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Mechanism design is a branch of economics, social choice theory, and game theory that deals with designing games to implement a given social choice function. Because it starts at the end of the game and then works backwards to find a game that implements it, it is sometimes called reverse game theory.
In mechanism design, a strategyproof (SP) mechanism is a game 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.
In tabletop games and video games, game mechanics are the rules or ludemes that govern and guide the player's actions, as well as the game's response to them. A rule is an instruction on how to play, a ludeme is an element of play like the L-shaped move of the knight in chess. A game's mechanics thus effectively specify how the game will work for the people who play it.
Paul Robert Milgrom is an American economist. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at the Stanford University School of Humanities and Sciences, a position he has held since 1987. He is a professor in the Stanford School of Engineering as well and a Senior Fellow at the Stanford Institute for Economic Research. Milgrom is an expert in game theory, specifically auction theory and pricing strategies. He is the winner of the 2020 Nobel Memorial Prize in Economic Sciences, together with Robert B. Wilson, "for improvements to auction theory and inventions of new auction formats".
Social choice theory or social choice is a branch of welfare economics that studies the processes of collective decision-making. Social choice incorporates insights from economics, mathematics, and game theory to find the best ways to combine individual opinions, preferences, or beliefs into a single coherent measure of the quality of different outcomes, called a social welfare function. Social choice theory includes the closely-related field of voting theory, and is strongly tied to the field of mechanism design, which can be thought of as the combination of social choice with game theory.
In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players hold private information relevant to the game, meaning that the payoffs are not common knowledge. Bayesian games model the outcome of player interactions using aspects of Bayesian probability. They are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information.
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. As we change parameters of the objective, the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contribute to the change in the objective function. The envelope theorem is an important tool for comparative statics of optimization models.
In game theory, the outcome of a game is the ultimate result of a strategic interaction with one or more people, dependant on the choices made by all participants in a certain exchange. It represents the final payoff resulting from a set of actions that individuals can take within the context of the game. Outcomes are pivotal in determining the payoffs and expected utility for parties involved. Game theorists commonly study how the outcome of a game is determined and what factors affect it.
A mechanism is called incentive-compatible (IC) or truthful if every participant can achieve their own best outcome by acting according to 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 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).
Implementation theory is an area of research in game theory concerned with whether a class of mechanisms can be designed whose equilibrium outcomes implement a given set of normative goals or welfare criteria.
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 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. Market design principles have been implemented in auction theory and matching theory.
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.
In mechanism design, an agent is said to have single-parameter utility if his valuation of the possible outcomes can be represented by a single number. For example, in an auction for a single item, the utilities of all agents are single-parametric, since they can be represented by their monetary evaluation of the item. In contrast, in a combinatorial auction for two or more related items, the utilities are usually not single-parametric, since they are usually represented by their evaluations to all possible bundles of items.
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.
References
- ↑ Roth, Benjamin N.; Shorrer, Ran I. (March 2015). "Mechanism Design in the Presence of a Pre-Existing Game". Working Paper.
- 1 2 Blumrosen, Liad; Feldman, Michal (2013-11-01). "Mechanism design with a restricted action space". Games and Economic Behavior. 82: 424–443. doi:10.1016/j.geb.2013.03.005. ISSN 0899-8256.
- 1 2 Gibbard, Allan (1978). "Straightforwardness of Game Forms with Lotteries as Outcomes". Econometrica. 46 (3): 595–614. doi:10.2307/1914235. ISSN 0012-9682. JSTOR 1914235.
- ↑ Ozdaglar, Asu. "Game Theory with Engineering Applications" (PDF). Archived (PDF) from the original on 2024-06-29.
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