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A firm’s choice of location is of great importance as proximity to its customers and competitors determines profitability. Ben and Jerry (B and J) work for the same soft drink company and their job is to sell soda at a popular beach. They work at the same beach and by company policy, must charge the same price. The company gives each salesperson a commission of $1 per can sold. Due to requirements of refrigeration, each salesperson must work from a stationary booth on the beach. The only decision the salesperson has to make is the location of the booth on the beach at the beginning of the day. Ben and Jerry select the locations of their booths independently and simultaneously. The beach is divided into 5 regions of equal size, labeled 1, 2, 3, 4, 5, from leftmost (region 1) to center (region 3) to rightmost (region 5).

Booths can be located in any one of these five regions. It is also possible for both salespeople to locate in the same region. On any given day, 10 people in each region will wish to purchase one soda each. The customers will walk to the nearest booth to make their purchase. If the customers of a given region are indifferent between the two booths, they go to each of them with probability one-half. Ben and Jerry seek to maximize their profits.

(a) Write down the normal form of the game.

(b) Use Iterated Elimination of Strictly Dominated Strategies to find the outcome of the game.

(c) Can you think of other applications of this model?

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Jarrod Robel
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11 Jun 2018

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Related questions

There is a beach that runs east-west. Ice cream vendors can choose any of nine locations along the beach. Location 1 is at the west end, location 2 is just to the east of 1, 3 is just to the east of 2, and so on. There are 10 consumers at each location. Consumers follow these rules:

If they buy ice cream, they will buy from the closest vendor. If there are two vendors the same distance away, half will buy from one and a half from the other.

Each consumer will buy one ice cream cone as long as they do not need to walk more than two locations. So, for example, customers at 4 will buy from a vendor at 2, 3, 4, 5, or 6 but they will not buy from a vendor at 1, 7, 8, or 9.

If there is no vendor within two locations, a customer will not buy ice cream.

 

Vendor A and vendor B will choose their locations simultaneously. Each wants to maximize the number of ice cream cones it sells. They could choose the same location.

Find the Nash equilibrium (or Nash equilibria if you believe there is more than one) of this game.

5. 1. Player 1 and Player 2 will play the following game. Player 1 will choose x1 and Player 2 will choose x2 simultaneously. Their payoffs Ï1 and Ï2 are

Ï1 = 90x1 x12 x1x2

Ï2 = 90x2 x22 x1x2

(a) Find each player's best reply.

(b) Show that x1 = x2 = 30 is the Nash equilibrium of this game.

2. Determine the labor market classification for each of the following. E.g. employed, cyclically unemployed, out of the labor force, frictionally unemployed, or structurally unemployed. The correct answer to each question below is one of these. A category may be used more than once. Simply saying the person is “unemployed” is always an incorrect answer. You must provide the exact category of labor market status from the list of choices provided above. You may use a category more than once.

a. Homer lost his job last week at the nuclear power plant in Springfield. The plant was closed when taxpayers agreed on a ballot issue to replace it and all nuclear power plants with hydroelectric plants. Homer has special job skills that were unique to nuclear power plants.
Homer’s labor market status is ____________________


b. Bob was run over by a bicyclist yesterday. He must spend 3 days in the hospital and another 2 days at home recovering from his injuries before he can return to work for the U.S. Postal service. What is his labor market status during this 5-day time?
Bob’s labor market status is _____________________________________.

c. Ernie, a formerly unemployed computer analyst, now works 20 hours a week as a part-time employee at Home Depot.
Ernie’s labor market status is _____________________________________.

d. Tom is 50 years old. He resigned from his job as a gravedigger because he was finding it difficult to climb out on his own once the job was complete and was too embarrassed to ask for help even though the union contract with the company indicates that management will provide stepladders. He is currently looking for an above-ground job. He has been interviewing with landscape companies and is very optimistic about his future employment prospects. He continues to fill out job applications.
Tom’s labor market status is _____________________________________.

e. Michael won the largest lottery in US history. His after-tax lump sum lottery winnings were $450 million. He was never happy at his job at the Walmart in Springfield Massachusetts stocking shelves 30 hours a week (two less than the minimum to qualify for any health or retirement benefits) so he simply did not report to his job one day, never told anyone at work, changed his legal name and moved to Florida where he purchased a secluded home on a one of the Florida Keys. The strange thing is no one even called to see if he was OK. They just assigned someone else to his job. He now spends every day reading or walking along the beach. He is also reading travel brochures and soon will move to New Zealand for several months where he plans to play semi-professional rugby.
Michael’s labor market status is _____________________________________.

F. Bill was finally arrested convicted for skimming (i.e. stealing) $5 million from the university where he was employed as a senior administrator even though no one at the university was looking for the money despite knowing it was missing. It took the work of a dedicated IRS agent reviewing university budgets 6 years after this event happened. Fortunately, it was still a few months before the statute of limitation expired. Now Bill lives in “free federal housing” in Connecticut where he is locked into his 7 feet by 9-feet cell or room as he calls it, each night until his 20 years are up.
Bill’s current labor market status is __________________________.

CASE 2-3: Starnes-Brenner Machine Tool Company: To Bribe or Not to Bribe?

The Starnes-Brenner Machine Tool Company of Iowa City, Iowa, has a small one-man sales offi ce headed by Frank Rothe in Latino, a major Latin American country. Frank has been in Latino for about 10 years and is retiring this year; his replacement is Bill Hunsaker, one of Starnes-Brenner’s top salespeople. Both will be in Latino for about eight months, during which time Frank will show Bill the ropes, introduce him to their principal customers, and, in general, prepare him to take over. Frank has been very successful as a foreign representative in spite of his unique style and, at times, complete refusal to follow company policy when it doesn’t suit him. The company hasn’t really done much about his method of operation, though from time to time he has angered some top company people. As President Jack McCaughey, who retired a couple of years ago, once remarked to a vice president who was complaining about Frank, “If he’s making money—and he is (more than any of the other foreign offi ces)—then leave the guy alone.” When McCaughey retired, the new chief immediately instituted organizational changes that gave more emphasis to the overseas operations, moving the company toward a truly worldwide operation into which a loner like Frank would probably not fi t. In fact, one of the key reasons for selecting Bill as Frank’s replacement, besides Bill’s record as a top salesperson, is Bill’s capacity to be an organization man. He understands the need for coordination among operations and will cooperate with the home offi ce so that the Latino offi ce can be expanded and brought into the mainstream. The company knows there is much to be learned from Frank, and Bill’s job is to learn everything possible. The company certainly doesn’t want to continue some of Frank’s practices, but much of his knowledge is vital for continued, smooth operation. Today, Starnes-Brenner’s foreign sales account for about 25 percent of the company’s total profi ts, compared with about 5 percent only 10 years ago. The company is actually changing character, from being principally an exporter, without any real concern for continuous foreign market representation, to having worldwide operations, where the foreign divisions are part of the total effort rather than a stepchild operation. In fact, Latino is one of the last operational divisions to be assimilated into the new organization. Rather than try to change Frank, the company has been waiting for him to retire before making any signifi cant adjustments in its Latino operations. Bill Hunsaker is 36 years old, with a wife and three children; he is a very good salesperson and administrator, though he has had no foreign experience. He has the reputation of being fair, honest, and a straight shooter. Some back at the home offi ce see his assignment as part of a grooming job for a top position, perhaps eventually the presidency. The Hunsakers are now settled in their new home after having been in Latino for about two weeks. Today is Bill’s fi rst day on the job. When Bill arrived at the offi ce, Frank was on his way to a local factory to inspect some Starnes-Brenner machines that had to have some adjustments made before being acceptable to the Latino. government agency buying them. Bill joined Frank for the plant visit. Later, after the visit, we join the two at lunch. Bill, tasting some chili, remarks, “Boy! This certainly isn’t like the chili we have in America.” “No, it isn’t, and there’s another difference, too. The Latinos are Americans and nothing angers a Latino more than to have a ‘Gringo’ refer to the United States as America as if to say that Latino isn’t part of America also. The Latinos rightly consider their country as part of America (take a look at the map), and people from the United States are North Americans at best. So, for future reference, refer to home either as the United States, States, or North America, but, for gosh sakes, not just America. Not to change the subject, Bill, but could you see that any change had been made in those S-27s from the standard model?” “No, they looked like the standard. Was there something out of whack when they arrived?” “No, I couldn’t see any problem—I suspect this is the best piece of sophisticated bribe taking I’ve come across yet. Most of the time the Latinos are more ‘honest’ about their mordidas than this.” “What’s a mordida ?” Bill asks. “You know, kumshaw , dash , bustarella , mordida ; they are all the same: a little grease to expedite the action. Mordida is the local word for a slight offering or, if you prefer, bribe,” says Frank. Bill quizzically responds, “Do we pay bribes to get sales?” “Oh, it depends on the situation, but it’s certainly something you have to be prepared to deal with.” Boy, what a greenhorn, Frank thinks to himself, as he continues, “Here’s the story. When the S-27s arrived last January, we began uncrating them and right away the jefe engineer (a government offi cial)— jefe , that’s the head man in charge—began extra-careful examination and declared there was a vital defect in the machines; he claimed the machinery would be dangerous and thus unacceptable if it wasn’t corrected. I looked it over but couldn’t see anything wrong, so I agreed to have our staff engineer check all the machines and correct any fl aws that might exist. Well, the jefe said there wasn’t enough time to wait for an engineer to come from the States, that the machines could be adjusted locally, and we could pay him and he would make all the necessary arrangements. So, what do you do? No adjustment his way and there would be an order canceled; and, maybe there was something out of line, those things have been known to happen. But for the life of me, I can’t see that anything had been done since the machines were supposedly fi xed. So, let’s face it, we just paid a bribe, and a pretty darn big bribe at that—about $1,200 per machine. What makes it so aggravating is that that’s the second one I’ve had to pay on this shipment.” “The second?” asks Bill. “Yeah, at the border, when we were transferring the machines to Latino trucks, it was hot and they were moving slow as molasses. It took them over an hour to transfer one machine to a Latino truck and we had ten others to go. It seemed that every time I spoke to the dock boss about speeding things up, they just got slower. Finally, out of desperation, I slipped him a fi stful of pesos. and, sure enough, in the next three hours they had the whole thing loaded. Just one of the local customs of doing business. Generally, though, it comes at the lower level where wages don’t cover living expenses too well.” There is a pause, and Bill asks, “What does that do to our profi ts?” “Runs them down, of course, but I look at it as just one of the many costs of doing business—I do my best not to pay, but when I have to, I do.” Hesitantly, Bill replies, “I don’t like it, Frank. We’ve got good products, they’re priced right, we give good service, and keep plenty of spare parts in the country, so why should we have to pay bribes? It’s just no way to do business. You’ve already had to pay two bribes on one shipment; if you keep it up, the word’s going to get around and you’ll be paying at every level. Then all the profi t goes out the window—you know, once you start, where do you stop? Besides that, where do we stand legally? The Foreign Bribery Act makes paying bribes like you’ve just paid illegal. I’d say the best policy is to never start: You might lose a few sales, but let it be known that there are no bribes; we sell the best, service the best at fair prices, and that’s all.” “You mean the Foreign Corrupt Practices Act, don’t you?” Frank asks, and continues, in an I’m-not-really-so-out-of-touch tone of voice, “Haven’t some of the provisions of the Foreign Corrupt Practices Act been softened somewhat?” “Yes, you’re right, the provisions on paying a mordida or grease have been softened, but paying the government offi cial is still illegal, softening or not,” replies Bill. Oh boy! Frank thinks to himself as he replies, “Look, what I did was just peanuts as far as the Foreign Corrupt Practices Act goes. The people we pay off are small, and, granted we give good service, but we’ve only been doing it for the last year or so. Before that I never knew when I was going to have equipment to sell. In fact, we only had products when there were surpluses stateside. I had to pay the right people to get sales, and besides, you’re not back in the States any longer. Things are just done different here. You follow that policy and I guarantee that you’ll have fewer sales because our competitors from Germany, Italy, and Japan will pay. Look, Bill, everybody does it here; it’s a way of life, and the costs are generally refl ected in the markup and overhead. There is even a code of behavior involved. We’re not actually encouraging it to spread, just perpetuating an accepted way of doing business.” Patiently and slightly condescendingly, Bill replies, “I know, Frank, but wrong is wrong and we want to operate differently now. We hope to set up an operation here on a continuous basis; we plan to operate in Latino just like we do in the United States. Really expand our operation and make a long-range market commitment, grow with the country! And one of the fi rst things we must avoid is unethical . . .” Frank interrupts, “But really, is it unethical? Everybody does it, the Latinos even pay mordidas to other Latinos; it’s a fact of life— is it really unethical? I think that the circumstances that exist in a country justify and dictate the behavior. Remember, man, ‘When in Rome, do as the Romans do.’” Almost shouting, Bill blurts out, “I can’t buy that. We know that our management practices and relationships are our strongest point. Really, all we have to differentiate us from the rest of our competition, Latino and others, is that we are better managed and, as far as I’m concerned, graft and other unethical behavior have got to be cut out to create a healthy industry. In the long run, it should strengthen our position. We can’t build our future on illegal and unethical practices.” Frank angrily replies, “Look, it’s done in the States all the time. What about the big dinners, drinks, and all the other hanky-panky that goes on? Not to mention PACs’ [Political Action Committee] payments to congressmen, and all those high speaking fees certain congressmen get from special interests. How many congressmen have gone to jail or lost reelection on those kinds of things? What is that, if it isn’t mordida the North American way? The only difference is that instead of cash only, in the United States we pay in merchandise and cash.” “That’s really not the same and you know it. Besides, we certainly get a lot of business transacted during those dinners even if we are paying the bill.” “Bull. The only difference is that here bribes go on in the open; they don’t hide it or dress it in foolish ritual that fools no one. It goes on in the United States and everyone denies the existence of it. That’s all the difference—in the United States we’re just more hypocritical about it all.” “Look,” Frank continues, almost shouting, “we are getting off on the wrong foot and we’ve got eight months to work together. Just keep your eyes and mind open and let’s talk about it again in a couple of months when you’ve seen how the whole country operates; perhaps then you won’t be so quick to judge it absolutely wrong.” Frank, lowering his voice, says thoughtfully, “I know it’s hard to take; probably the most disturbing problem in underdeveloped countries is the matter of graft. And, frankly, we don’t do much advance preparation so we can deal fi rmly with it. It bothered me at fi rst; but then I fi gured it makes its economic contribution, too, since the payoff is as much a part of the economic process as a payroll. What’s our real economic role, anyway, besides making a profi t, of course? Are we developers of wealth, helping to push the country to greater economic growth, or are we missionaries? Or should we be both? I really don’t know, but I don’t think we can be both simultaneously, and my feeling is that, as the company prospers, as higher salaries are paid, and better standards of living are reached, we’ll see better ethics. Until then, we’ve got to operate or leave, and if you are going to win the opposition over, you’d better join them and change them from within, not fi ght them.” Before Bill could reply, a Latino friend of Frank’s joined them, and they changed the topic of conversation.

QUESTIONS

1. Is what Frank did ethical? By whose ethics—those of Latino or the United States?

2. Are Frank’s two different payments legal under the Foreign Corrupt Practices Act as amended by the Omnibus Trade and Competitiveness Act of 1988?

3. Identify the types of payments made in the case; that is, are they lubrication, extortion, or subornation?

4. Frank seemed to imply that there is a similarity between what he was doing and what happens in the United States. Is there any difference? Explain.

5. Are there any legal differences between the money paid to the dockworkers and the money paid the jefe (government offi cial)? Any ethical differences?

6. Frank’s attitude seems to imply that a foreigner must comply with all local customs, but some would say that one of the contributions made by U.S. fi rms is to change local ways of doing business. Who is right?

7. Should Frank’s behavior have been any different had this not been a government contract?

8. If Frank shouldn’t have paid the bribe, what should he have done, and what might have been the consequences?

9. What are the company interests in this problem?

10. Explain how this may be a good example of the SRC (selfreference criterion) at work.

11. Do you think Bill will make the grade in Latino? Why or why not? What will it take?

12. How can an overseas manager be prepared to face this problem?

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