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: