2.2 Changing the rules: The structures of the economy

To understand how the rules of the game affect how the game is played, we start with an example of the Worker’s outside option improving.

When their outside options improve, it means that workers have opportunities somewhere else for a job that has a better salary, or the same salary with less pollution, or similar outcomes where they have better options somewhere else. When the Worker’s outside options improve, it means that their opportunity cost of working elsewhere is greater compared to before the improvement. Seeing how the Worker’s outside option improves shows us the importance of the rules of the game principle, which is the focus of this chapter.

When the Worker’s outside options improve, the owners of the firm must offer the Worker a larger share of the gains from cooperation so that working for Bunker is better than the Worker’s outside option.

Recall from Figure 1.5 that the feasible outcomes given the two actors’ outside options (leaving town) are indicated by the green triangle of the feasible gains from cooperation, which we show again in Figure 2.2. When Bunker is first mover, we know that the outcome is point B, with the Worker’s quality of life being 51, which is only slightly better than what it would be if the Worker leaves town (50). At point B, Bunker receives 169: a much larger share of the gains from cooperation.

Changing outside options

How could the Worker’s quality of life (and the environment) be improved? One way is to improve the Worker’s outside option, shifting the dashed vertical line in from 50 to the right, say, to 80, as shown in Figure 2.2.

The Worker’s outside option could improve if:

• the government provides free training so that welders and other people working for Bunker could more easily find well-paying jobs with employers elsewhere
• firms in nearby towns emit little pollution and offer better employment opportunities for workers with the same skills as Bunker’s workforce
• the government increased the payment (called unemployment insurance) that it makes to unemployed people who are unemployed, making the period of searching for a new job less costly to the Worker
• a powerful job search engine becomes available on the Worker’s cell phone, making it easier to find a well-paying alternative to working for Bunker
• Bunker, under pressure from a labor union that represents its workers, agrees to certify the skills and job experience of each of its workers, making it easier for Bunker’s workers to find equivalent jobs elsewhere.

Proceed through the steps of Figure 2.2 to see how the feasible gains from cooperation change when the worker’s outside offer improves.

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Outcomes of the bargaining game: the situation after an improvement in the Worker’s outside option.

Figure 2.2 Outcomes of the bargaining game: the situation after an improvement in the Worker’s outside option. The figure shows what happens when the Worker’s quality of life somewhere else increases, which shows a change in the Worker’s outside option. Initially, the outside option of the two actors (both leaving town) is given by point Z. Bunker’s profits are 60 and the Worker’s quality of life is 50. The bargain they initially had was given by point B where the Worker got 51 and Bunker got 169. After the improvement in the Worker’s outside option, given by point Z\(^*\), the Worker’s quality of life somewhere else has risen from 50 to 80. Bunker’s outside option has not changed. The change in the Worker’s outside option changes the offer that Bunker will make to the Worker from B to B\(^*\) where the Worker now gets 81 and Bunker gets 139.

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https://books.core-econ.org/uoe-101/02-02.html#figure-2-2a

Starting point

We start with Figure 1.5 from Chapter 1, which shows the outcome of the Worker and Bunker bargaining over the gains from cooperation when Bunker moves first and the Worker has an outside option of 50. At point B, the Worker receives 51 and Bunker receives 169.

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https://books.core-econ.org/uoe-101/02-02.html#figure-2-2b

Shift in the Worker’s outside option

Consider the shift in the Worker’s outside option from 50 to 80. The result is a shift of the participation constraint, as shown by the arrow.

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https://books.core-econ.org/uoe-101/02-02.html#figure-2-2c

Reducing the potential gains from cooperation

Because the participation constraint has shifted, the allocation corresponding to the outside options for the two has changed from point Z (50, 60) to point Z’ (80, 60). The result is a reduction in the size of the area for the potential gains from cooperation from the light green triangle (from Figure 1.5) to the smaller dark green triangle now shown.

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https://books.core-econ.org/uoe-101/02-02.html#figure-2-2d

Bunker’s payoff decrease

Because of the improvement in the Worker’s outside option from 50 to 80, the offer that Bunker must offer to the Worker has to increase in a corresponding way. That is, Bunker must now offer the Worker at least 81 to stay rather than to leave. (At an offer of 80, the Worker will be indifferent between staying and going.) The Worker previously accepted an offer of 51. Now, because their outside offer has increased by 30, the minimum they will be willing to accept will increase by 30 units too, from 51 to 81. The payoff that Bunker receives must decrease by a corresponding amount of 30, from 169 to 139, because Bunker must pay 30 units more to the Worker (and their fellow workers).

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https://books.core-econ.org/uoe-101/02-02.html#figure-2-2e

New outcome

As a result of the Worker’s increase in quality of life somewhere else, Bunker needed to raise the offer that they would make to the Worker from 51 at B to 81 at B*. Because they are already on the feasible frontier, Bunker therefore needs to reduce its profits from 169 at B to 139 at B*. The new outcome demonstrates how changing the rules of the game alters the distribution of gains from cooperation among the players.

Now that the Worker’s outside option is a quality of life of 80, think about how the game will be played. Bunker, knowing the Worker will do the best they can, will figure out that if it pollutes so much that the Worker’s quality of life in Kellogg will be less than 80, then the Worker (and the other workers) will leave and Bunker will have to close down its operations in Kellogg, reducing profits to 60. So it will limit its emissions, and the outcome of the game will be point B* in the figure, an improvement in the Worker’s quality of life to 81, and a reduction in Bunker’s profits to 139.

power

The ability to do and get the things we want in opposition to the intentions of others.

The distribution of the benefits of cooperation is determined by the exercise of power. If the Worker and workers or citizens around the country advocate for the policies in the bullets above and succeed, they have exercised power. They changed the payoff they received by changing the structure of society.

Here, the workers exerted power by changing the setting in which the game takes place—changing the Worker’s outside options—in ways that improved the payoffs they received at the final bargain with Bunker. Here, the worker’s power concerned the capacity to alter the overall structure of society: the society’s government policies, the presence of other firms that will hire workers and the quality of the jobs those firms offer, and the information that players can acquire.

Question 2.1

Consider Question 2.1 Figure (I) depicting the payoffs to the Worker (player A) and Bunker (player B) on the same set of axes with a set of points highlighted:

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https://books.core-econ.org/uoe-101/02-02.html#question-2-1-figure-i

Question 2.1 Figure (I) The Worker’s quality of life and Bunker’s profits with a set of hypothetical points.

The coordinates of each point are:

• Point Z: (50, 60)
• Point Z’: (75, 60)
• Point Z’’: (50, 85)
• Point Z’’’: (75, 85)
• Point A: (159, 61)
• Point B: (51, 169)
• Point G: (110, 110)
• Point H: (75, 145)
• Point I: (135, 85)

Which of the following statements are true?

• If the players’ outside options are given by point Z’’, then, at a bargain given by allocation G, the players will receive rents of 25 and 60 to A and B, respectively.
• If the players have outside options given by point Z’, then, if Bunker is the first mover, Bunker could offer 75 to the Worker and the Worker will not choose to leave Kellogg because their payoffs to staying are better than their payoffs to leaving.
• If the players have outside options given by point Z’’, then the minimum feasible level of emissions is one that guarantees Bunker maximum profits of $85 million; Bunker could not obtain profits of more than $85 million in a bargain with the Worker.
• Comparing points A and B, the total rents available are 110 and the rents the players receive at each point are mirror images of each other (the rents A gets at one point, B gets in the other and vice versa).
• If the structure of the economy shifts such that the players’ outside options increase from point Z to point Z’’’, then the size of the set of feasible gains from cooperation increases by the same proportion as the increase in the size of the outside options.

• If the Worker’s fallback option is 50 and they receive 110 at allocation G, then their rent is 110 − 50 = 60. If Bunker’s fallback option is 85 and they receive 110 at allocation G, then their rent is 110 − 85 = 25. Therefore the statement is true.
• If the Worker’s outside offer is 75, then what does this mean for their choice to stay vs. leave if Bunker offered them 75, too?
• Are you sure Bunker could only get $85 million? What would the Worker have to offer Bunker in order for Bunker not to leave if Bunker’s outside option is $85 million?
• At point B, the Worker gets 51 and Bunker receives 169, for a total of 220. Their fallbacks are 50 and 60 for a total of 110, therefore the total rent available is 220 − 110 = 110. Similarly, at point A, the total rent available is 110 (do the calculation as an exercise). At point A, the Worker receives 51 and their fallback is 50, therefore their rent is 51 − 50 = 1; Bunker receives 169, their fallback is 60, therefore their rent is 109. Similarly, the Worker receives a rent of 109 and Bunker receives a rent of 1 at point B. Therefore the statement is true.
• The size of the outside options has increased, but has anything happened that also shifts the feasible frontier?