1.7 People doing the best they can

Recall that the rules of this particular game specify that Bunker is the first mover because it owns the plant in which the Worker works.

So, Bunker goes first and chooses a level of emissions. Then, the Worker chooses whether or not to remain employed by Bunker or to leave town, escaping whatever level of emissions results from Bunker’s choice.

doing the best you can

Doing the best you can means that, from the set of actions available to them, people will choose the action that they believe will result in the outcome that they value the most, taking into account what they believe the other player will do in response to their choice.

To understand how a game will most likely be played you have to put yourself in the shoes of each player and ask what they would do at any point in the game where they have a choice of which action to take. Each player will choose the action that they believe will result in the highest payoff, taking into account what they believe the other player will do in response to their choice. This is the principle of doing the best you can.

Put yourself in Bunker’s shoes. Bunker is the first mover and so announces and implements its strategy before the Worker makes their choice. Bunker cares about profits, which means saving money by not installing filters and other emission-lowering devices.

But Bunker’s choice also means more pollution for the Worker, who is free to leave if the pollution is too high. Bunker will not make any profits in Kellogg if the Worker (and their fellow workers) leave, with no other citizens moving in to replace them. So, to make its choice, Bunker must think ahead and figure out what the Worker will do in response to the action that Bunker takes. Bunker will reason backward:

• First, Bunker will figure out what the Worker will do in response to each of its actions; and then …
• Bunker will determine which of its own actions will result in the highest profits, taking into account the Worker’s response.

We do something similar when engaging in everyday strategic interactions.

So, reasoning backward, doing the best you can for Bunker means avoiding very high levels of emissions that will result in the Worker choosing to leave. Therefore, Bunker will choose a level of emissions that is just high enough so that the Worker will stay rather than leave. Bunker knows that the Worker may leave if emissions per day are too high (190 or higher), and so Bunker chooses a level of emissions of 189 where they receive a payoff of 169 and the Worker receives a payoff of 51, which is 1 unit greater than the Worker would receive somewhere else (what the Worker would get if they left).

best response

Given an action by another person, the action selected by doing the best you can is called the best response to the other’s action.

Now put yourself in the Worker’s shoes. To predict what the Worker will do, we need to figure out how the Worker will respond to Bunker’s choice. The Worker, like Bunker, does the best they can when choosing an action in response to others that they believe will result in the outcome that they value the most. When the Worker does the best they can in response to Bunker, we call it the Worker’s best response to Bunker.

Once Bunker has chosen the action “Emit the maximum amount that the Worker will tolerate so that they will stay,” then the Worker does not have many options. If they stay, they experience high levels of emissions, but not quite high enough to provoke them to leave. So, given that Bunker has chosen to emit a high, but not too high level of emissions of 189, the Worker doing the best they can is to stay and to have quality of life 51. Because the Worker stays, Bunker will receive the profits made possible by emitting 189 units of pollution—that is, a payoff of $169 million.

And this will be the outcome of the game: 169 and 51 for the players and a high level of emissions for the environment (as shown in Table 1.1). We explore how to depict the game and find the outcome in the next section.