[Two home-improvement stores (Good Home and Happy Home) in a growing urban area are interested in expanding their market share. Both are interested in expanding the size of their store and parking lot to accommodate potential growth in their customer base. Two possible actions for both the firms are: 'increase the size of the store and parking lot' and 'do not increase the size of the store and parking lot'. Payoffs are defined in terms increase in annual profits in $million. The following table describes the payoffs for both the firms to alternative actions taken by each of them.]

		Happy Home
		Increase	Do not increase
Good Home	Increase	Happy Home = $1.0 million Good Home = $1.5 million	Happy Home = $0.4 million Good Home = $3.4 million
Do not increase	Happy Home = $3.2 million Good Home = $0.6 million	Happy Home = $2.00 million Good Home= $2.5 million

1. [Let's say, each store is pursuing its own best interest. What will be a rational (or dominant) strategy for Happy Home to follow? What will be a rational (or dominant) strategy for Good Home to follow?
2. [What will be the annual profit growth for each store, if they both follow their dominant strategy? What is a Nash equilibrium here and why? (Find out the Nash equilibrium using the pay-off matrix as shown above).
3. [Suppose the owners of Happy Home and good Home meet for a friendly game of golf one afternoon and happen to discuss a strategy to optimize growth-related profit. What should be the joint strategy they should both agree to? What will be annual profit growth for each store under this agreement?
4. [Under the competition laws, such agreements are illegal i.e. they are not enforceable by any legal frameworks and are subject to prosecution if discovered by regulators. Given the illegal nature of the above-mentioned agreement, cooperation is difficult to maintain here. Can you think of a scenario (or game as we studied in the lecture) where cooperation is possible for these duopolists?