Game Theory Flashcards
The prisoners dilemma
Two people have been arrested on suspicion of having committed a crime and are being interrogated separately. If they both confess they will both go to jail for 6 years. If both dont confess they will go to jail for 2 years. If one confesses but the other doesnt then the confessor is free and the other gets 10 years.
How can a game theoretic situation be represented?
In strategic form
Strategic form
A table outlining the players, the strategies and the payoffs
Players
the people in the scenario
the stratgies
the actions that each player can decide to undertake
payoff
what each set of actions results in
Matching Pennies
Two Children hold concealed pennies in their hands. The simultaneously reveal their pennies to each other. If their pennies match child 1 gives child 2 their penny, if they dont match then child 2
Battle of the Sexes
A man and a woman are trying to decide how to spend a weekend together. Both would prefer to spend the evening together rather than apart, but the man prefers to go to a football game and the woman prefers to go to a concert. The payoffs are represented in utility
Game theory
Used to study situations where each person’s payoff depends upon his own actions as well as the actions of other people
A strategic form game is characterised by..
1) A set of n players, indexed by i=1,2,…n
2) For every player i, a set of strategies denotedby Si, with si denoting a particular strategy
3) For every player i, a utility function ui(s1,s2…sn)
4) We denote a n-player strategic form game by: G={S1,S2..Sn;u1,u2…un}
Dominant strategy equilibrium
If one of the payoff is preferable more so than the other. I.e. the prisoners dilemma, C1 strictly dominates NC1 and C2 strictly dominates NC2. As such the dominant strategy is
What is the main problem with the concept of the dominant strategy equilibrium
It does not exist for most games e.g. matching pennies and battle of the sexes
Nash Equilibrium
A pair of strategies of a two player strategic form game is a nash equilibrium iff s1bar is the best response to s2bar and simultaneously vice versa
Cournot Duopoly
two firms in a market where the price is fixed. The firms choose the quantity to produce.
Finding the Nash equilibrium of the Cournot duopoly.
Sub the inverse demand function into Q=q1+q2. Then find the payoff for company 1 and 2. Find the max equation for each company by finding the FOC. Solve for q1 and q2 when q1=q2.