advertisement

Mechanism Design Mechanism design is the sub-field of microeconomics and game theory that considers how to implement good system-wide solutions to problems that involve multiple self-interested agents, each with private information about their preferences. In recent years mechanism design has found many important applications; e.g., in electronic market design, in distributed scheduling problems, and in combinatorial resource allocation problems. Basic Theory The Number of Players (Agents) = 1,2, … , Alternatives = , , We call as public alternative, because choosen alternative affects all players in Basic Theory Each player privately observes a signal or ‘s type ∈ Θ determines ‘s preferences over outcome, and Θ (Set of Preferences) can be finite or infinite. All players type = (1, 2, … ) Is called state of the word The state is drawn randomly from state space ≡ 1 2 … Which is the set of all possible profiles of types Θ Each is according to some prior distribution () Basic Theory • is player private information • is common knowledge Payoff • Every alternative has a money equivalent value, and preferences are additive in money • Player is given amount of money equal to ℝ • As mechanism design allows transfer of money from every player then if < 0 means the money is taken away from • If the public choosen alternative is , the player ’s payoff is described • , , = , + • , means money equivalent value of alternative Outcome Outcome = combination of choice of public alternatives together with monetary amounts that each player gets or pays. Then outcome can be represented as = , 1, … , Mechanism Designer • Assumption : mechanism designer doesnt have source of funds, then the monetary payments that players make or receive have to be selffinanced ≤ 0 =1 • Monetary transfer can be negative, means the designer can keep some of the monet raised by players Mechanism Design’s Objectives • = ( , 1 , … , ) • and (1 , … , ) is transfer rule Mechanism Game • Mechanism designer desires to implement . , but he cannot do this dorectly because the choice rule depends on unobserved state of the world () • In order to implement state-continget choice rule, designer has to ask players to reveal their types, however players may have not incentives to reveal their true types. Bayesian Game • Because is only observed by player and not other’s players (incomplete information), and players given prior over types (), then this set up follows Bayesian Game In formal game, we have : Mechanism = Θ1, … , Θ, . Strategy profile ∗ . = ∗ . , … , ∗ . Outcome ∗ . = (. ) , Revelation Principle • Mechanism = Θ1, … , Θ, . that implements social choice function . using equilibrium strategy profile ∗ . = ∗ . , … , ∗ . , ∗ . = (. ) • If the players are playing a mechanism that results in the implementation of (. ) then by construction of equilibrium beliefs they must know that (. ) will be implemented, and hence the mechanism designer might as well implement it directly