1.4 How do people interact strategically?

Economics combines facts and models to understand the economy.

Models

model

An economic model is a simplified representation of reality used to explain and predict behavior or outcomes.

A model is a simplification of an aspect of reality. It helps us better understand the real thing by focusing our attention on what is important and ignoring less important things.

We use models all the time. An example is the statement “The sun rises in the east.” This statement is a simplification. To an astronomer, it’s not strictly true (Earth’s rotation accounts for dawn, not the sun’s movement). But the model provides a reliable prediction about where you should look if you want to see the sun rising.

Here is another example: Based on some simple calculations (a model) we say “Water boils at 100 degrees Celsius (212 degrees Fahrenheit).” But that statement is a simplification; it’s true only at sea level. At higher altitudes, water boils at lower temperatures (70 degrees Celsius at the top of Mt. Everest, for example, and just over 101 degrees Celsius on the Dead Sea, which is below sea level).

The model that produced the “Water boils at 100 degrees” statement deliberately left out the influence of altitude. Like “The sun rises in the East” for most of the world’s people, who live close to sea level, the commonly understood boiling temperature of water is good enough for most purposes. That is, it’s a reasonable model.

Models are also used in engineering. For example, ideas for new designs of airplanes are explored in wind tunnels, but the models simplify the situation by not including seats and other interior content of the plane.

Games and strategic action

game

A game (in game theory) is a model of a strategic interaction including a list of players, the order of play, the actions (or strategies) available to each player, and the payoffs resulting from each possible combination of players’ payoffs.

A game is a common model used in economics. In everyday language, the word game usually means something we do for fun, but the economic definition of a game is quite different. In economics, a game is a model of strategic interaction including a list of players, the order of play, and the payoffs resulting from each possible combination of players’ payoffs. (Games are also used in military science, business, biology, computer science, psychology, and political science.)

strategic interaction

A strategic interaction is an interaction in which each actor knows that what they get from the interaction depends on what they do and on what other people do, including how others respond to each person’s action.

A game is a model of strategic interactions, which are situations in which each actor knows that what they get from the interaction depends on what they do and on what other people do, including how others respond to each person’s actions. Strategic interactions are an example of the interdependence principle at work.

We engage in strategic interactions daily. In friendships, we know that how things turn out depends on what each friend does: how each friend responds to what the other friend does affects how happy each friend is. For example, if two friends disagree about where they want to eat lunch, they may decide to alternate who gets to pick where they eat. Other examples of strategic interactions are two businesses competing for customers in a market, and the combat between two military forces or opposing political parties competing for voters.

A game in economics has four components:

payoff

The players’ payoffs are a list of numbers identifying how much the players value each combination of actions that they can take in the game.

• Players: A list of all of the players in a game. In the Kellogg example, the players are the residents of Kellogg, the owners of the Bunker Hill Company, and the government.
• Order of play: The rules of the game may specify that actors play simultaneously, each selecting an action at the same time, like the game of rock paper scissors. Or the game may require sequential play, in which one player goes first and then the other player moves, as in chess, checkers, or go.
• Actions: A list of all actions that each player can choose. Actions could include staying and working for the Bunker Hill Company as a worker, or choosing to leave the job and find work elsewhere. 
• Payoffs: The players’ payoffs are a list of numbers identifying how much the players value each combination of actions that they can take in the game. Players choose the action that will result in the highest possible payoff. For example, Bunker Hill’s payoffs could be the profits that it made in Kellogg, and the workers’ payoffs could be a combination of the wages they earn, the benefits to them of living in Kellogg, Idaho with their family and friends, plus the costs to them of the environmental damage that mining and smelting has done to their health and wellness.

Here is an example of a game and its four components.

• Players: (1) The owner of the Bunker Hill Company, which operates in the city of Kellogg, and (2) a worker of the company, who is a resident of Kellogg. The Worker represents all the workers in Kellogg at Bunker. Because they could be any of the many workers at the company, we simply call them “the Worker.”
• Order of play: Bunker is the first mover because it owns the plant. Bunker chooses its action, then the Worker responds as the second mover.
• Bunker’s action: Choose More pollution or Less pollution. Select a technology that results in more emissions or fewer emissions.
• The Worker’s action: Stay or Go. Remain living and working in Kellogg, or leave and seek employment somewhere else.
• Bunker’s payoffs: The more pollution it emits, the higher Bunker’s profits are, as long as the Worker continues to live in Kellogg and work for the company.
• The Worker’s payoffs: The Worker’s quality of life is higher if there is less pollution emitted, as long as Bunker continues to employ them (that is, does not leave town).

Payoffs are often expressed in terms of money, and for Bunker, the payoff is indeed money (profits) and nothing else, because Bunker is not exposed to the pollution that results from its actions. But the term “payoff” also refers to other things that a player cares about. For example, payoffs to the Worker might include not only an hourly wage but also other factors, such as how much they value working and how much they worry about the health risks to which their family are exposed by living in an environment that is polluted by their employer.

To take account of the many different things that are important to workers, we can call the payoff to the Worker their quality of life. In general, players choose a situation with a higher quality of life over one with a lower quality of life. Our starting point for quality of life is that a person receives a salary, for example of $50,000, each year. Other benefits they receive or costs they incur, which may not have a specific monetary value, will add or subtract from that value. For example, living in a beautiful environment with parks and unpolluted natural environments adds value. Experiencing poor health from pollution takes away value. The value of the Worker’s “quality of life” puts all this together in one number. So if someone’s salary were $50,000, we’ll give that a value of 50. But if they experienced benefits from good education and a park for their children that had a value of 10, and costs from emissions damaging their family’s health of 9, then the total payoff would be 51 (50 + 10 − 9 = 51).