Takuro Yamashita is assistant professor at TSE. He holds a
PhD degree from Stanford University and he is specialized in mechanism design theory.
In 2007, Leonid Hurwicz, Eric Maskin, and Roger Myerson wereawarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Novel, for their fundamental contributions in mechanism design theory. In this article, I try to introduce mechanism design theory very briefly. I hope some of you get interested in this theory and grab any textbook to get really introduced. Mechanism design theory is about "optimal design of a mechanism". But, what is a mechanism? A famous example is a "market mechanism". If you have taken a microeconomics course, I believe you encountered the notion of "markets". In a market, consumers and producers announce their demand and supply, and the price is determined to equate the total demand and supply. Everyone trades at this price. This is the "rule" in a market, and any participant must follow this rule to make their transactions. Roughly speaking, a mechanism means a rule of transaction.
Perhaps you have also learned that this particular rule of transaction, the market mechanism, sometimes achieves the efficient allocation of goods, but sometimes not. If the market mechanism does not work well, the rule may be modified (for example, by taxes or subsidies). Or perhaps, completely different rules of transaction than the market mechanism may work better, which may involve more complicated procedures such as bargaining or contracting among some groups of individuals, or even voting. There are plenty of alternative mechanisms. Which one is the best mechanism? This is (one of) the fundamental question of mechanism design theory, and to answer the question, we need to describe the problem more formally.
Formally, a mechanism specifies two objects. The set of "messages" for each individual, and the "outcome function". Each individual selects one message in the message set, and send it to the mechanism. You can think of the mechanism as a kind of a computer, in which, each individual inputs a message. Once everyone sends his/her message, then the mechanism outputs an "outcome", based on the outcome function. In the market mechanism, each consumer's message is a demand function, each producer's message is a supply function, and given their messages, the market mechanism outputs the outcome, which is the amount of the goods each individual buys or sells, based on the market- clearing price.
To evaluate a mechanism, we need to know how individuals would behave in the mechanism (called a "solution concept"), and which outcomes are induced by their behaviors. Usually, each individual is assumed to have his own preference over the outcomes, and chooses a message to achieve the outcome that is more preferable to him. Of course, the best message for him may depend on which messages the other individuals choose. Thus, often, we adopt a Nash equilibrium behavior (or its generalization such as a Bayesian Nash equilibrium) as the solution concept, i.e., they choose the messages so that each individual's choice is the best choice given the others' choices.
The mechanism designer's task is, then, to find a mechanism (i.e., message sets plus an outcome function) in which Nash equilibrium message choices induce desirable outcomes. Or, in other words, a mechanism is carefully designed in order to "incentivize" each individual to choose a message that induces desirable outcomes. For example, consider a good produced by a monopolist. Let the monopolist's marginal cost of production be constant, but suppose that only the monopolist knows the actual value of his marginal cost. To attain the highest possible efficiency, we may want the monopolist to produce more if the marginal cost is lower, and less if it is higher, but the monopolist would do so only when such a choice is consistent with his profit-maximization behavior. Thus, a mechanism must be designed so that the monopolist's choice is aligned with the objective of the mechanism designer (e.g. social planner).
So far, I explained mechanisms and mechanism design problems in an environment with "consumers and producers", but we can think of many other examples. Here are a few of them:
A seller owns an object. Each bidder has private information about how much he can pay (his "willingness to pay") for the object. In an auction mechanism, each bidder sends a message, and depending on their messages, the winner and the price of the object are determined. The objective of the mechanism designer is, for example, (i) surplus maximization, i.e., to make the bidder with the highest willingness to pay the winner, or (ii) profit maximization, i.e., to make the payment by the bidders as high as possible. The surplus maximization scenario may be more relevant if the mechanism designer is a government who regulates certain auctions to achieve efficient trades. The profit maximization scenario may be more relevant if the mechanism designer is the seller himself.
Public good provision
A group of PhD students wants to buy a new coffee machine (a public good) in their office, which costs a hundred euro. Each student has private information for his/her willingness to pay. In a public-good mechanism, each student sends a message about how much he/she is willing to pay, and depending on their messages, the decision about the purchase of the coffee machine and and the cost allocation among the students are determined. A mechanism needs to be carefully designed to avoid ``free riding’’ as much as possible, because each student may pretend to be less interested than he/she truly is to save the payment.
Workers work together in a company, and the company’s profit is determined by effort levels the workers make. The head quarter wants to design a wage scheme to incentivize each worker to make an effort, but efforts themselves are only observable to the workers. What is the optimal wage scheme that maximizes the profit, through incentivizing high effort choices?
These problems have different environments (i.e., a set of individuals, their information structure and preferences, and a set of feasible outcomes) and different criteria for desirable outcomes (e.g., efficiency, profit) to each other. However, they have a fundamental problem in common: whether and how can we incentivize the individuals to choose the self-revealing choices that induce desirable outcomes? Identifying incentives as an important issue in economics was one of the main contributions of mechanism design theory, and especially, of the work of the above mentioned three prize winners.
Even though there has been a huge accumulation in the literature, there are still many open questions. Let me describe some of these questions as "puzzles". As explained above, once you specify a mechanism design problem, which consists of an environment, an objective of the mechanism designer (i.e., which outcomes are desirable), and a solution concept (i.e., how individuals would behave in each mechanism), then you can start searching for an optimal mechanism. However, sometimes, the optimal mechanism you find may look "weird": It may look very different from what is typically used in reality, and/or it may look too complicated to understand, etc. The mechanism design literature has been quite successful for some class of problems, but there seem to be cases in which the optimal mechanisms found look "weird". In such a case, one may think that there is something wrong in the way the mechanism design problem is set up. In particular, some recent papers study optimal mechanisms in different solution concepts than the "standard" concepts in the literature (such as the Nash or Bayesian Nash approaches). These attempts have been (and will be) stimulated by recent developments in other fields of economics such as behavioral and experimental economics, and by other disciplines of science such as psychology and computer science, through deeper understanding of human behaviors in decision making.
For those who are interested in more detailed explanation of the contribution by the three prize winners, see "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2007", Nobelprize.org, http://www. nobelprize.org/nobel_prizes/economics/laureates/2007/ press.html. It also has links to some related articles and textbooks.