Question

Scenario:

Between 2017 and 2019, Company 1 developed product A and Company 2 developed product B.

Both companies were manufacturing their own products.

Unless both companies agreed on producing only one product, consumers would not buy or consumers purchasing incentives were low.

Consumers were worried about investing in the wrong product in case one product type was faulty.

Both companies could choose to produce either product - i.e. Company 1 could produce product A AND B and vice versa.

Although, if Company 1 were to produce product B rather than product A, they would need to pay 20 million dollars in royalties to Company 2 for selling their products.

The same concept works for Company 2, if they were to produce product A rather than product B, they would need to pay 20 million dollars in royalties to Company 1 for selling their products.

If both companies agreed on selling one product, their profit would be 100 million dollars in products each per year - before paying royalties.

Question (a)

What are the elements of a strategic game?

Question (b)

Model the interaction between Company 1 & Company 2 as a strategic game, in which Company 1 and Company 2’s strategies are given by the products they produce and their preferences are given by their profits after paying for or receiving royalties.

Question (c)

What is Company 1’s dominant strategy? What is Company 2’s dominant strategy? What is the solution in dominant strategies? Please explain your answer.

Question (d)

Determine the Nash equilibrium (or the Nash equilibria) of the game. Please explain your answer.

Answer 1

(a) Elements of a strategic game are:

1. Number of players

2. Strategy set of each player in the game

3. A payoff matrix mapping the strategies to payoffs.

(b) To model the strategic interaction between the two companies, consider the payoff matrix below:

	Company 2 product A	Company 2 product B
Company 1 product A	(120,80)	(0,0)
Company 1 product B	(0,0)	(80,120)

Now consider the cells one by one.

Cell 1: Since both companies produce the same product, both receive a profit of 100 million dollars. Company 1 earns 20 million dollars in royalties, company 2 pays out 20 million dollars for royalties.

Cell 2: Since both the companies produce different products, they earn no profit.

Cell 3: Again, companies produce different products and earn no profit. Even if we assume that they pay our $20 million in royalties irrespective of sales, then they receive $20 million in royalties too, cancelling out the effect of royalties.

Cell 4: Cell 4 is similar to cell 1, only the payoffs are reversed for the two companies.

(c) Company 1's dominant strategy: To find out the dominant strategy for company 1, consider company 2. If company 2 chooses to produce product A, it is in company 1's best interests to produce product A. Likewise, if company 2 produces product B, it is in company 1's best interests to produce product B. Thus, company 1 changes strategies corresponding to company 2's strategy. Thus, it does not have a dominant strategy.

Company 2's dominant strategy: By an identical logic as given above, we can say that company 2 does not have a dominant strategy either.

Thus, there is no dominant strategy equilibrium in the game.

(d) There are 2 Nash equilibrium of the game: (Company 1 product A, Company 2 product A), and (Company 1 product B, Company 2 product B). We can check that no player has an incentive to deviate from an equilibrium, if we fix the strategy of the second player.