US government. For this reason, the “New York Times” called this auction “the largest auction in history.”
write at the end
So far, the length of this introduction has far exceeded my expectations. Nevertheless, I still feel that these 10,000 words are not enough to summarize the contributions of the two Nobel Prize winners this year. Although today, when academic publications are rising, these two publications may not be comparable to some rising stars, but when it comes to the impact on theory and reality, there are probably few living economists who can match them.
A few words at the end: In the past few days, someone has been asking me what do you think is the biggest contribution of this year’s Nobel Prize winner. I thought for a long time, and now I finally found the answer. Compared with their own theories, in fact, their greater contribution is to train many outstanding students. Under Wilson, there are Holmstrong, Milgrom, Rose(Alvin Roth) and others established sects separately and won the Nobel Prize. Under the guidance of Milgrom, Susan Assi(Susan Athey), Joshua Gans(Joshua Gans)Wait for the outstanding new generation of economists. I think this kind of continuous inheritance is probably more important than any theory.
This article is from WeChat official account:Economic Observer Observer (ID: eeoobserver), author: Chen Yongwei