Robert Wilson was born in the United States in 1937 and received his bachelor's, master's and doctoral degrees from Harvard University in 1959, 1961 and 1963.

[Nobel Prize Special Topic] Robert Wilson's Academic Contribution to Contemporary Economics - Nobel Prize in Economics Winners' Review

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Robert Wilson

Robert Wilson (Robert Wilson)

Wilson was born in the United States in 1937 and obtained a bachelor's degree (mathematics), master's degree and doctoral degree from , Harvard University in 1959, 1961 and 1963 respectively. Since then, he has been teaching at Stanford University's Business School. Its main research areas are: general theory of economics, economics mathematical method , game theory and trading theory. He is an outstanding member of the American Federation of Economics and a bachelor of Economics at the National Academy of Sciences.

Wilson tried to use game theory as the basis to reconstruct economic theory, and used game theory to introduce phenomena that often occur in reality into economic theory, such as "strategic behavior", "informational disparities", dynamic adjustment of action, etc. The core issue it is concerned about is what impact each force has on " economic efficiency " in the transaction process (such as bargaining process, auction, inquiry process), signing contracts, and forming a company. In Wilson's view, the existing market theory only provides a lot of practical knowledge and has not yet established a perfect theory; in particular, since economists have not yet had an in-depth understanding of the product market and the factor market (especially the labor market), the true welfare economics has not been established. So Wilson tried to contribute in these areas.

To sum up, Wilson's most important contributions include the following three aspects: (1) Contributions regarding nonlinear pricing. Its "Nonlinear Pricing" published in 1993 has become an important reference book in the theoretical and business circles. (2) Sequential equilibrium idea. Together with Kreps (Kreps Wilson, 1982), he proposed the idea of ​​sequential equilibrium, which had a significant impact on game theory. They point out that when beliefs and behaviors are self-reinforcing, there will be multiple equilibriums in a game, and using the idea of ​​sequential equilibrium, meaningful equilibrium can be found from multiple equilibriums. (3) Contributions related to auction theory. Its research on competitive auction mechanisms, dual auction mechanisms, overall auction mechanisms, and sharing auction mechanisms is very in-depth, and has had a profound impact on economic theory. Wilson also co-designed the US federal communication spectrum auction mechanism with P. Milgrom and P. McAfee and participated in the design of the US electricity market pricing mechanism. Wilson's other contributions include: contribution to risk sharing theory (R. Wilson, 1968); contribution to information economics in (R. Wilson, 1975, 1978a; Kennan Wilson, 1993); contribution to social choice theory in (R. Wilson, 1969, 1972), etc. Regarding risk sharing theory, his publication of Syndicate Theory (1968) has become an important reference in the fields of finance and accounting; regarding information economic theory, his publication of Information, Efficiency and Economic Nuclearity (1978a) has become the core literature for understanding asymmetric information and efficiency issues; regarding social selection theory, his publication of Social Selection Theory without Pareto Principle (1972) has become the basic literature for game theory tools to analyze political issues.

. Contribution to nonlinear pricing theory

In the 1980s, the widespread use of information technology made many industries have become increasingly complex in the relationship between initial fixed investment and variable cost when providing services. The fixed costs caused by initial investment are also called "capacity costs". Enterprises need to distribute production capacity costs directly to consumers, but how to distribute them? No research on optimal pricing policy that prevailed in the 1980s involved this.The classic paper "Capacity Pricing" published by Wilson et al. (Oren, Smith Wilson, 1985) fills this theoretical gap.

Wilson et al.'s capacity pricing theory is an extension of the linear pricing theory of Panzar Sibley (1978). In Panza and Sibuli's research, production capacity, service cost and price are linear, while in Wilson et al.'s model, the more common situations in reality are analyzed: production capacity, service cost and price are nonlinear. The work of Wilson et al. is also an extension of the nonlinear theory proposed by Mirman Sibley (1980), making the simulation of "nonlinearity" more realistic about the cost and price. For example, in Wilson et al.'s model, the possibility that different orders lead to different production capacity costs is considered. The important phenomenon considered in the capacity pricing theory of

The important phenomenon considered is: the "quantity" and "quality" of different consumers' demand for products and services are different. "Quantity" refers to the quantity of products and services; "Quantity" refers to the manufacturer's "delivery time" or "duration time of service provision". The heterogeneity of consumer demand in terms of quantity and quality makes the "capacity cost" incurred by manufacturers different from the "variable cost". For example, in order to meet the service volume demand of a certain scale, only lower-priced Class A equipment is needed; in order to meet the service volume demand of a larger scale, higher-priced Class B equipment is needed; but the service speed of Class B equipment is slower than that of Class A equipment. Facing different consumers, manufacturers must choose different equipment and technologies. From this point of view, the cost of the manufacturer depends on the needs of consumers; for specific consumer needs, there will be corresponding capacity costs and variable costs. What makes the problem more complicated is that consumers understand that their consumption needs will affect the costs of manufacturers, and will make decisions on the "time model" of their use of services and will specifically analyze the impact of their "peak demand" on capacity costs. In turn, the “quantity” of consumer demand and the “time pattern of demand” will determine what equipment manufacturers should install, what technology should produce these services according to what size of labor and what maintenance costs should be provided.

Wilson et al. (Oren, Smith Wilson, 1985) gave a very good summary of this complex problem. They proposed the concepts of "capacity charges" and "service charges". The "capacity asking price" is determined by the maximum output of the equipment, while the "service asking price" (income to make up for maintenance and operation costs) is determined by the equipment's operating time; when the manufacturer formulates an "optimal price schedule), it uses consumer preference differences to obtain more consumers' remaining on the basis of calculating capacity costs and service usage costs. On the premise that there is no income effect (preventing the same consumer from seeking discounts for purchasing services at different points) and resale market (preventing consumers from independently implementing the transfer of consumer surplus between different consumers), Wilson et al. came up with the "two-dimensional nonlinear pricing rules" of "capacity asking price" and "service asking price". The core idea of ​​this rule is to discriminate against price on heterogeneous consumers, thereby maximizing monopoly profits. The "two-dimensional" here refers to the difference between consumers' "quantity" and "quality" in consumption needs. The important convenience brought by this pricing principle is that manufacturers do not need to understand the "preferences" of each consumer they face; that is, they do not need to know more "preference characteristics" of specific consumers in bargaining and then determine the price. All manufacturers need to do is to master the structure of their preferences in the entire market (which is much easier than mastering the preferences of each consumer), and use the "self-selection properties" of consumers to make consumers with different preferences automatically take the seat in the "optimal price plan".For example, consumers with low "quantity" demand will pay a lower "capacity asking price" (make up for fixed costs) and a relatively higher "service asking price" (make up for marginal costs); while consumers with large "quantity" demand will pay a higher "capacity asking price" and a relatively lower "service asking price". It is precisely because this "optimal price plan" takes advantage of consumer preference differences, which brings more consumer surplus to manufacturers. Wilson et al. (R. Wilson, 1989; Chao Wilson, 1987) has a similar idea about "priority service ration" and is also to use consumer preference differences to obtain more consumer surplus for manufacturers.

"Optimal price plan" that considers the cost of production capacity will lead to the behavior of "consumer cutting and consumption". Consumers always want to maximize the difference between utility and cost. In a pricing scheme that does not take into account capacity costs, consumers will choose any output in which “marginal utility is greater than marginal cost” in their revenue budget. For example, electricity costs 1 yuan and 1 kilowatt-hours, which means that the marginal cost of electricity is 1 yuan. If the marginal utility of the consumer using the first kilometer of electricity is 2 yuan (assuming that the consumer is a steel mill and needs electricity, the marginal income of 1 kilometer of electricity is 2 yuan), the consumer will have the motivation to consume the second kilometer of electricity, because the marginal utility is greater than the marginal cost. Assuming that the marginal utility decreases to 1 when using 80,000 kWh of electricity, the manufacturer will buy exactly 80,000 kWh of electricity. At this time, the marginal cost of electricity is equal to the marginal utility. Now let’s look at the “optimal price plan” that considers capacity cost. In this plan, if you purchase electricity less than 75,000 kWh (inclusive), the unit price is 1 yuan; since you provide electricity more than 75,000 kWh, the power consumption loss on the line will be greater, so the cost will be higher. The price list stipulates that if you purchase electricity more than 75,000 kWh, the unit price is 1.2 yuan. At this time, the optimal purchase volume of consumers is not 80,000 degrees, but 75,000 degrees. At this time, consumers "cut" their consumption. If consumers do not cut this additional consumption, they will not be able to make up for the increase in "capacity costs" brought about by the increase in power plant production capacity. The nonlinear optimal price method prompts consumers to cut consumption and increase the monopoly profit of manufacturers.

"Optimal Price Solution" is nonlinear because the cost behind it is nonlinear. Since the production efficiency of the equipment (efficiency that provides "quantity" and "quality") varies with time; the "quantity" and "quality" of consumer demand also varies with time, the cost of a unit of service produced by a "specific unit of production capacity" is different in "specific time". In order to minimize the sum of this nonlinear cost, manufacturers must find an optimal technology mix. The general rule here is: "Low-capacity cost technology" is used to meet "peak demand"; "low-marginal cost technology" is used to meet "bottom demand"; "technology with moderate capacity cost and marginal cost" is used to meet "middle demand". The process of achieving the optimal technology combination leads to nonlinearity of costs.

Wilson et al. (Oren, Smith Wilson, 1982) also analyzed the situation where consumer demand interdependence has led to nonlinear pricing becoming necessary. For example, in the communication market and copyright market, people's purchasing behavior has "demand externalities" (demand externalities); when more people use communication services and more people purchase copyrights, the marginal production capacity cost of communication equipment and the marginal cost of communication services will be reduced; the copyright usage fee may also decrease due to the larger purchase scale. Wilson et al.'s model proposes the optimal pricing principle when there is demand externality. At this time, there are three factors that determine the manufacturer's profits: production capacity, usage and market share. And these three influence each other. Production capacity and usage affect unit cost and thus affect market share; market share affects technology selection and thus affects production capacity and usage.Although the problems are very complex, Wilson's model makes these relationships clear and provides standard steps for people to formulate a "nonlinear price list": (1) Understand the "preference structure" of consumers for products and services in the entire market, and determine the boundary value of the "demand quantity" of each type of consumers; (2) Based on the consumer's demand for "quality" (such as delivery time preference), determine the principle of selecting production capacity of each type of consumers, thereby determining the "marginal capacity asking price" and "marginal service asking price"; (3) Determine how much market penetration is needed, thereby determining the initial fixed investment; (4) Developing a "nonlinear price list" to guide consumers to automatically take the seat according to their preferences.

2. Contribution to game theory: sequential rationality

The sequential equilibrium idea proposed by Kreps Wilson (1982) had an important influence on game theory. This study is based on the groundbreaking research by R. Selten (1975) and related research by J. Harsanyi (1975). The concept of "sequential equilibria" is an extension of the concept of "perfect equilibria" proposed by Zelten (1975). Wilson and Kreps directly obtained the definition of "sequential equilibrium" based on the concept of "sequential rationality"; while Zelten (1975) used an indirect way to draw a very strict definition of "perfect equilibrium", which brought difficulty to the application of the definition. "Sequential equilibrium" is a broader definition than "perfect equilibrium". The proposal of the concept of "sequential equilibrium" has brought convenience to research. In the study of

Zelten (1975), the deviation of the equilibrium path is called "trembling hands". The concept of "sequential equilibrium" proposed by Wilson and Kreps does not need to propose additional concepts for explanation of the deviation of the equilibrium path, but only needs to be explained with the concept of "belief" contained in "sequential reason", making the theory more concise.

The standard for achieving "sequential equilibrium" is that the strategy of each participant is "sequential rational": each strategy starting with each information set is the optimal strategy among all the remaining games. This requires that every participant has some kind of "belief": the belief about how the game evolves on each information set, and also the belief about the game evolution on the uneven path. In the game of incomplete information and imperfect information, sequential rationality requires the satisfaction of Savage axiom (Savage, 1954): the future strategy of any participant at each point has the following properties, from the perspective of the probability estimates of all uncertain events (including the probability estimates of choices that other participants have made but have not observed), this strategy is optimal; only by satisfying such properties can the equilibrium of choices under uncertainty conditions be achieved. Therefore, Wilson and Kreps proposed that an equilibrium is not a simple strategy, but also includes the estimation of the following two types of probability: a participant's belief in which position he is in the game tree and when to take action (a probability estimate); and a participant's belief in how the game will develop in the future after adopting a certain strategy (a probability estimate). On each information set, participants will use this belief and Bayesian law to calculate future beliefs (subsequent beliefs). In particular, such a calculation of belief does not exclude sets of information deviating from the equilibrium path. Therefore, the so-called sequential equilibrium is a continuous rational estimate of a series of beliefs and strategies. Wilson and Kreps (1982) prove that for each extended game, there is at least one sequential equilibrium; each perfect equilibrium is sequential equilibrium, but the other way around is wrong. This is exactly what Wilson and Kreps have made.

"sequential balance" concept covers the concept of "perfect balance".Zelten's perfect equilibrium requirements meet the following two points at the same time: (1) Perfect equilibrium "hints" that participants will inevitably have some belief in the information set deviating from the equilibrium path; (2) requiring participants' strategy to be balanced in the above beliefs. In sequential equilibrium, it is clearly stated that participants must have some belief in deviating from the information set on the equilibrium path, but the above second point is not required. Therefore, any perfect equilibrium is sequential equilibrium, but any sequential equilibrium is not necessarily a perfect equilibrium. However, Wilson and Kreps (1982) prove that as long as Zelten's first condition is true, the second condition is rarely true. Therefore, in "almost all" games, "perfect equilibrium" and "sequential equilibrium" overlap. The only possible exception is weak equilibria, in which case the two do not overlap. Therefore, in a mathematical sense, these two concepts are almost the same.

Why does it need to propose a new concept of "sequential balance"? It is mainly based on two points: (1) The need for pragmatism. This makes many analyses simple (e.g., Kreps Wilson, 1981; Milgrom Roberts, 1982). Because it is much simpler to prove that a equilibrium is sequential equilibrium than to prove that it is perfect equilibrium; (2) The idea of ​​explicitly proposing "belief" brings benefits: the construction of beliefs off the equilibrium path analysis brings convenience to us to discuss which beliefs are "feasible" and which are "unfeasible". And this kind of discussion is impossible under the analytical framework of Zelten's implicit beliefs. Kreps Wilson et al. (1981) gave an example to illustrate that the equilibrium selected according to the principle of sequential equilibrium is the same as the equilibrium selected according to the principle of perfect equilibrium, and that this equilibrium has the following properties: there is a unique equilibrium path behavior, and its beliefs are intuitive. It is precisely because of the explicit introduction of the idea of ​​"belief" (concepts about where the participants are in the game tree, when to take action, and how the game will develop in the future), that sequential equilibrium has become a concept that is easier for non-professionals to understand than perfect equilibrium. The proposal of sequential equilibrium in

sequential equilibrium deepens people's understanding of complex equilibrium phenomena. The weakest criterion for equilibrium in game theory is the so-called Nash equilibrium (J.Nash, 1951): If the strategy of each participant is the optimal response of all other people's strategies, the strategy is called Nash equilibrium. The importance of Nash equilibrium is to help people realize that if all participants are to form a "uniformly agreed" behavior agreement, these behaviors must constitute a Nash equilibrium; otherwise, someone will find it profitable to betray this agreement. R. Selten (1965) developed the concept of Nash equilibrium and proposed a more stringent "uniform agreement" behavioral agreement: sub-game refines Nash equilibrium. R. Selten (1975) further proposed a more complex "perfect equilibrium". Use μ to represent "belief" and use π to represent "strategy". A participant will have n beliefs, and in each belief, there will be a strategy. Therefore, a participant's estimate of the game can be written as (μn, πn). If sequentially {(μn,πn)}n=1,2…converges, that is, limn→∞(μn,πn)=(μ,π), this is called "perfect equilibrium". The difference between strategy πn and extreme strategy π is: πn is the optimal strategy to deal with other participants who have a very small probability of making mistakes or “trembling”. If the probability of the other party "trembling" is extremely small, then there is πn =π. The ultimate strategy π means that in any information set, even if there is a "defection" for the estimated (the prior probability of occurrence of 0), the ultimate strategy π will continue to be used. In other words, a certain initial "betrayal" will not make the second "betrayal" more likely to occur, so the participants continue to use the ultimate strategy π. Imagine a participant i is predicting the behavior of participant j. Participant i will definitely think that j is predicting all other people's behavior. Then, the Nash standard requires that j's behavior is the optimal response to the behavior of everyone else predicted by j.Obviously, Zelten proposed a more stringent equilibrium standard: j's behavior must also be the optimal response to strategy πn under the different beliefs of other participants (and this strategy converges to the extreme strategy π). When a "divergence" occurs, j will interpret this event with a priori probability of 0 as "caused by a small mistake". Within Zelten's framework, i must know the payment of j. In sequential equilibrium, i does not need to know the payment of j, allowing i to have uncertainty about the payment of j. In this way, the strategy that only requires j is the optimal response to i's "perturbed strategies", that is, the payment of the belief closest to j.

Wilson conducted outstanding research on "competitive auction mechanism", "dual auction mechanism", and "overall auction and sharing auction mechanism".

Wilson (1977) proved that the price formed by competitive auctions satisfies the large number theorem: for an auction item with a certain currency value but no one knows exactly, each participant uses his own private information about the value of the product to quote. The private information of participants is an independent distribution of the value of the goods, and the private information of participants is the same distribution. In a sealed quote auction, the auctioneer sells the auction item to the highest quoter. This highest offer happens to be the true value of the auction item. Therefore, although no bidder knows the true value of the auction item, this mechanism makes the sale price obtained by the seller happen to be its true value.

Wilson described this problem using a non-cooperative game model. Assuming that the bidder has n, n2, and i-th bidders' information on the value of the auction item is si, the auctioneer determines its quotation bi based on this sample information. Assuming that the true value of the product is v, then the utility of a successful auction for the auction will be u(si,v) and the net income will be u(si,v)-bi. Wilson proves that competitive auctions will ultimately reveal true value v. Wilson shows that although the assumption that the payment function has about the quotation being linear excludes the possibility that the bidder may be risk aversion, even if there is such a possibility, the results will not be substantial. The most critical thing about the competitive auction mechanism is that no one can observe the real value v. Each bidder only has private information about the auction item, and each person's price bi only depends on si and the number of bidders n. Despite this, as the number of bidders increases, this non-cooperational game of incomplete information will cause the final sale price to converge to the "real value". Its important theoretical meaning is: (1) The sale price in the market conveys the "all" relevant information of relevant participants in the market; (2) The price formation theory and the value theory are inherently consistent. Wilson (R. Wilson, 1978b) extended this study to an analysis of the structure of the competitive market in .

In a study on dual auctions (R. Wilson, 1985), Wilson tried to find out the incentive efficient principle of trading among participants whose preference was private information, and analyzed the welfare implications of these participants' Nash equilibrium strategy. An effective trading rule means that under existing trading rules, there is no longer the following common knowledge: There are other trading rules that can increase the expected returns of a certain participant without detracting from the expected returns of others. This is an application and development of the theory of Holmstrom et al. (1983).

In this dual auction model, only the participants know their "type", which affects their own preferences; however, the distribution of the types formed by all participants is a common knowledge. What is a double auction? An auction with the following trading rules is called a double auction: assuming that the i-th bidder is ri; the j-th seller is bj. If the k-th highest quotation among all quotations ri is rk=ri(k); in all sellers' quotations bj, the k-th lowest quotation is bk=bj(k), then the transaction volume reached is k=max{k|rk≥bk}.The goal of this auction mechanism is to maximize transaction volume.

Double auction includes three behaviors: (1) The behavior of the bidder. The bidder's quote will be balanced at the level where the expected return of the quote is equal to the expected loss. Expected returns are affected by quotation strategies. Robert Wilson (1985) assumes that bidders quote at decreasing prices, such as each discount dp. If the price reduction is successful, the expected return is exactly dp; the expected loss is the difference between utility (maximum reserved price) u and equilibrium price p, that is, the consumer residual loss (u-p). Success in price reduction refers to: his new quotation just prompts the transaction to be successful, and the equilibrium transaction price drops due to his quotation; at this time, the bidder happens to be the "marginal buyer". On the one hand, the probability of this event depends on the extent to which the bidder affects the equilibrium transaction price. If the sum of demand for bidders is m and the sum of supply for sellers is n, then the relative force of bidders to reduce the transaction price is λ1=m/(m+n), and the relative force of seller to reduce the transaction price is λ2=n/(m+n). In Wilson's model, the game between bidders and sellers drives the price to maintain a upper limit (pmax) and a lower limit (pmin) (set (pmin, pmax), then the equilibrium price p0 can be written as: p0=λ1pmax+λ2pmin, that is, if the bidder's total demand accounts for the sum of total demand and total supply, the greater the price is, the closer the upper limit. The economic intuition is that if demand is greater than supply, the price tends to be raised; on the contrary, if the seller's total supply accounts for the sum of total demand and total supply. The larger λ2, the more likely the price is to approach the lower limit. The economic intuition is that if the supply is greater than demand, the price tends to be pushed down. On the other hand, the bidder's quotation happens to be the probability of equilibrium the upper limit of the price pmax. (2) The behavior of the seller. The seller's quotation will also be balanced at the level where the expected return of the quotation is equal to the expected loss. The analysis is similar to the above. (3) The game between the bidder and the seller. Wilson proves that as long as the number of bidders and sellers is large enough, the game between the two under the dual auction mechanism is "incentive" (incentive). Efficient): Under this mechanism, people's bidding and quotation behaviors will automatically reveal the joint probability distribution of the type of transaction participants, and the distribution of each participant's reliance on the type of reserved price. That is to say, the strategic behavior formed by traders using their own private information under the dual auction mechanism is economically efficient; there are no other equilibrium prices, so that the expected returns of anyone among the bidder and sellers will increase without detracting from the expected returns of others.

Wilson (1979) also compared the "unit" auction and the "share" The difference between these two auction mechanisms. In the overall auction, a commodity or service is sold as a whole to the highest bidder; in the sharing auction, a commodity or service is divided into several parts, and the price paid by each bidder just makes the supply of that part equal to demand. Wilson (1979) concluded that the equilibrium price under the sharing auction mechanism is lower. In many cases, the price of the sharing auction is only half of the overall auction.

In the overall auction, there is only one observable commodity or service, and each bidder seals the auction item as a whole; the seller gives the auction item according to the highest price Sold to the highest bidder. US Department of the Interior auctions the development rights of the foreign continental shelf oil and natural gas plots in this way. In a sharing auction, an observable commodity or service is divided and sold to multiple bidders. Each bidder states his or her own quotation system in the envelope: different quotations for different shares. For example, if you purchase 20%, the unit price is 100 yuan, and if you purchase 30%, the unit price is 95 yuan, and so on. In practice, it is often done: state how much shares you are willing to buy at each price. For example, if the unit price is 60, the unit price is 100%, the unit price is 70, and 50%, and if you purchase 98, the unit price is 30%, and so on.The seller chooses from the quotes of all bidders, so that all shares can be sold according to the principle of maximizing returns. The price paid by each bidder is exactly the corresponding price he has quoted. Philips Auction on OCS system rental is carried out in this way. The original intention of the latter auction mechanism design is to encourage small enterprises with risk preference characteristics to participate in the auction of high-risk projects, so as to achieve the effect of risk sharing. The advantage of this auction mechanism is that it can attract more buyers and can control the risks faced by each buyer; the dispersed use of resources may also promote the full utilization of resources. However, one question that needs to be answered is, if this auction method is adopted in public resource auctions, will the government's auction revenue increase or decrease? An important question here is whether this sharing auction mechanism will cause large enterprises with large capital and risk aversion to deliberately lower their quotations in their quotations, prompting a reduction in government auction revenue.

Wilson (1979) assumes that the true value of the auction item to each bidder is V. Two situations are considered: (1) At the time of auction, this value is known to the bidder for sure. (2) At the time of auction, this value was not known to the bidder for sure. In the first case:

) At the time of auction, this value is known to the bidder for sure. (2) At the time of auction, this value was not known to the bidder for sure. In the first case: the only optimal strategy of the auctioneer is to make the offer equal to the real value. Eventually, one bidder will receive the item, and the price it pays is exactly the appraisal of the bidder. If you are using a shared auction, the final transaction price will be only 1/2 of the real value. In the second case, Wilson proved that sharing the auction was not good. When the bidder is not sure about the real value of the auction item and considers the risk aversion characteristics of the bidder, the price may be lower than half of the real value. The reason is that the seller's expected returns cannot benefit from the increase in bidders; when allowing bidders to list quotation systems instead of single prices, this gives sellers more opportunities to maximize their consumer surplus, which is not good for sellers. In a shared auction, it seems that sellers can use price discrimination to maximize returns, but Wilson proves that in fact, bidders will actively change their quotation strategy when quoting to deal with price discrimination by sellers. Wilson also stated that another version of the sharing auction, Vickrey auction, is not as good as the overall auction. Vickery (1961) proposed that all bidders should submit a quotation system, and the seller would give each quoter a certain amount of "rebate" to allow the quoter to quote a higher price. Wilson proved that under this auction mechanism, bidders will adjust their quotation strategy, which will reduce the amount of space left by the seller to seize consumers.

. Other contributions

Wilson also made important contributions in the fields of risk sharing theory, information economics theory, etc.

"Syndic Theory" (1968) published by Wilson has become an important reference in the fields of finance and accounting. The so-called "syndication" refers to a group of people who take joint actions under uncertain conditions and share the results of the action. Wilson studied the application of Pareto optimality principle in the formation of syndicate organizations and proposed the ideas of "group utility function" and "group probability assessment", which are of great reference significance for designing financial tools. People often have different risk preference characteristics and different risk tolerance characteristics; people often have different estimates of the probability of uncertain events affecting payments. So, when can people form "syndicates"? Wilson (R. Wilson, 1968) began his research on the sharing rules of total payments for collective action.Sharing rules are very important in organizational decision-making, because for any member, the value of a decision depends on how much he can get from the total payment obtained by the action after the decision. Wilson's criterion for finding this sharing rule is the Pareto optimal principle: a sharing rule is Pareto optimal. If there is no alternative rule again, this alternative rule increases the expected utility of a certain (or some) member, but no member's expected utility decreases. The syndicate with such rules is "organized", "cooperative", "stable", rather than loose. Such syndicates satisfy the "Savage Axiom": under uncertain conditions, an organization can make consistent decisions. The important idea of ​​this study is that when a syndicate attempts to choose an action for a certain bet, the condition for reaching consensus among members is not how big the "bet" is, but whether each member's estimate of the probability of an uncertain event affecting the bet will be consistent. That is, whether there is a "group utility function" and a "group probability estimation function". If there is, the risk tolerance level of the syndicate organization is the sum of the risk tolerance level of each member; the payments shared by each member are consistent with the risk they share. The profound insight provided by Wilson (1968) is that to make any joint action possible, it is necessary to require everyone in the joint action to be "completely consistent alert" about the risks that the action may have.

Wilson (1978a) also has a very famous study on the relationship between information and economic efficiency. Wilson studied the exchange efficiency between economic participants with different information endowments and defined the idea of ​​"the Core of an Economic". "Efficiency" in the sense of information economics means that given the information of each participant, under a given resource allocation, every economic participant feels that there is no other better way to allocate resources. The so-called "economic core" means that in the economy formed by X participants, there is already such resource allocation: there will be no subset of economic entities formed by x individuals (1≤x≤X) and there will be opportunities and motivations to find new resource allocation solutions. That is to say, in an economic core, there will be no new alliances trying to break the established resource allocation situation. The "economic nuclear" provides insurance for everyone; and everyone in a small economy uses "communication systems" to share the benefits of information sharing. When the insurance of the "economic nuclear" is not as good as the new benefits discovered after small collective communication, the economic nuclear nuclear will be broken. The more “communication” is allowed, the smaller the economic nuclear power will be. The important insight provided by this study is that the private information that people have is not easily known, and everyone will "wear different hats" in different negotiation occasions (R. Wilson, 1978a), revealing part of private information in the large economic nuclear, and revealing another part of private information in the small economy; if there is a good communication mechanism within the small collective under the economic nuclear, it may lead to greater economic benefits in the interaction of private information, and thus the large economic nuclear will be broken.

. Independent economist Du Meng briefly commented on

Wilson's economic research has the following three distinct characteristics: (1) Trying to use game theory to re-express the basic theory of microeconomics. For example, Wilson (1978b) used a brand new game theory paradigm to express the "competitive market theory". Wilson (1978b) interpreted market trading behavior as a "non-cooperative game" and proved that the Nash equilibrium of this game can form an "economic nuclear", and, in the extreme sense, the allocation of this "economic nuclear" happens to be a "Walrasian allocation". In other words, competitive quotations in the non-cooperative game process are equivalent to "market" in the extreme sense. In Wilson's explanation, the so-called "perfect competition" means: if a participant does not trade according to the requirements of the "economic nuclear", he will find that all his trading requirements will be rejected and expelled from the market.If all participants face "perfect competition", the "Vallas configuration" will be the only result. Wilson used game theory to re-express the theory of market competition to avoid the major problem of the traditional Vallas model - the Vallas model needs to determine who can clear the market, which is a problem that cannot be solved so far. (2) Introducing profound insights into reality into economic analysis has greatly promoted the development of basic economic theories. In the analysis of Debreu Scarf (1963), economic trading is described as a cooperative game between traders, but Wilson (1978b) made more realistic improvements, describing it as a non-cooperative game between traders, and developing the non-cooperative model proposed by Shapley (1976) and Smeidler (1976) and others, and concludes that the Nash equilibrium formed by the non-cooperative game between traders is exactly an important conclusion of the Vallas equilibrium. Wilson observed that the pricing theory described by Panza and Sibri (1978) was not fully portrayed reality, and introduced the cost nonlinear phenomenon in reality into the optimal pricing theory. The "nonlinear pricing theory" proposed had an important impact on the theoretical community and showed huge application prospects. For example, Wilson and Kreps (1982) noticed that the "perfect equilibrium" proposed by Zelten (1975) was too abstract, introducing the concept of "belief" that is easier to understand, and deepening people's understanding of more complex game equilibrium. (3) Pay attention to the integration of empirical analysis and normative analysis, and pay attention to the welfare results of the economic process. Wilson believes that the true sense of welfare economics has not been established, and its research often includes welfare economics analysis. In Wilson's research mentioned above, many studies have introduced welfare economics analysis. For example, in the study of dual auction mechanisms, Wilson (1985) took the "incentive effective" trading rules in the sense of welfare economics as the research focus: trying to explore whether the dual auction mechanism is such a rule. Under this rule, there is no other trading rules that can increase the expected returns of a certain participant without detracting from others. Wilson's research on risk sharing (1968) attempted to find sharing rules in the sense of welfare economics: under this rule, there is no alternative rule, which increases the expected utility of a certain (or certain) member, but no member's expected utility has decreased. Furthermore, Wilson's (1978a) idea on "economic nuclear" is both an empirical analysis and a normative analysis. In short, Wilson's research has made important contributions to the development of economic theory.

(Source: "Economic Dynamics")

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https://www.sys.com/ Du Meng, President of Financial Street Telecom, Chairman of CECU China Enterprise Capital Alliance, is a famous independent economist and Ph.D. in economics. He is known as one of China's four major financial geeks and a Ph.D. in Ghost Town. Party member of the Peking University branch of the Democratic League. Representative works: "Monetary", "Monetary Banking", "Introduction to Investment Management", "Real Estate Development and Operation", "Ghost City Theory", etc. He has been in charge of the daily operation and management of the group headquarters and listed companies, and has controlled the development area of ​​tens of millions of square meters of investment areas and subsidiaries. He has a background of the main person in charge of domestic and foreign listed companies, and has dual work experience in capital operation and real estate investment and development. He is a representative figure of the academic and practical people in the financial and real estate industry. He has successively served as executives of enterprises with different backgrounds such as military enterprises, state-owned enterprises, school enterprises, and listed groups.

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