Lab 3: Contracts, Courts, and Reputation
Textbook reading: This lab assumes you have had Class 5.
Key Ideas
Two routes to credibility
- Commitment: tie your own hands so that keeping the promise becomes your best response
- Reputation: hold a reputation worth more than what breaking the promise would gain
- The commonest hand-tying device in business is a contract
Three ifs
- A contract binds only if:
- the courts enforce it,
- the wronged party would actually sue, and
- the penalty is large enough
- Today tests each if with numbers
Same tool, one new node
- Draw the tree, put payoffs at the ends, work backward
- A court’s verdict is uncertain: at a court node, take the expected payoff, as for Nature in Class 3
- The threat to enforce a contract is itself a credibility problem
Bianca runs a chain of bakeries. Her secret is a bread recipe, and recipes cannot be patented: anyone who learns it can use it. Paolo runs a chain of pizza restaurants, and he wants Bianca’s recipe for its pizza crust. With the recipe, Paolo’s pizza profits would rise by $20 million. But once Paolo has the recipe, nothing stops him from opening bakeries and competing with Bianca.
Paolo offers Bianca $10 million for the recipe and promises to use it only for pizza. If Paolo keeps the promise, Bianca earns the $10 million fee and Paolo earns $20 million minus the fee, so $10 million each. If Paolo opens bakeries anyway, he earns an extra $10 million and Bianca loses $20 million of bakery profit: Bianca ends up at −$10 million after the fee, Paolo at $20 million. If Bianca refuses to sell, both get 0.
Draw the tree and find the Nash Equilibrium with backward induction.
Now suppose Paolo signs a contract: pizza only. If he opens bakeries, Bianca can sue. She wins for certain and Paolo must pay her $20 million. Going to court costs Bianca $12 million and Paolo $9 million. Add Bianca’s sue or not sue decision to the bakeries branch, with payoffs. Find the Nash Equilibrium with backward induction.
Extensions:
A murky contract. Same as (b), but the contract’s wording is unclear (“Paolo may use the recipe in his restaurants”), and Bianca has only a 0.3 chance of winning. Each side pays its own court costs, win or lose. Redo the backward induction. Does the contract work?
Punitive damages. As in (c), but if Bianca wins, there is a 2/3 chance the court also awards punitive damages of $60 million, paid to Bianca. Does the contract work now?
Punitive damages to charity. As in (d), but punitive damages go to a charity: Paolo still pays them, but Bianca collects only the $20 million. Paolo’s expected loss if sued is the same as in (d). Does the contract work? Explain why the answer differs from (d).
State as a rule what must be true for a contract to make a promise credible. Your rule must mention the wronged party’s decision to sue.
Solutions
(a) Paolo prefers bakeries (20) to pizza only (10), so he opens bakeries; Bianca, expecting that, refuses to sell. This is the trust game; the promise is cheap talk.
(b) After Paolo opens bakeries, suing gives Bianca −10 + 20 − 12 = −2, better than −10, so she sues. Paolo, sued, gets 20 − 20 − 9 = −9, worse than 10, so he sticks to pizza. Bianca sells and earns 10. The contract works.
(c) Suing gives Bianca −10 + 0.3(20) − 12 = −16, worse than −10, so she does not sue. Paolo opens bakeries, and Bianca does not sell. The penalty is fine; the threat to enforce it is not credible.
(d) Suing gives Bianca −10 + 0.3(20) + 0.3(2/3)(60) − 12 = −4, better than −10, so she sues. Paolo, sued, expects 20 − 0.3(20) − 0.3(2/3)(60) − 9 = −7, worse than 10, so he sticks to pizza. The contract works: punitive damages made suing worth Bianca’s while.
(e) Paolo would still lose if sued (−7), but Bianca’s payoff from suing is back to −16 against −10. She would not sue, Paolo knows it, and he opens bakeries. The contract fails. What makes a contract work is the wronged party’s willingness to impose the penalty.
(f) A contract makes a promise credible when, after a breach, the wronged party is better off suing than not, and given the suit, the breaching party is better off keeping the promise. The first condition is the one that tends to be forgotten.