Exercises: Incentives, expectations, and game theory

Define what an economic incentive is and classify the following as a positive or negative incentive: a double-parking ticket, a discount for paying the annual gym fee in one payment, and a tax credit for installing solar panels. Justify each classification.

A supermarket starts charging $\$0.15$ for each plastic bag, which were previously free.

1. a) What incentive does the charge create and who does it act upon?
2. b) Predict what will happen to the number of bags used and explain the mechanism.

The figure shows the payoff matrix of a prisoner's dilemma between two rival bakeries deciding whether to lower their prices or maintain them. The first number in each cell is the profit of Alba's Bakery and the second is that of Bego's Bakery, in thousands of dollars.

1. a) What profit does each bakery get if both maintain prices? What if both lower them?
2. b) If Alba lowers prices and Bego maintains them, who comes out winning and by how much?

Distinguish between monetary and non-monetary incentives, and classify the following: a medal for the best academic record, a bonus in your paycheck, the embarrassment of arriving late, and applause from the audience. Add one example of your own of each type.

Explain what expectations are in economics and why they matter. Illustrate it with this case: word spreads that gas will go up on Monday and on Sunday lines form at gas stations. What has driven people: today's price or the one they expect tomorrow?

What is a strategic decision, one in which your best option depends on what others do? Give two everyday examples (choosing the supermarket checkout line by looking at the others, deciding whether to leave for break early to avoid waiting in line at the cafeteria) and explain what you are anticipating in each one.

In game theory, a "game" has players, strategies and payoffs. Identify those three elements in this situation: two friends must choose, without agreeing beforehand, between going to the movies or to the park, and they only truly enjoy it if they end up together.

A school pays students $\$2$ for every book they read and discovers that they all choose the thinnest, simplest books. Explain what a perverse incentive is and why this reward is an example: what behavior did it seek and what has it actually caused?

The federal government announces that in three months it will raise the tax on sugary drinks.

1. a) What can consumers and stores be expected to do before the increase?
2. b) Explain what role expectations play in that reaction.

Distinguish between risk and uncertainty and classify these situations, justifying each decision: buying a lottery ticket, opening an ice cream parlor in a new neighborhood, taking out cell phone insurance, and planting an unfamiliar crop in the face of climate change.

In the prisoner's dilemma, both players end up worse off than if they had cooperated.

1. a) Explain why, despite this, each has reasons not to cooperate.
2. b) Give a real-life example (in class, sports, or among neighbors) with the same logic and analyze it in the same way.

A day care center fined parents who arrived late to pick up their children and, against all expectations, lateness increased: the cheap fine turned embarrassment into a paid service.

1. a) What has gone wrong with the incentive?
2. b) What does this case teach about the difference between monetary incentives and moral or social incentives?

A state government decides to pay a bonus to teachers whose students improve on standardized tests.

1. a) What predictable strategic responses can it provoke (teaching only to the test, inflating internal grades, dropping content that does not come up)?
2. b) Redesign the incentive so that it rewards real improvement without those effects.

If all workers and firms expect prices to rise by $5\ \%$, union contracts demand $5\ \%$ increases and firms pass them on to prices, which end up rising by $5\ \%$.

1. a) Explain in what sense the expectation has fulfilled itself.
2. b) Why are central banks, such as the Federal Reserve, so concerned about "anchoring" inflation expectations? Explain your reasoning.

Two food trucks must choose where to park on a one-kilometer boardwalk along the waterfront. Customers go to the nearest truck and, in the event of a tie, they split between them.

1. a) Explain why, if each one chooses while thinking about the other, both end up parking together in the center.
2. b) Is that the best outcome for the people strolling by? Relate the game to the difference between individual interest and collective outcome.

After taking out a comprehensive insurance policy, some cyclists leave their lock loose or park in theft-prone areas.

1. a) What is this phenomenon called (moral hazard) and what does it have to do with incentives?
2. b) Explain what insurers do to limit it (deductibles, no-claims discounts) and why these measures work.

"Norte" and "Sur" are the only two ice cream parlors on a beachfront boardwalk. If both sell an ice cream cone for $\$3$, they each make $\$500$ per week; if one lowers the price to $\$2.50$ and the other does not, the one that lowers it makes $\$750$ and the other $\$200$; if both lower it, they each make $\$300$.

1. a) Construct the payoff matrix and analyze what each ice cream parlor will do if they cannot reach an agreement.
2. b) Compare that outcome with the one they would achieve by cooperating and explain the paradox.

A city subsidizes each family that installs solar panels by $\$200$ per year. After a year, it is discovered that a company is offering "paper installations": fake panels that only serve to collect the grant.

1. a) Explain what went wrong in the design of the incentive.
2. b) Redesign the subsidy so that it is difficult to game without losing its objective.

The class representative proposes a points system: anyone who clears their table after finishing lunch in the cafeteria earns points redeemable for leaving earlier for recess.

1. a) Analyze the proposed incentive: what behavior does it respond to, and what strategic responses or unintended consequences could it generate?
2. b) Propose an improvement to the system and justify it using what you have learned about incentives.

A city council wants more recycling and is considering three options: charging a fee for each bag of non-recycled trash, rewarding the neighborhood that recycles the most, and refunding $\$0.10$ for every container returned.

1. a) Explain the incentive each option activates and who it acts upon.
2. b) Anticipate one unintended effect of each (illegal dumping, cheating, costs).
3. c) Which would you choose, combining effectiveness and cost? Defend your design.

Two rival private academies decide whether to run an advertising campaign. If neither does, each earns $4$ (thousands of dollars); if both do, they earn $2$ each; if only one does, that one earns $5$ and the other $1$.

1. a) Construct the payoff matrix and reason what each academy will do if they cannot cooperate. Is there a prisoner's dilemma?
2. b) Explain how the analysis changes if the game is repeated every year and the academies can "punish" the one that advertises.

The federal government creates a rental aid program for young people worth $\$250$ a month and, the following year, rents in the areas popular with young people have risen by almost that amount.

1. a) Explain what has happened to the incentive: who has captured the aid and why (think about the supply of apartments)?
2. b) What conditions should the housing market meet for the aid to reach renters? Propose an alternative design.

A city wants students to leave their cars and use public transit. Compare three policies: a free transit pass for students, a $50\ \%$ discount on the monthly pass, and more speed cameras and speeding tickets.

1. a) Analyze the incentive of each measure, its cost to the public budget and its expected effect.
2. b) Design the combination you consider most effective and justify it using what you have learned about positive and negative incentives.