Game theory

Question 1

what is a strictly dominant strategy

Answer 1

a strategy where regardless of what the other player does, one strategy earns the player a strictly higher payoff than any other

Question 2

what is the first solution concept for game theory

Answer 2

rational players don’t play strictly dominated strategies

Question 3

why do some people not like the predicted solution using strict dominance for the prisoner’s dilemma (confess, confess)

Answer 3

because it is not a pareto efficient outcome, both players would be better off if they played (deny, deny)

Question 4

what are the steps for solving with strict dominance

Answer 4

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

Question 5

what is rationalizability

Answer 5

common knowledge of rationality which means we can iteratively eliminate strictly dominated strategies

Question 6

what is a best response ** (need to learn write down answer)

Answer 6

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*)

Question 7

nash equilibrium d

Answer 7

stable equilibrium where no participant can gain an advantage by changing strategy if the strategies of the others remain unchanged

Question 8

nash equilibrium in equations ** learn

Answer 8

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

Question 9

how do you find nash equilibrium in a prisoner’s dilemma sort of game

Answer 9

you think if player 2 did this what would player 1 do and then underline that side of the payoff etc

Question 10

what is another way to look at nash equilibrium

Answer 10

a set of strategies for which there is no profitable deviation for any player

Question 11

how do you do a cournot-nash equilibrium *

Answer 11

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

Question 12

is a cournot equilibrium always a nash equilibrium

Answer 12

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

Question 13

what does bertrand equilibrium mean they compete in

Answer 13

the two firms compete in prices, not quantities

Question 14

what is the player’s payoff from a mixed strategy *

Answer 14

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

Question 15

can the expected payoff of playing a mixed strategy be higher than playing a pure strategy

Answer 15

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

Question 16

what is a mixed strategy denoted as

Answer 16

σ1 or σ2,

subscripts

Question 17

what does every finite game have

Answer 17

if a game has a finite number of players and actions, there exists at least one nash equilibrium, possibly involving mixed strategies

Question 18

what is a node

Answer 18

a node is a decision point

Question 19

what is a subgame

Answer 19

a node together with all the nodes that follow it, and includes the player and action labels, and payoffs at the terminal nodes

Question 20

subgame perfect equilibrium d

Answer 20

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

Question 21

when writing down the SPE do you write down just the actual SPE when writing strategies

Answer 21

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)

Question 22

a subgame is a proper subgame if it is what

Answer 22

a subgame is a proper subgame if it is not equal to the initial game

Question 23

for an infinitely repeated game when would blackadder wish to stay in the equilibrium

Answer 23

Blackadder will wish to stay in the equilibrium whenever the value of deviating is less than the value of cooperating

Question 24

as long as the future is valuable enough what is the nash equilibrium

Answer 24

as long as the future is valuable enough, cooperation is a nash equilibrium

Question 25

what is the best response of the other player if one player plays the trigger strategy

Answer 25

if either player plays the trigger strategy, the other player’s best response is to play the trigger strategy as well

Question 26

Perfect baysian equilibirum (PBE) of an extensive form game d

Answer 26

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)

Question 27

sequential rationality d

Answer 27

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)

Question 28

consistency of beliefs d

Answer 28

the belief function is given by Bayes’ rule whenever possible (backpage 10)

Question 29

what is a pooling equilibrium

Answer 29

when both ‘types’ of player 1 play the same strategy

Question 30

What does Nash equilibrium mean **

Answer 30

There is no profitable deviation for any player