game theory

Question 1

what is a game defined by?

Answer 1

players - the decisions makers eg oligopolistic firm
strategy - action taken by a player eg price in bertrand or quantity in cournet/stackelberg
payoff- outcome evalution of each player eg profits

Question 2

what are the two kinds of strategies?

Answer 2

a pure strategy - primative strategy eg in rock-paper-scissors , play rock
a mixed strategy - a probability weighted mix of pure strategies eg in rock-paper -scissors chose rock, paper, scissors each with probability of 1/3

Question 3

what is a strategy profile?

Answer 3

a list of one strategy per player eg player A plays rock and player B plays paper

Question 4

what is a payoff matrix?

Answer 4

a table with players, strategies and payoffs

Question 5

how do you predict the outcome of strategic interactions?

Answer 5

iterated elimination of strictly dominated strategies
or
nash equillibrium

Question 6

what is a dominant strategy?

Answer 6

a strategy that maximises payoffs no matter what others do

Question 7

what is a dominated strategy?

Answer 7

a strategy that gives worse payoff than another strategy whatever the others do

Question 8

what is a nash equillibrium?

Answer 8

a stategy from which no player has incentives to deviate unilaterally ie each player is best responding to the opponents action

Question 9

is an iterated elimination of dominated strategies solution a nash equillibrium?

Answer 9

yes the solution is a nash equillibrium

Question 10

what are the characteristics of a sequential game?

Answer 10

one player is the leader and the other player is the follower. one plyaer then moves first and the other observes this action before making their move. players can make decisions condtional on what other players have done

Question 11

what are the charactertics of a repeated games?

Answer 11

extensive form representation
it makes the temporal structure explicit
it shows both the choice and the timing of a players actions
it represents a finite sequential game as a rooted tree

Question 12

what is a root>

Answer 12

intial node where the first decision is made

Question 13

what are nodes>

Answer 13

points at which the players can take actions

Question 14

what are internal nodes?

Answer 14

they are nodes that are labelled with player identifiers

Question 15

what are branches?

Answer 15

they connect the nodes and represent the actions that may be taken at that node. they are labelled with players choices

Question 16

what are terminal nodes?

Answer 16

end of the game it shows the payoffs earned by each player if the game ends at that node. it works by backwards induction. you look ahead and reason backwards

Question 17

what is a credible threat?

Answer 17

when a threat made by a player in a sequential game that would be in the best interest for the player to carry out. this can be created by a commitment strategy which will change the payoff matrix