game theory

Question 1

strategic interactions

Answer 1

when 2 or more people engage in interactions with mutual awareness of the cross -effect of their actions

Question 2

game theory

Answer 2

a set of models of stratgeic interactions

strategic intercations modelled as instances of games

Question 3

parts of a game

Answer 3

players
strategies: what actions are open to players
order of play
information: what players know when making decisons
payoffs: outcome for each player for each possible combos of actions

Question 4

sequential moves

Answer 4

moves occur one after the after
“if i do this how will my opponent react”
Second player can observe choice of first player and use that info to inform their choice.
eg chess
use game tree

Question 5

simultaneous moves

Answer 5

occur at same time
“what is my opponent going to do right now”
Isolated choice, players have same amount of info when they make choices
eg rock paper scissors, silent auction
game table

Question 6

game table

Answer 6

row player
column player

cell notation (row strategy, column strategy)
start with row player- first payoffs
then column player- second payoffs

Question 7

payoffs

Answer 7

outcome for each player for each of possible combos of actions
gives complete numerical scale to compare different outcomes
can be monetary income, profit, ratings etc

Question 8

nash equilibrium

Answer 8

a list of strategies, one for each player, such that no player can get a better payoff by switching to some other strategy that is available while the other players adhere to the strategies specified for them

mutual best response, no incentive for either to move away

Question 9

dominant strategy

Answer 9

a strategy that is always a players best response
regardless of chosen strategy of other player, best response strategy is constant

Question 10

dominant strategy equilibrium

Answer 10

when both players have a strictlt dominant strategy
NE known as dominant strategy eqm

Question 11

dominated strategy

Answer 11

is never the best response strategy, regardless of other players chosen strategy

Question 12

social optimality

Answer 12

adding payoffs within each cell to calculate total payoff to society under each outcome

Question 13

types of games

Answer 13

invisible hand game
assurance game
battle of the sexes game
prisoners dilemma game
ultimatum game

Question 14

invisible hand game

Answer 14

nash equilibirum and social optimum coincide
Adam Smith: players acting independently and in their own self-interest that will reach an eqm that is in joint interest of all players and for society
invisible forces can guide players to outcome for everyone

Question 15

assurance game

Answer 15

2 Nash equilibria
both players play same strategy
both players strictly prefer same NE over the other NE

Question 16

battle of the sexes game

Answer 16

2 nash equilibria
both players play same strategy
each player strictly prefers a different NE

Simultaneous move game
You want to move as your partner does but you prefer different things.

Question 17

prison dilemma game

Answer 17

dominant strategy eqm outcome is worse for both players than the dominated strategy outcome

illustrates how two rational individuals, acting in their own self-interest, can lead to a suboptimal outcome for both

Question 18

ultimatum game

Answer 18

responder and proposer play against each other
sequential move game: proposer makes choice, responder observes then responds
proposer decides
responder can reject offer (both players get nothing) or accept offer (responder keeps offered amount, proposer keeps remainder)

Question 19

parts of game tree

Answer 19

proposer @initial/root node
decision nodes show where actions can be taken
branches : show what actions can be taken from that node
terminal nodes to end game
add payoffs to show final outcome of combos of choices
solved using backward induction + pruning branches

Question 20

eqm vs outcome

Answer 20

eqm : pair of strategies
outcome: pair of payoffs