Term 1 Lecture 1 Flashcards
(8 cards)
Defining a game in Strategic Form:
- A list of players, I = 1,2,…I
- A description of all the actions each player can take
- e.g. si = (rock, paper, scissors), for I = 1,2
- strategy profile taken = vector s = (s1,s2…,sI)
- set of all possible strategy profiles, S = (s1,…,si) - Utility function ui(s) = ui(s1,…,si)
What’s strict dominance?
A mixed strategy strictly dominates the pure action, iff player i’s payoff when she pays oi and the other players play actions si is strictly higher
Whats weak dominance?
A mixed strategy weakly dominates iff playing it as at least as good as the alternate option
Common knowledge of rationality
- Every player is rational
- Every player knows the other player is rational
- Every player knows the other player knows every other player is rational, etc etc
Nash equilibrium
- strict
There is no incentive to unilaterally deviate from the strategy
- strict is when each player has a unique best strategy and no other strategy gives the same payoff and deviating would make them worse off
Ways to find NE
- Iterative elimination of strictly dominated strategies
- Underlining rule
- Mixed strategy
- Intersection of best responses - differentiation
5 Observations of the intersection of best responses method
- Generalisation of the underlining method to continuous actions
- If a player had many best responses, all should be included in the best response function
- Possible a player does not have a best response
- Generalises to n players as there are as many equations as actions
- No intersection = no NE exists
3 interesting concepts
- how many NEs and which to pick?
- what is Pareto Efficiency?
- what’s a risk dominant equilibrium?
- Many games have more than 1 NEs, which makes it difficult to predict which will be chosen
- PE if there is no other outcome where both players can be better off
- An equilibrium is risk dominant if it is the safer option regardless of what someone picks
