chapter 11 Flashcards
(29 cards)
what is game theory ?
the branch of micro economics concerned with the analysis of optimal decision making in competitive situations. in which the actions of each decision maker have a significant impact on the tortures of rival decision makers.
what happens in a one shot, simultaneous-move game?
two or more players make a single decision at the same time
define these game elements
a. players
b. strategies
c. outcomes
d. payoffs
e. nash equilibriums
a. agents participating in the game
b. the actions that each player might take under every conceivable circumstance that the players might face
c. the various possible results of the game
d. amount each player can expect to get under different combinations
e. occurs when each player choses a strategy that give sit the highest payoff, given the strategy chosen by the other players in the game “rational self interest”
why is the nash equilibrium a plausible outcome of the game ?
the outcome is self enforcing even though it DOES NOT necessarily maximise collective interest
if each party expects the other to chose its NE then both parties will infect chose their NE
what is the prisoners dilemma ?
a game situation in which there is a tension between the collective interest of all players and the self interest of individual players
the nash equilibrium does not coincide with the outcome that maximises the collective payoffs of players in the game
what is the dominant strategy ?
a strategy is better than any other that they could chose no matter what the other player choses
what is a dominated strategy ?
when the player has a different strategy that gives it a higher payoff, no matter what the other players chose to do.
dominant and dominated strategies are opposite
what is a pure strategy ?
a strategy that plays a single action
what is a mixed strategy nash equilibrium ?
a mixed strategy is one in which a player plays his available pure strategies with certain probabilities
if there are no pure strategy equilibrium then there must be a unique mixed strategy equilibrium
how do you find the best responses
if a mixed strategy is a best response then each of the pure strategies involved in the mixed must itself be a best response
in particular each must give the same expected payoff
that is the players chose randomly among their options in equilibrium
how do you find the NASH in all situations ?
- if both players have a dominant strategy , those constitute their nash equilibrium strategies
- if one player has a dominant strategy then that is that players nash, and then the other players best response is the second players best response
- if neither has a dominant, you just find the best response to each of the players strategies and vice versa
- if there are no nash in pure we look at mixed
what is the repeated prisoners dilemma ?
- a one shot game
- game could turn out differently if it was played over and over again by the same players
- when the players are allowed to interact repeatedly , there is a possibility that each player can make decisions based on what their opponent did previously.
- this alters the array of strategies and can dramatically change the game’s outcome
what are the two strategies that can help achieve players cooperating ?
- grim trigger strategy
- tit for tat strategy
describe grim trigger strategy
a. - player a starts with coop and player b will also as long as player a does
- the first time that player a cheats player b will chose cheat the next round and all after that
- this may lead player a to continue cheating
player bs strategy is the grim trigger because one episode of cheating triggers a permanent breakdown of cooperation between the two
describe tit for tat strategy
a strategy in which you do to your opponent what they did to you in the last period
the prospect of eventual retaliation and the corresponding reduction in profit beyond the initial period is what provides an incentive for a player to maintain coop behaviour. even though cheating is dominant in a one shot this shows that in the repeated prisoners dilemma cooperation can under circumstances result from self interested behaviour
under what conditions does the likely hood of a cooperative outcome increase ?
- the players are patient ( value future payoff )
- interactions between players are frequent
- cheating is easy to detect
- the one time gain from cheating is relatively small
what important lessons does game analysis teach us ?
- in competitive settings you must anticipate the reactions of your competitors
- the longer you are going to have to interact the more important this becomes
what are sequential move games ?
where player one takes action and then player two having observed player ones actions
what is backwards induction ?
looking at the end of the decision tree to see whats the optimal decision for the player at each decision point
define these terms associated with risky outcome ?
a. lottery
b. probability of an outcome
a. an event with an uncertain outcome
b. likelihood of an event occurring
describe a probability distribution
it depicts all the possible payoffs in the lottery and their associated outcomes
define subjective probabilities
Pr that effect subjective beliefs about risk events
what is the expected value and how do you calculated it ?
measure of the average payoff that the lottery will generate
EV = Pr(A).A + Pr(B).B + Pr(C).C
what are the variance and standard deviation of a lottery ?
the variance of a lottery is the sum of the probability weighted squares deviation between the possible outcomes of the lottery and the expected , its a measure of the lotterys riskiness
Var = (A-EV)^2(Pr(A)) + (B-EV)^2(Pr(B)) + (C-EV)^2(Pr(C))
the standard deviation is the square root of the variance, its an alternative measure of risk
