Lecture 7: Game Theory (coordination game, focal point, iterative elimination, nash equilibrium)

What are the 3 components of game theory?

1. Players

2. Strategies

3. Payoffs

What is a dominant strategy equilibrium?

If a payoff is always higher → strictly dominant

If a payoff is higher/same → weakly dominant

DSE → Game solution, the rational solution

What is the soft drink advertising game?

What is the prisoners’ dilemma?

What is soft drink advertising with high costs?

What is the coordination game without a focal point?

Has no dominant strategy

What is the coordination game with a focal point?

Also has no DSE → but reasonable that they would both pick C1

What is the battle of the sexes?

No dominant strategy equilibrium due to different preferences

What is heads or tails?

A winner or loser → 1 has to lose for the other to win

No DSE

What is iterative elimination of dominated strategies?

Removing strategies that are clearly worse → doesn’t work for some games

What is nash equilibrium?

A mixed strategy when can’t find a dominant strategy

• the best outcome for players is to follow imaginary agreed up agreement

• The dominant strategy is always a nash equilibrium

How do you find nash equilibrium?

Find the best response given what other player does

1. For player 1’s best strategy → identify player 2’s best response

2. If player 2’s response is the best, given player 1, that’s the NE!

What is a mixed strategy equilibrium?

An even weaker form that incorporates probabilities

What is a cournot duopoly?

Duopoly → 2 firms competing

What is an English auction & 2n'd price auction?

n buyers & bidders

→ single price for single item

2nd Price Auction:

• Buyers submit sealed bids → bid at true value