Game Theory
Nash Equilibrium
A set of strategies, one for each player, such that each player's strategy is a best response to the others'
Common knowledge
All players know the rules of the game they are playing. All players know that everybody else playing the game knows the rules
Trigger strategies under Infinite time horizon
Begin by cooperating Cooperate as long as your rivals do Upon observing a defection: immediately revert to a period of punishment of specified length in which everyone plays noncooperatively
Tit-for-Tat Strategy
Begin cooperating Cooperate if your rival cooperated in the most recent period Cheat (for instance deviate from a collusive agreement and lower your price) if your rival cheated in the most recent period
Grim Trigger Strategy
Begin cooperating Cooperate until a rival deviates Once a deviation occurs, play non-cooperatively for the rest of the game
Payoffs
Earnings or utility associated to each possible outcome of the interaction
Two Trigger Strategies
Grim Trigger Strategy; Tit-for-Tat Strategy
Players
Group of people whose earnings and well being are affected by each other's actions
Best Response
If everybody is playing a best response, no one has incentive to unilaterally change its strategy
Repeated Interaction
Ongoing relationship between players; The same game is repeated over time; Current actions affect future interactions, In other terms, strategies are history-dependent
Rationality
Players have full knowledge of their interests and choose the strategies that better realize their interests; They don't make mistakes
Axelrod's Simulation
Prisoner's Dilemma repeated 200 times: Winner: Tit-for-Tat. Reasons: a player choosing it is "nice," never the first to defect "forgiving," able to cooperate after a defection. "provocative," retaliating for defection with defection. "clear," their strategy is easy for other players to understand. 1816
Basic Assumptions
Rationality; Common knowledge
Strategic Decisions
Study of rational behavior in interactive or interdependent situations; Non - cooperative game theory: each individual acts so to maximize her individual benefit/utility/return
Infinite time horizon
The relationship among players never ends: No last period, so the opportunity cost of cheating (forgone profits from cooperation) is always positive. The use of history-dependent strategies is now possible
Strategies
complete plan of action; When players act sequentially, a strategy specifies a decision for each possible decision by other players
Dominant strategy Equilibrium
each player does the best it can, regardless of the strategies played by all other players
Finite Repetition
the only rational outcome is for both to charge a low price in each period. Cooperation is not sustainable if time horizon is finite: