LeBron is a 6’8 economics student who enjoys giving his peers romantic advice, and people seem to enjoy hearing his advice for the new framework he provides. Having attachment issues? That's Becker & Murphy (1988). Part of a fraternity and trying to see the impact of others' reputations on your romantic prospects? That's Tirole (1996). Interested in multiple people at once? There's Bar-Isaac & Deb (2014) for that. Now LeBron is single, but that's okay, as being single grants him more time to study, and the more he studies, the more models he can use to help others out. He occasionally fancies himself as something of an econ cupid.

One day, LeBron is doing his real analysis homework when someone messages him. It's an acquaintance of his, Sheila.

"Hey LeBron?"

"Yeah?"

"Can I talk to you about Josh and myself for a bit?"

"Sure."

In the set of all his romantic clients, the subset of ladies having relationship issues with their boyfriends makes up about 20-25% of the entire set, which is not an insignificant amount. Thinking about this, LeBron realized that this itself could be generalized into something of a basic model. He observes states R_i \in {R_f, R_b}, where R_f indicates that the relationship can be fixed, and R_b indicates that the lady should break up with her boyfriend. Given this, LeBron can choose some advice i \in {f, b}, where f is advice to fix, and b is advice to break up. LeBron has probabilities beta_i for i \in {f, b}, where β_i is the probability of LeBron giving advice i upon observing R_i.

So LeBron's listening to Sheila, and after 15 minutes he's heard enough. Her boyfriend, Josh, is using her as a risk-free state-contingent claim: during tough times for him, he hangs out with her, but when life is swell, he ignores her. Classic Huggett (1993).

"Sheila, break up with him."

"Are you sure?"

"Yes, this guy isn't good for you."

"Okay, thanks."

Now LeBron has an impeccable reputation as an advice-giver. Everyone around knows that he can accurately depict whether a relationship can be fixed or not. The man even used New Keynesian nominal rigidity to help a professor with unhealthy emotional attachments! Needless to say, Sheila took LeBron's advice and broke up with Josh that day.

Two days later, LeBron's walking out of his probability class, thinking about the gamma density function, when he runs into Sheila.

"Hey LeBron! Wanna grab lunch?"

"Hmm, sure, but only for 38 minutes."

The two have lunch together, then LeBron leaves. He's walking back to him dorm when a hand grabs him and pulls him into an alley.

"What were you doing with Sheila?!?"

Uh oh. It's Josh.

"I know you're the one who told her to break up with me. Okay, that's cool and all and I need to work on myself, but now that she's single you're going to try and win her over?!?"

Hmm, Josh had clearly misunderstood LeBron's intentions.

"No sir, we just had a friendly lunch, that's all. I'm not interested in anyone right now."

"You can't trick me, punk. You just tell girls to break up with their boyfriends so you can go after them yourself. This is your endgame, huh? HUH?"

Now LeBron's university had a problem with guys who would do this exact thing; LeBron was one of the only male advice-givers ladies could trust, because most others would tell the ladies that their relationships were unfixable so as to, as LeBron would put it, "get them back into the dating market". Thus, LeBron was popular because, in addition to being accurate, he had a record for integrity.

Let j=/= i. When an advice-giver recommends i (again, \in {f, b}) upon observing R_i, the advisee receives a payoff g. However, when an advice-giver recommends i upon observing R_j, the advisee receives payoff -b, where |-b| > |g| > 0. Ladies would only seek male advice from a guy if, for each i,

β_i ≥ β^* ≡ (b-g)/(b g) > 0

Intuitively, the worse the payoff from bad advice, the higher the probability that the advice-giver would give the correct advice needed to be. Of course, β_i for LeBron equaled 1, and everyone knew it.

Josh shoves LeBron down and goes away. Wew. This doesn't bother LeBron, however. He goes back to his room, works on probability homework, then takes a nap.

When he wakes up, however, his phone has exploded. Dozens of Facebook notifications, texts, messages, Snaps, the works. He opens them up…and photos of LeBron's lunch with Sheila went viral. Everyone know that LeBron told Sheila to break up with Josh, and now it's looking like LeBron did that just to try and get with Sheila. Oh no.

LeBron is on edge. His reputation, shattered. He goes to Church to pray and calm down, then decides to analyze this situation using economics.

Okay, so here's the situation. People now believe with some probability μ that I am a "bad" advice-giver. We'll define "good" as an advice-giver whose payoffs match up with his advisees, so he always gives proper advice. A "bad" advice-giver, however, provides advice independent of the state of the relationship. These often manifest themselves in our school's epidemic of guys simply telling girls to break up to get them back on the market; those guys receive a higher payoff from giving that advice, even if it's wrong.

Now, when μ is less than some critical value π^* < 1, the advisee will expect the advice-giver to give the correct advice, and so will ask that person for advice. However, when π^* < μ < 1, the advisee will choose not to go to that advice-giver.

Given this game-theoretic framework, LeBron realizes that he now faces his own meta-optimization within the realm of romantic advice. Now that he has a μ > 0, he must signal himself to be good if he is to receive more clients in the future.

At that moment, his phone buzzes. It's from a good friend of his, Jane.

"Hey LeBron, I've been hearing terrible, terrible things about you."

"Yeah, I know. It's blowing up across the campus meme groups and pages."

"Well, I still believe that you're a good, honest guy. Hey, mind if I eat dinner with you?"

45 minutes later, Jane walks into the lounge where LeBron's waiting with Chinese take-out. LeBron couldn't walk outside without facing the ire of the campus, so she was kind enough to bring him some food.

As LeBron eats his orange chicken with rice, Jane begins to open up to him. LeBron had helped her get with her current boyfriend, Max, about 3 months ago. Max, however, had begun to exhibit certain problems within the past month or so that were bothering Jane. As LeBron listened, it became clear. Max and Jane's relationship was on the saddle path to destruction. They needed to break up.

LeBron is about to tell Jane an optimal way to break up with Max when, outside the window, he sees a bush move. Someone's there. Watching. Listening. His conversation with Jane is not private.

Don't tell her to break up.

A voice in his head suddenly rang throughout his mind.

Model this out, LeBron! You are an advice-giver. Assume that there is an infinite continuum of ladies who choose whether or not to come to you for advice. They can observe the advice that you gave previous women, but as of today they do not know whether or not the advice you gave was proper.

If you keep telling ladies to break up even when they have to, YOU WILL RECEIVE NO MORE CLIENTS. Your reputation is in jeopardy because μ > 0. Face it. You need to start telling some ladies with unfixable relationships that their relationships can, in fact, be fixed.

That last thought reverberated across the walls of his mind. No. He can't. He must be a man of integrity. But the thoughts continue.

For each i \in {f, b}, a good advice-giver chooses a probability β_i^k (h^k ), which makes the probability of good advice at time k a function of the advice-giver's history h^k. Given a discount factor δ, a good advice-giver will maximize the expected discounted average payoff. For now, let's say that bad-advice givers always tell advisees to break up.

LeBron looks at Jane's face, full of trust in him to give the right advice. But the thoughts continue.

Each advisee decides whether or not to go to the advice-giver based on μ^k (h^k ), the probability that the advice-giver is bad based on advice history, and \bar{β_i^k } ≡ E (β_i^k | h^k ), the expected behavior of a good advice-giver based on history h^k. When π^* < μ < 1, the advisee will never go to the advice-giver for advice. When u^k (h^k ) < π^* , the customer only goes to the advice-giver if \bar{β_i^k } > β^* > 0 for all i.

So here's the dealio, Bronnie boy! Now, you're trading off the payoff you get from giving proper advice in a one-shot scenario with maintaining a serviceable reputation in the long run. So this depends on how patient you are. How close is your δ to 1?

LeBron is an extremely patient person. His δ, thus, is very close to 1.

So! You're very patient! That means you care about future payoffs very much! Well here's the situation. There's a creep hiding in a bush outside this window recording the conversation. You're at a critical point. Give Jane the proper advice to break up now, and you receive the payoff now. However, the creep will spread the recording of this conversation all around campus, and you'll never receive a client again. However, tell her that this can be fixed, and you live to advise another day. The choice is yours!

"No…no…no," LeBron muttered quietly to himself.

"Hmm?" Jane asked.

"This relationship with Max…it's…it's…fixable."

LeBron was broken, succumbing to the pressure of the outside campus.

"…and if you do that, you should be on a pathway to a healthy relationship."

"Thanks LeBron!"

Jane and him finish their dinner, then Jane leaves.

LeBron remains there, motionless. The mysterious figure in the bush leaves about 30 seconds after Jane does.

A single tear falls down LeBron's cheek.

I'm sorry, Jane. I'm so sorry.

Based on Ely & Välimäki (2003).