Game Theory Flashcards
Game Theory
Game Theory is the formal study of the interactions and decision making of a group of agents (players) who behave strategically
enables to model strategic behavior by the agents who understand that their actions affect the interests of the other agents
What is a Game?
formal description of a strategic situation, and
consists of…
A set of players (not necessarily a person)
A set of strategies for each player
The payoffs to each player for every possible choice of strategies by
all the players
Conventional Assumptions
Rationality
A player seeks to maximise her own payoff
or if she has well-defined objectives (preferences) over the set of possible outcomes and she implements the best available strategy to pursue them
Complete information
No private information, all the details including strategies and payoffs of the game are all common knowledge to all players
Common knowledge
A fact X is common knowledge if every player knows it, and every player knows that every player knows it, and every player knows that every players knows that every player knows it, and so on…(infinite!)
Nash equilibrium
An outcome of a game where each strategy is a best reply to the other
No player can unilaterally change her strategy and get a higher payoff
NE always exists (in finite games)
A NE may not necessarily be the best outcome
A game may have many Nash equilibria
A dominant strategy
No matter what the other player plays, your best reply is always
Price competition in a Duopoly (Bertrand competition)
The NE is that firms compete on price, undercutting each other, and making zero profits.
The NE is inefficient because if the firms would collude and fix prices at a higher level, both would make higher profits (but collusion is not a NE because each firm has an incentive to undercut the other firm).
Repeated Games
We now consider a strategic game that is repeated over a number of periods (finite or infinite)
Strategy in repeated game
A complete plan how the player will act in the whole course of the game in all possible situations in which he can find himself
Grim trigger strategy
Cooperate until the other player has defected, after that defect forever (not forgiving, punishes forever)
Tit for Tat
Cooperate in first round
On every round thereafter, if opponent cooperated in the previous round, then
cooperate, if opponent defected, then defect (forgiving, punishes for one period)
Sequential Play Games
Games in which one player plays before
another player
The player who plays first is the leader (first mover)
The player who plays second is the follower (second mover)
Pure strategy
A specific choice of a strategy from the player’s possible strategies in a game
Mixed strategies
A mixed strategy is an assignment of a probability to each pure strategy
Coordination Games
Simultaneous play games in which the payoffs to the players are largest when they coordinate their actions.
Famous examples are:
Battle of the sexes
Prisoner’s dilemma
Assurance games
Games of Competition
ZERO SUM GAME
Simultaneous play games in which any increase in the payoff to one player is exactly the decrease in the payoff to the other player
Constant (payoff) sum games
