Game Theory

1
Game Theory

• strategy a plan,
• a method, an approach

2
Terminology

• Strategic Form Game
• Consists of a set of players.
• Each player has a strategy set.
• For each outcome, there is a pay-off.
• Dominant Strategy
• A choice which is always best.
• Nash Equilibrium
• Self-enforcing
• Pareto optimal
• Zero Sum Game

3
Normal Form Representation

• Pay-off Tables
• Rules Matter !!!
• Simultaneous vs. Sequential
• One-period vs. Multi-period

4
Some Examples
5
Some Examples
6
Some Examples
7
Prisoners Dilemma
8
Subgames

• Extensive Form Representation
• Player 1 chooses an action, a1.
• Player 2 observes a1, then chooses a2.
• Pay-offs are known.
• Moves occur in sequence.
• All previous moves observed prior to next move.
• No noncredible threats.

9
Example
 
10
Infinitely Repeated Games

• One time deal
• Can cheat and get away with it.
• Repeated Games
• Each firm can influence rival strategy
• by signalling
• by threatening to punish
• As time goes on, collusion more likely!!

11
Threats

• Effectiveness of threat depends on
• Interest rate
• Higher interest rate, lower present value of
  future profits.
• Lower interest rate, more effective threat.
• Length of Game
• Longer game, more effective threat.
• Credibility
• Firms will ONLY act in their own best interest.