Game Theory Flashcards
Nash equilibrium
A set of strategies one for each player that are each best responses against one another
All games have at least one
Not every NE involved dominant strategies
Extensive form
Representation of game as a tree
How to find Nash equilibrium
- Via inspection
- pick an outcome and see if either player has an incentive to unilaterally deviate. If not = equilibrium - Via underline
- underline for each player, the payoff he would get if he played his best response to each other players actions
- 2 underlines = equilibrium
Dominant strategy
Best response to all of the other players strategies
Pure strategy
A single action played with certainty
Mixed strategy
Randomly selecting from several possible actions
Players must be indifferent between actions that are played with positive probability
Common knowledge of rationality assumptions
Players all ow all other players are rational
Therefore know what the other players will never do and eliminate them from consideration
Players won’t play a strategy if another strategy is always better against this decrease set of possibilities
= iterated strict dominance (ISD)
–> strategies with ISD = rationalisable strategies
Proper sub game
Part of the game tree including an initial decision not connected to another in an oval and everything branching out below it
Each fame starting from point where player knows persons choices
Sub-game perfect Nash equilibrium (SPNE)
Strategies that form a Nash equilibrium on every proper sub game
Trigger strategy
Strategy is repeated game where one player stops cooperating in order to punish another player for not cooperating
Grim trigger strategy
= if other players fails to cooperate in one period play the (dominated) actions that makes them worse off in all later periods
Best response
A strategy that produces the highest pay off among possible strategies for applier given the other player is doing
