Term 2 game theory Flashcards
How do you prove that the nash equilibrium in rock papers scissors is unique?
-proof by contradiction
-Start with assumption that each action has to be played with same probability of adjacent action
-Start by supposing this is not the case.
-Suppose p(rock) > p (scissors)
-This can be exploited by just playing paper.
-Suppose p(rock) < p(scissors)
-(should not paper) you have two remaining options, could we play rock?
-if P(scissors) > p(paper) you simply play rock.
-if p(scissors) less or equaled to paper
then you should pick scissors.
-Therefore if p(two adjacent actions) is different then it can be exploited by a pure strategy and hence is not a nash equilbirium.
WHy are mixed strategies criticised by economists?
- Humans are not great randomisers
- The opponent cannot correctly conjecture the probability with with each is playing
What is evidence of the gamblers fallacy?
This is after an event has occurred on many instances people believe that something is more or less likely.
What is a restriction of nash equilibrium
- The assumption that players cannot communicate on choices
-The relaxation of this was proposed by Aumann that is a correlated equilbrium. Allows preplay concepts.
What is a convex hole?
What does it tell us?
This is a graph with each nash equilibrium with the expected payoff in the middle.
The expected payoff forms a convex hole.
Payoff, expected payoff and coin toss equilibrium
-that corellated equilbiriums that are dictated by a random mechanism can push out the eq
What is the difference between a static and dynamic game in game theory?
Static - individuals make decisions simultaneously
Dynamic - individuals make decisions sequentially.
What does a dashed line mean between player 1 and 2 in a decision node?
It means the player after does not know what action the player before has made.
What does no dashed line mean between player 1 and 2?
It means that player 2 observes what player 1 does and then makes a decision.
In a sequential game, how does a player have complete knowledge?
if the extensive form is common knowledge.
In a sequential game how does a player has perfect knowledge?
if at every instance a player has to make a move, they know full history of moves before making her choice.
How do you solve a game by backward induction?
you look at the final node and then decide the best decision and then go back and decide the best decision again.
What is a sub-perfect equilbirium?
How do you work out how many sub games there are?
- The whole game is a sub game
-Then the games that player 2 must decide at.
What is a sub game and a proper sub game
A proper sub game is a game that is not the whole game.
What is the benefit of finding a perfect sub-game equilibrium?
-it removes non credible threats as they could be a general nash equilibrium.
