Game theory Flashcards
what is a strictly dominant strategy
a strategy where regardless of what the other player does, one strategy earns the player a strictly higher payoff than any other
what is the first solution concept for game theory
rational players don’t play strictly dominated strategies
why do some people not like the predicted solution using strict dominance for the prisoner’s dilemma (confess, confess)
because it is not a pareto efficient outcome, both players would be better off if they played (deny, deny)
what are the steps for solving with strict dominance
check to see if any strategies are strictly dominated by any of the other strategies,
eliminate those that are,
then see if the question asks you to use rationalizability and if not then that is as far as you can go
what is rationalizability
common knowledge of rationality which means we can iteratively eliminate strictly dominated strategies
what is a best response ** (need to learn write down answer)
ui(si*,s-i) > ui(si,s-i)
strategy si* is a best response if it is the strategy that maximises the payoff of player i taking as given that the other players are playing s-i
(s-i the -i is subscript like the si*)
nash equilibrium d
stable equilibrium where no participant can gain an advantage by changing strategy if the strategies of the others remain unchanged
nash equilibrium in equations ** learn
ui(si,s-i) > ui(si,s-i*),
set of strategies in a game is a nash equilibrium if and only if each strategy is a best response to the other
how do you find nash equilibrium in a prisoner’s dilemma sort of game
you think if player 2 did this what would player 1 do and then underline that side of the payoff etc
what is another way to look at nash equilibrium
a set of strategies for which there is no profitable deviation for any player
how do you do a cournot-nash equilibrium *
write down total revenue for firm one in terms of q1 q2 and p,
differentiate wrt q1 and set equal to 0 to find max and then work out q1 and q2
is a cournot equilibrium always a nash equilibrium
no, work out the quantity for firm 1 using original equation and it might give a higher total revenue for one firm so not a nash equilibrium
what does bertrand equilibrium mean they compete in
the two firms compete in prices, not quantities
what is the player’s payoff from a mixed strategy *
the player’s payoff from a mixed strategy profile is the expected value - a weighted average - of the payoffs she obtains from her pure strategies
can the expected payoff of playing a mixed strategy be higher than playing a pure strategy
no, a player’s payoff from any mixed strategy profile is no larger than her maximal payoff from a pure strategy, holding the other player’s strategies fixed