Class 5: Credibility and Reputation
Textbook reading: Kreps, Chapter 4, “Credibility and Reputation.” The subsection “What if Cheap Talk Is a Little Expensive?” is optional.
Key Ideas
Credibility
- When a player makes a promise or a threat, is it credible?
- Only if it’s the player’s best response
- But that player can sometimes change their payoffs to make their promises credible by tying their own hands or by developing a reputation
Fix 1: tie your own hands
- 1916: UPS drivers were asked to make an up-front investment learning routes, working hard, and treating customers well, trusting that UPS would treat them well in turn.
- Why should they have that trust? Jim Casey invited the Teamsters union to organize his employees, standardizing work rules and making sure UPS was a fair employer.
- Casey tied his own hands not to be an abusive employer, which made drivers able to trust him.
Fix 2: reputation
- An instrumental reputation: a pattern of behavior kept up at a short-run cost because it changes how others treat you later
- Ex: Firm A faces a stream of potential entrants. Fighting any single entrant is costly, but if A fights the first ones, later entrants stay out fearing A will fight again. A chooses to fight to get a reputation for toughness.
Problems of the Day
Q13: Growling
Two firms. B is deciding whether to enter A’s market. If B stays out, A earns 2 and B earns 0. If B enters, A can acquiesce (1 each) or fight a price war (−1 for A, −2 for B).
Draw the tree and solve it by backward induction. Now A announces, loudly and in public, that she will fight any entrant. Does this change your answer?
Before B decides, A can switch to a production technology with very high fixed costs. It lowers her payoff on every branch: 1.5 if B stays out, −1.5 if she fights, −2 if she acquiesces. B’s payoffs are unchanged. Draw the new tree beneath the old one and solve both by backward induction. Which technology should A choose, and what does she earn?
List three other things a real incumbent could do to itself that work the way the high fixed-cost technology does. For each, say what happens if B enters anyway.
Q14: UPS and the Teamsters
Consider the trust game: B decides whether to trust A (0, 0 if not); if he does, A can treat him fairly (1, 1) or abuse him (2, −1). Find the Nash Equilibrium using backward induction.
UPS (A) faced this game with their drivers (B). Should B invest in learning routes and training, trusting A won’t be an abusive employer? To solve this dilemma in 1916, Jim Casey tied his own hands by inviting the Teamsters to organize his employees into a union. Change one payoff in the game in part A to model how Casey’s choice changed the Nash Equilibrium and resolved his dilemma.
Q15: Has Anyone Ever Seen Her Fight?
A plays the threat game from Q13 against a new challenger every round. After each round there is another with probability 0.8. Each new B can ask the previous one what A did. A’s reputation is “tough” until the first time she acquiesces, after which it is “wimp” forever. Bs do not challenge a tough A and always challenge a wimp.
Suppose some B challenges anyway. If A fights she gets −1 now and 2 in every future round; if she acquiesces she gets 1 now and 1 in every future round. The future is worth 0.8 of the present each round. Compute both streams. Does A fight?
Replace 0.8 with p. Find the p at which A stops defending her reputation.
Toyota deals with hundreds of suppliers on handshake contracts. Any single supplier is too small to punish Toyota, and Toyota double-sources most parts, so it could squeeze any one of them freely. Why doesn’t it? And why does Toyota want its suppliers to talk to each other?
Answers
- Q13:
- If B enters, A compares acquiesce (1) with fight (−1) and acquiesces. B compares enter (1) with stay out (0) and enters. Outcome (1, 1). The announcement changes no payoff, so backward induction ignores it: cheap talk.
B | +---------+---------+ | | stay out enter | | (2, 0) A | +---------+---------+ | | acquiesce fight | | (1, 1) (-1, -2)- New tree: stay out (1.5, 0); enter then acquiesce (−2, 1); enter then fight (−1.5, −2). Now A fights (−1.5 beats −2), so B stays out (0 beats −2). A earns 1.5 with the new technology versus 1 with the old, so she switches. The commitment costs her 0.5 relative to the 2 she would earn if the threat were free, and if B entered anyway she would be stuck at −1.5.
B | +---------+---------+ | | stay out enter | | (1.5, 0) A | +---------+---------+ | | acquiesce fight | | (-2, 1) (-1.5, -2)- Any self-inflicted change that makes fighting cheaper than acquiescing: build excess capacity; sign longer leases, sign long-term customer contracts with price-match clauses so a price cut is automatic. In each case, if B enters anyway, A must actually fight and eat the loss.
- Q14:
- If trusted, A compares fair (1) with abuse (2) and abuses. B compares trust (−1) with don’t trust (0) and does not trust. Nash equilibrium: B does not trust, A would abuse if trusted. Outcome (0, 0), although (1, 1) is better for both.
B | +---------+---------+ | | don't trust trust | | (0, 0) A | +---------+---------+ | | treat fairly abuse | | (1, 1) (2, -1)- Lower A’s payoff from abuse below 1. With a union contract and grievance procedure, abusing drivers now brings strikes, arbitration and turnover, so abuse pays UPS something like 0 rather than 2. Fair (1) becomes A’s best response, B trusts, and the equilibrium moves to (1, 1). Any abuse payoff below 1 works; the exact number does not matter. Casey made UPS better off by making it weaker.
B | +---------+---------+ | | don't trust trust | | (0, 0) A | +---------+---------+ | | treat fairly abuse | | (1, 1) (0, -1)
- Q15:
- Future rounds are worth 0.8 + 0.8² + … = 0.8/0.2 = 4 rounds of the present. Fight: −1 + 2(4) = 7. Acquiesce: 1 + 1(4) = 5. A fights.
- Fight: −1 + 2p/(1 − p). Acquiesce: 1 + p/(1 − p). A fights when p/(1 − p) ≥ 2, so p ≥ 2/3. Fighting costs 2 now (−1 instead of 1) and buys 1 extra per future round; the future has to be worth at least two rounds.
- Toyota’s reputation is one asset observed by hundreds of partners at once. Squeezing one supplier gains a little from that supplier and costs Toyota the trust of all the others, who would then demand contracts, guarantees and higher prices. The future stream that disciplines Toyota is the sum over all its relationships, not any single one. Toyota wants suppliers to talk for the same reason each B in (a) asks the previous B: the reputation only binds if every partner learns how the others were treated.