Lecture 14: Game Theory and Mixed Strategies Equilibrium
Two players with two strategies. You & him
3 Types of Equilibrium - Downward Strategy (DS) always best
Prisoners Dilemma - Thera is built in thereat if there are 2 periods. Thereat won't work because there is no period 3. Only when you don't know when the game ends, pacts work. A repeated game work only if there are infinite number of times. ("Long term cheating")
Example 1: Tree Diagram
Start at bottom of tree and work up. Player 2 will always confess so better for player 1 to confess so too. So DS is confess, confess.
Sub Game Perfect - Doesn't matter who is on top of tree
Second type of e is Nash Equilibrium - Look for DS first
A Cournot Oligopoly is a Nash equilibrium - Stable is an outcome stable?
If play order is different, e is different. "First mover advantage."
Mixed Strategies Equilibrium - Last one to look for!
Confusing your opponent. Soccer. probability to keep the other players indifferent between strategies.
So of Top left, bottom right, bottom left, top right.
Asymmetric Payoff - Ex. #9 is not symmetric to #1. If both ask some girl they get 0. Game of discoordination. Bruce is indifferent but Adam has a preference dating Carly. Adam needs to beep Bruce indifferent between left & right but he already is! So . keeps indifferent between top & bottom. What is ?
- All DS are Nash - If we got DS, it is stable
- If there is a DS, there can't be a mixed strategy