Mechanism design
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Mechanism design is a sub-field of game theory. It is the art of designing rules of a game to achieve a specific outcome. This is done by setting up a structure in which each player has an incentive to behave as the designer intends. The game is then said to implement the desired outcome. The strength of such a result depends on the solution concept used in the game.
Mechanism designers commonly try to achieve the following basic outcomes: truthfulness, individual rationality, budget balance, and social welfare. More advanced mechanisms attempt to resist harmful coalitions of players.
Most of the results in mechanism design have been established by economists, but some mathematicians, computer scientists and electrical engineers also work in the field.
One branch of mechanism design is the creation of markets, auctions, and combinatorial auctions. Another is the design of matching algorithms such as the one used to pair medical school graduates with internships. A third application is to the provison of public goods, and the optimal design of taxation schemes by governments.
A common exercise in mechanism design is to achieve the desired outcome according to a specific solution concept. The celebrated Gibbard-Satterthwaite theorem shows that any outcome that can be implemented as a dominant strategy equilibrium is necessarily dictatorial. This is similar to Arrow's Impossibility Theorem. By contrast, implementation in Nash equilibrium is possible for a much wider range of social choice rules.
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