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Mechanism design, sometimes called implementation theory or institutiondesign, is a branch of economics, social choice, and game theory that deals with designing game forms to implement a given social choice function. Because it starts with the end of the game and then works backwards to find a game that implements it, it is sometimes described as reverse game theory.
In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly-dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private information, and the strategy space of each player consists of the possible information values, a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player. An SP mechanism is also called dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility.
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction and gives bidders an incentive to bid their true value. The auction was first described academically by Columbia University professor William Vickrey in 1961 though it had been used by stamp collectors since 1893. In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction.
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures used to combine individual preferences into a coherent whole. It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory.
A double auction is a process of buying and selling goods with multiple sellers and multiple buyers. Potential buyers submit their bids and potential sellers submit their ask prices to the market institution, and then the market institution chooses some price p that clears the market: all the sellers who asked less than p sell and all buyers who bid more than p buy at this price p. Buyers and sellers that bid or ask for exactly p are also included. A common example of a double auction is stock exchange.
In game theory and economics, a mechanism is called incentive-compatible (IC) if every participant can achieve their own best outcome by reporting their true preferences. For example, there is incentive compatibility if high-risk clients are better off in identifying themselves as high-risk to insurance firms, who only sell discounted insurance to high-risk clients. Likewise, they would be worse off if they pretend to be low-risk. Low-risk clients who pretend to be high-risk would also be worse off. The concept is attributed to the Russian-born American economist Leonid Hurwicz.
The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism. It can be seen as a kind of mirror image to Gibbard's theorem. The revelation principle says that if a social choice function can be implemented with some non-honest mechanism—one where players have an incentive to lie—the same function can be implemented by an incentive-compatible (honesty-promoting) mechanism with the same equilibrium outcome (payoffs).
A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest bidder pays the price that was submitted.
Revenue equivalence is a concept in auction theory that states that given certain conditions, any mechanism that results in the same outcomes also has the same expected revenue.
Algorithmic mechanism design (AMD) lies at the intersection of economic game theory, optimization, and computer science. The prototypical problem in mechanism design is to design a system for multiple self-interested participants, such that the participants' self-interested actions at equilibrium lead to good system performance. Typical objectives studied include revenue maximization and social welfare maximization. Algorithmic mechanism design differs from classical economic mechanism design in several respects. It typically employs the analytic tools of theoretical computer science, such as worst case analysis and approximation ratios, in contrast to classical mechanism design in economics which often makes distributional assumptions about the agents. It also considers computational constraints to be of central importance: mechanisms that cannot be efficiently implemented in polynomial time are not considered to be viable solutions to a mechanism design problem. This often, for example, rules out the classic economic mechanism, the Vickrey–Clarke–Groves auction.
Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments.
Distributed algorithmic mechanism design (DAMD) is an extension of algorithmic mechanism design.
Market design is an interdisciplinary, engineering-driven approach to economics and a practical methodology for creation of markets of certain properties, which is partially based on mechanism design. In market design, the focus is on the rules of exchange, meaning who gets allocated what and by what procedure. Market design is concerned with the workings of particular markets in order to fix them when they are broken or to build markets when they are missing. Practical applications of market design theory has included labor market matching, organ transplantation, school choice, university admissions, and more.
Arunava Sen is a professor of economics at the Indian Statistical Institute. He works on Game Theory, Social Choice Theory, Mechanism Design, Voting and Auctions.
In mechanism design, a Vickrey–Clarke–Groves (VCG) mechanism is a generic truthful mechanism for achieving a socially optimal solution. It is a generalization of a Vickrey–Clarke–Groves auction. A VCG auction performs a specific task: dividing items among people. A VCG mechanism is more general: it can be used to select any outcome out of a set of possible outcomes.
A sequential auction is an auction in which several items are sold, one after the other, to the same group of potential buyers. In a sequential first-price auction (SAFP), each individual item is sold using a first price auction, while in a sequential second-price auction (SASP), each individual item is sold using a second price auction.
The Price of Anarchy (PoA) is a concept in game theory and mechanism design that measures how the social welfare of a system degrades due to selfish behavior of its agents. It has been studied extensively in various contexts, particularly in auctions.
Guoqiang Tian is a Chinese-American economist. He is the Alfred F. Chalk Professor of Economics at Texas A&M University. He is Honorary Dean of Institute for Advanced Research at Shanghai University of Finance and Economics.
Truthful resource allocation is the problem of allocating resources among agents with different valuations over the resources, such that agents are incentivized to reveal their true valuations over the resources.
In game theory and related fields, a game form, game frame, ruleset, or outcome function is the set of rules that govern a game and determine its outcome based on each player's choices. A game form differs from a game in that it does not stipulate the utilities or payoffs for each agent.
References
- 1 2 Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. doi : 10.1016/S1574-0005(02)03024-2.
- 1 2 Maskin, Eric. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. doi : 10.1016/S1574-0110(02)80009-1.
- ↑ Vickrey, William. "Counterspeculation, Auctions, and Competitive Sealed Tenders." The Journal of Finance 16, no. 1 (1961): 8–37. doi : 10.1111/j.1540-6261.1961.tb02789.x. JSTOR 2977633.
- ↑ Jackson, Matthew O. "A Crash Course in Implementation Theory." Social Choice and Welfare 18, no. 4 (2001): 655–708. doi : 10.1007/s003550100152. JSTOR 41106420.
- ↑ Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).