Introduction to Game Theory
Today's Agenda
Components of a Game
The Extensive Form (Ch. 2)
Strategies and the Normal Form (Ch. 3)
Beliefs, Mixed Strategies, and Expected Payoffs (Ch. 4)
Components of a Game
Components of a Game
The Extensive Form
The extensive form of the game is a tree diagram showing:
Nodes:
Branches:
Initial node: where the game begins
Decision nodes: where a player makes a choice; specifies player
Terminal nodes: where the game ends; specifies outcome
Individual actions taken by players; try to use unique names for the same action (e.g. "left") taken at different times in the game
Information sets:
Sets of decision nodes at which the decider and branches are the same, and the decider doesn't know for sure where they are.
Strategies
A strategy is a complete, contingent plan for a player in the game.
The Normal Form
Notation
Strategy:
Strategy Space:
Strategy profile:
Strategy profile space:
Payoff functions:
Different extensive forms may have the same normal form.
Beliefs, Mixed Strategies, and Expected Payoffs
\sigma_i = \text{player $i$'s mixed strategy}
\theta_j = \text{player $i$'s beliefs about player $j$'s strategy}
Econ 51 | 09 | Introduction to Game Theory
By Chris Makler
Econ 51 | 09 | Introduction to Game Theory
Notation for understanding games
