term 2 lecture 10- game theory Flashcards
what are the characteristics of a game?
a game consists of :
- a set of players
- a set of strategies /actions for each player
- the payoffs to each player for every possible combination of strategies played by the players
what is game theory?
game theory is the general theory that helps to model strategic behavior by agents who understand that their actions affect the payoffs of other agents ie that there is an interdependence between the agents payoffs.
it is generally depicted in a mathematical form
what is the defintion of a game?
a game is an interactive situation whose result depends on the actions taken by its participants
when is a players strategy dominant?
a players strategy is dominant if it yields the player a payoff strictly higher than any other strategy, for any combination of other players strategies
when is a players strategy weakly dominant?
a players strategy is weakly dominant if the payoffs it yields are not lower than those yielded by other strategies and sometimes even higher
how is the prisoners dilemma shown for the cartel?
cartel members can charge the monopoly price or a lower price, cheating firms can increase profits, cartel members possible strategies include abiding by their agreemement to cheating, given market conditions, the best strategy is charging the low price, as both firms will charge lower price they will be worse off.
how does the prisoners dilemma apply to advertising?
all firms advertising tend to equalise their effects, everyone would gain if no one advertised
how can you simplify your choices in a game?
you can simplify your choices through the iterated elimination of dominated strategies
what is the process of the iterated elimination of dominated strategies?
find and dominated strategy and remove it from the game
check if there is any more dominated stategy in the reduced game, if so remove it also. repeat process until there is only one profil of strategies left or until there are no more dominated stratergies
what is a mixed strategy using heads and tails as an example?
instead of playing purely heads or tails, player 1 selects a probability distribution (p,1-p) meaning that with probability p player 1 will play heads and with probability 1-p will play tails
so player 1 is mixing over the pure strategies heads and tails
what is the mixed strategy nash equillibrium?
{(p, 1-p), (q, 1-q)} = {(0.5,0.5), (0.5 , 0.5)}
what is the general result of existence?
the general result is that a game with a finite number of players, each with a finite number of pure strategies, has at least one nash equillbrium. this does not mean that there is guarenteed existence of a pure nash strategy but that there must at least be one mixed nash equillibrium
how can we find mixed strategy nash equillibrium of large games?
only strategies that survive iritative eliminated dominated strategies can be used in mixed nash equillibria
what does simultaneous play mean?
it means that when each player chooses his/her strategy, he/she is not aware of the other players moves
what is sequential play games
the player who plays first is the leader. the player who plays second is the follower
