Games Flashcards
Q
A
What is rationality (pt1)?
A player has beliefs about the other players’ decisions
What is rationality (pt2)?
A player maximises utility based on those assumptions
What is a strict dominating strategy?
A strategy that always outperforms another strategy, no matter my beliefs about other players’ decisions.
Common knowledge
Every player knows that every one knows what everyone knows….
What is a mixed strategy?
A lottery over your pure strategies
Why is Nash Equilibrium problematic (assumption)
We need to know our opponent has a correct belief about our strategy
Indifference curves in the three lottery space
Parallel and straight
How is indifference presented in expected utility notation
Weak preference in both directions
How is strong preference presented in expected utility notation
Weak preference one way, and not the other way
What is completeness (Axiom 1 of expected utility)?
Agents can give you a preference between two lotteries (or be indifferent) for every lottery
What is Transitivity (Axiom 2 of expected utility)?
If A is better than B, and B is better than C, A must be better than C
Theorem of expected utility
If we have a finite number of transitive and complete ranks of lotteries, we can build a utility function
What is Independence (Axiom 3 of expected utility)?
Where lotteries split into multiple lotteries, giving identical probabilities of outcomes, we should be indifferent between this setup in the original
What is Continuity? (Axiom 4 of expected utility)
If we have three lotteries, we can make an indifference condition through a lottery between the higher and lower preference utilities
What is the use of an extensive form game
When decisions happen over different periods of time, and people have dynamic information
What is the history of a game?
The sequence of decisions made to get to a certain point
What are the two types of histories
Terminal and Subhistories
How do you present a normal form (non table)
All strategies possible for each player listed
Compromise between NE and backwards induction
Subgame perfect NE
What is Zermelo’s theorem
In a two-player, finite game, with strict preferences win > draw > lose, there is a subgame perfect Nash equilibria
Rubenstein Bargaining model
Infinite bargaining setup where payoffs are discounted at a consistent rate each period
Critique of Independence of Irrelevant Alternatives
In bargaining situations, removing threats can lead to changes in solution
What is the Jury setup
Actions (acquit/convict), Types (looks innocent, looks guilty), State (Innocent, guilty), Payoffs (correct result gets 1, incorrect is 0)