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
what is a mixed strategy denoted as
σ1 or σ2,
subscripts
what does every finite game have
if a game has a finite number of players and actions, there exists at least one nash equilibrium, possibly involving mixed strategies
what is a node
a node is a decision point
what is a subgame
a node together with all the nodes that follow it, and includes the player and action labels, and payoffs at the terminal nodes
subgame perfect equilibrium d
a strategy profile of an extensive form game is a SPE if and only if the strategy profile it specifies on each subgame is a nash equilibrium of that subgame
when writing down the SPE do you write down just the actual SPE when writing strategies
no, you write down the action to be chosen at each node, even the nodes that are not played on the equilibirum path (example page 6 on back)
a subgame is a proper subgame if it is what
a subgame is a proper subgame if it is not equal to the initial game
for an infinitely repeated game when would blackadder wish to stay in the equilibrium
Blackadder will wish to stay in the equilibrium whenever the value of deviating is less than the value of cooperating
as long as the future is valuable enough what is the nash equilibrium
as long as the future is valuable enough, cooperation is a nash equilibrium
what is the best response of the other player if one player plays the trigger strategy
if either player plays the trigger strategy, the other player’s best response is to play the trigger strategy as well
Perfect baysian equilibirum (PBE) of an extensive form game d
a perfect baysian equilibrium of an extensive form game is a pair that satisfies the two properties of sequential rationality and consistency of beliefs (better definition backpage 10)
sequential rationality d
for any player, the action her strategy specifies at that information set must maximise her expected payoff given her beliefs as specified by u (mew) (backpage 10)
consistency of beliefs d
the belief function is given by Bayes’ rule whenever possible (backpage 10)
what is a pooling equilibrium
when both ‘types’ of player 1 play the same strategy
What does Nash equilibrium mean **
There is no profitable deviation for any player
