09 & 10 - Static Games of Incomplete Information Flashcards
What common characteristics do FPA (=first price auction) and SPA (=second price auction) share?
- participants are asked to make money bids
- the highest bidder obtains the object
- such auction forms are called “standard”
How do expected payoffs from standard auctions relate?
Suppose that bidders’ values are independently and identically distributed, and that all bidders are risk neutral.
Then any symmetric and increasing equilibrium of any standard auction, such that the expected payment of a bidder with value zero is zero, yields the same expected revenue to the seller.
Which assumptions need to be satisfied such that any symmetric and increasing equilibrium of any standard auction yields the same expected revenue to the seller?
- bidders’ values are independently and identically distributed,
- all bidders are risk neutral.
- the expected payment of a bidder with value zero is zero
What is Dutch (descending-price) auction?
- A publicly displayed price decreases “continuously” (starting high).
- At any price, each bidders either pushes a button or not.
- Once the first bidder pushes the button the price freezes, that bidder obtains the object and pays the displayed price.
What is English (ascending-price) auction?
- A publicly displayed price increases “continuously” (starting low).
- At any price, each bidders either pushes a button or not.
- Once the second-to-last bidder pushes the button the price freezes, the one that has not pushed yet obtains the object and pays the displayed price.
What question is “Mechanism Design” concerned with?
- How do the rules of a game have to be specified in order to achieve a given desired outcome?
- studies environments where players have private information which is unknown to the designer.
- A mechanism defines a static Bayesian game
What is the central question in implementation of mechanism design?
Central question: Which “social choice functions” f : T -> X can the designer implement as Bayesian Nash equilibrium, and how?
What is a direct mechanism?
A direct mechanism is a Bayesian game such that each agent i’s action space is Tᵢ,
=> each agent submits a type report, and the outcome of each possible action profile t is in X.
= each agent makes one single declaration, simultaneous move Bayesian game vs indirect mechanism, which involves a sequence of actions, Bayesian extensive form game
What is the revelation principle theorem?
Theorem (The Revelation Principle)
A social choice function f is implementable by some mechanism if and only if it is implementable by a direct and truthful mechanism.
How do mixed strategy nash equilibria relate to static games with incomplete information?
As incomplete information disappears, players’ expected actions in the pure-strategy BNE approach the mixed-strategy NE under complete information.
When is a direct mechanism truthful?
A direct mechanism is truthful (aka “incentive compatible”) if sᵢ : Tᵢ -> Tᵢ with sᵢ(tᵢ) = tᵢ for all agents i and types tᵢ constitutes a BNE.
= when the equilibrium strategy is to declare their type, i.e. write down all their private information
How can you mathematically show that a mechanism is truthful?
You must show that the strategy that maximizes expected payoff is the truthful valuation.
What does a model of knowledge define?
1) Ω = set of all possible states of the world
2) probability of each state of the world
3) Information partitions 𝒫ᵢ containing all events that individual 1 can distinguish
4) probability of each state in an event
