Mechanism design

The mechanism design theory or mechanism design is a subfield of game theory, the rules - and thus the incentives - for games sets to achieve a desired overall result, even if the player is only pursue their own interests. A mechanism is a set of rules to control interactions between players.

This is achieved through the implementation of a higher-order structure (design ) in which players receive an incentive to ensure that they behave in accordance with these rules. The result of this mechanism is referred to as an implementation of the desired overall result. The strength of this result depends on the solution concept, that of the established rules from. It is based on the Metaspielanalyse, which uses the methodology of game theory to develop new rules for a game.

In the mechanism design theory, a recursive application of game-theoretic analysis takes place: It is not asked how the players will play a custom game, but as a game designed (designed, design) must be in order to obtain a certain result. Decorated in the rules of the game are called mechanism. A classic application of mechanism design theory is the design of rules in a market.

  • 3.1 Basketball
  • 3.2 Distribution of the cake
  • 3.3 Vickreyauktion

Theory

The theory assumes that a market does not care if by an invisible hand for the optimal allocation of resources, but an imperfect market prevails. With the help of a non-optimal market mechanisms should be optimized.

Economic theory also shows that, under certain conditions, such as perfect competition, no externalities, no individual players have market power and so the rule can be implemented without any intervention by the market mechanism. The market mechanism can be used in this sense regarded as a form of implementation of the rule. Implementation coincides in this case with the work of the invisible hand.

The principle of mechanism design is also effective in other areas of life. Thus, the results and methods of the mechanisms Design also be applied in the field of economic and social sciences. This is then examined how the (mostly) legal framework can be modified to a certain, wanted behavior promoted or inhibited is unintentional.

A practical application of mechanism design theory is the question of how relationships with business partners should be designed to achieve the desired results ( the agreed rules are then the " mechanism ", which will be set ). In applied game theory, this rule design is popularly referred to as coopetition.

For their research in the field, scientists Leonid Hurwicz, Eric S. Maskin and Roger B. Myerson were awarded in 2007 the Nobel Prize in Economics.

Definition

Represents the number of players dar. Each player has a value that is called the player's type. In an auction, for example, this value would represent the reservation price of this player for the offered product (s). Depending on its type, the player will choose the action, where the enabled the mechanism of action alternatives for the player represents. An example of an action in a closed auction would be a bid by a certain amount. Each player has the benefit, the amount of the possible outcomes of the mechanism is. In an auction, the result would be the completed allocation of goods and the payments that must make every player. The benefits for each player would be in accordance with the reservation price of the goods allocated to him, minus the price to be paid.

Thus, a mechanism is defined as a pair, the possibilities for action for the players and the function represents the result of the player's actions to the result.

Direct mechanisms

One mechanism is direct when the action possibilities are equal to the number of values ​​of each player, for example. This is the case for auctions where each bid, the player announces its preference value for the product. However, there is no need for an actual vote, if a different strategy provides a better benefit. This leads to the idea of ​​direct truthful mechanisms.

Under a direct mechanism so each participating individual is asked about his private information. The announcements will be assigned here on the outcome of a social choice function. A central result of the theory of mechanism design is that every social choice function is implementable, can always be achieved by a direct mechanism. This result is referred to as Revelationsprinzip. The direct mechanism takes over as it were playing the type of player belonging equilibrium strategy. Is it to play under the indirect mechanism optimal for a certain type of strategy, it is optimal to advertise under the direct mechanism the type truthfully. A concrete example is the measurement of willingness to pay. To measure the willingness to pay, you can perform direct questioning, however, this direct mechanism has its limits, because the direct questioning is fraught with validity and Reliabilitätmängeln. In reality, the buyer always compares its benefits with the price, but here the price is considered in isolation.

Direct truthful mechanisms

Also known as incentive compatible mechanisms. A mechanism was directly truthful relative to a given game-theoretic solution concept, if the strategy, ie the truthful revelation of their own type, is that it is the equilibrium strategy in the chosen solution concept. The Vickrey -Clarke - Groves mechanism, for example, is directly truthfully in dominant strategies.

Dominant strategies exist for only a few mechanisms. Frequently mechanism design problems can be modeled as Bayesian games in which the player types are represented by random variables and the result of mechanisms in Bayesian Nash equilibrium interested.

Incentive compatible mechanisms to examine what rules need to be set so that both sides show in a certain situation, a certain behavior. At the core is the relationship between the outcome of negotiations and the details of the players on their respective private information. An example of an incentive- compatible solution to measure the willingness to pay would be the following scenario: The prospective buyer is for a product initially its price at which he would be willing to pay. Then is then randomly drawn a prize. If the price is below the stated willingness to pay, the applicant must buy the product to the drawn price, the price is drawn over it, there is no obligation to purchase. In this case, the mechanism is thus incentive compatible, because it is in the interest of the prospective buyer to reveal his true willingness to pay.

Social choice

A function is called a social choice function. A mechanism implements a social choice function ( with respect to a solution concept ), if there is a tuple of strategies with the following properties:

  • The tuple represents a balance in the chosen solution concept represents, and
  • It is, that is, in equilibrium, the selection function is.

Revelation principle

If there is a mechanism that implements a social choice function, then there is also a direct truthful (or incentive compatible ) mechanism which implements the same function.

Examples

Basketball

An example of the mechanism design is to define the rules for a sport. In the basketball game, the ball leading team must have completed their attack within 24 seconds, otherwise the changes possession. A draw does not exist in basketball. If the score after the end of normal time offset, an extension of five minutes each follows, until a team has won at least one point ahead. This mechanism leads the two teams at the game of basketball to a faster and more aggressive competition.

Division of the cake

There is a piece of cake for two children. How can this cake be split for two children, so that the two children are satisfied? The satisfaction of the two children is considered here as the intended result, and the distribution rule corresponds to the mechanism that is to be performed in this division game. A good mechanism here is: A child is to divide the cake piece into two parts, then child B is first select a part of it, the other part receives child A. Thus, one can avoid the imbalances distribution of the cake from A Child.

Vickreyauktion

→ Main article: Vickreyauktion

The Vickreyauktion is an example of a mechanism for auctions. All bidders enter simultaneously from covert bids and the bidder with the highest bid obtains the auctioned good. However, he only has to pay the price of the second highest bid. The rules here are so designed that it is for each bidder, the best strategy is just as much to offer as it is worth the Good.

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