Question

Albertsons is currently the only grocery store in the West Park area and acts virtually as the monopolist.

The Albertsons manager hears a rumor that another grocer, Sprouts, is considering entering the market

and building a grocery store in the same plaza as the Albertsons store. Since Albertsons is the incumbent

firm, Sprouts must match the wage that Albertsons pays their workers. Further suppose that Albertsons

workers are currently paid the minimum wage of $5/hour.

Each firm has two strategies: Albertsons can choose to increase (I) the wage to $8/hour or it can continue

to pay the workers minimum wage (NI). Sprouts can either enter (E) the market and compete with

Albertsons or not enter (NE). If Albertsons increases the wages and Sprouts enters the market, Albertsons

will maintain control of the market with profits of $8 million, while Sprouts earns negative profits of $-2

million because of the high wages it must pay their workers. If Albertsons does not increase its wages and

Sprouts enters the market, Albertsons earns profits of $10 million, while Sprouts earns profits of $5

million. If Sprouts does not enter and Albertsons gives their workers a raise, Sprouts will receive zero

payoffs and Albertsons will $13 million in profits. Finally, if Sprouts does not enter and Albertsons

chooses not to increase wages, Albertsons will earn $15 million and Sprouts will have zero payoffs.

(a) Draw an normal form game representation of the situation described above.

(b) List, in any, dominant strategies for Albertsons and Sprouts.

(c) List the best response strategies for each player.

(d) Find the pure strategy Nash Equilibrium for the game.

Now, suppose that the Albertsons manager is friends with the board members of the Irvine Company.

They have proposed the following option: If Albertsons is willing to bribe the board members, the Irvine

Company will increase the minimum wage of Irvine to $8.

(e) Could it be a profitable strategy for Albertsons to pay this bribe? Explain.

(f) What is the maximum amount that Albertsons will be willing to spend for this bribe?

Next, assume the timing of events is as follows. First, Albertsons has to decide to bribe (B) the board

members with b dollars or not (NB). Second, Sprouts has to decide to enter (E) or not enter (NE). Finally,

Albertsons has to decide whether they are going to increase the worker’s wages (I) or continue to pay

them minimum wage (NI).

(g) Draw the game in extensive form representation of the situation.

(h) Assuming b < $3 million, find the sub-game perfect Nash Equilibrium (SPNE).

Answer 1