the Rewarding Strategy

Marketing folks must understand psychology well. When trying to encourage a new behavior, we are supposed to give a reward every time the person does the behavior (continuous reinforcement). We then switch to a different reward schedule to keep the behavior going once it has established.

This is exactly how Starbucks works: we collect stars for every purchase. And for every 125 stars collected, we redeem for a freebie. We call the rewarding strategy fixed ratio schedule, where “reinforcement” is based on the number of stars collected, and the number is always the same. However, under this strategy, customers will buy a lot of coffee over a short period of time to collect certain amount of stars and get the freebie, but behavior will drop after that.

To stimulate and speed up the behavior all over, the coffee magnate is constantly launching the star dash program — providing bonus stars based on consecutive behaviors. For example, a variable amount of bonus stars come after 3 consecutive purchases, sometimes 5, sometimes 6, and so on. They use variable ratio schedule as a business stimulus: the reinforcement is based on how many times customer does the behavior, but it changes all the time.

By the goal-gradient effect, customers will accelerate their behavior as they progress closer toward a goal. So by having bonus stars, they think they already had some progress, they work faster to fill up what’s left for 125.

The rewarding strategy breaks purchasing goals into small and manageable steps, making customers feel that they have a good chance of reaching the goal so they are easily addicted to purchase over and over, less likely to switch to other coffee brands, too.

the Rewarding Strategy

Writing 8.357: On Modeling, 2

We build models because we want to highlight the most relevant factors of the circumstances. In a broad sense, language, music, painting are all different forms of modeling: they stress certain aspects of reality by ignoring the rest.

Models must be useful. Unlike simplicity and generality, usefulness is trickier to assess. The challenge arises from the parallel of two worlds: the real and the model world; so there is a gap one must be able to cross.

The main idea of modeling is that, if we isolate the substantive factors of a system into a model, then the outcomes generated by the model should also find counterparts in the real world. Or, if we observes certain outcomes in the real world, and the model produces similar outcomes, then these substantive factors should be determinants in the real world, too.

Both arguments rely on inductive inference. In general, the model and real world should share similarities in  structure, dynamics, and outcomes. Yet these similarities are no guarantee that two worlds move in lock step. Cases abound of otherwise. Thus, relevance has to be taken by faith, not by the logic reasoning. There are gaps that one must be willing to cross.


Writing 8.357: On Modeling, 2

Writing 7.358: On Modeling, 1

All disciplines use models. So what is a model? It is a useful abstraction of reality. It is an abstraction because it does not intend to recreate the real world in a one-to-one scale. Rather, it distills the essence of a situation so that it can be readily deployed in other similar situations.

One reason we need models is because we have limited cognitive capacity—you cannot keep track of all the details all the time. Modeling is a way to filter out irrelevance and to focus on what matters. So models are the lens we use to see the world we want to see. And simplicity is the first criterion.

The second criterion is generality. We don’t want to build a new model for every single situation; that would defeat the very purpose of modeling. Rather, we would like our models to have sufficient generality, so that we can apply the same models to different situations with limited modifications.

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Writing 7.358: On Modeling, 1

Writing 6.359: movie review, La La Land, 8/10

This beautiful movie tells a sad story. Mia is a barista who dreams of hollywood;  Sebastian is a jazz pianist, who aspires to run his own jazz bar with pure jazz. They fall in love in LA before they succeed in career. Later, when Mia has the door to her dream, Serbastian tells her to give all her has, even that means losing each other. Five years later, both realize their dreams, but live separate lives. In the last scene, Mia dreams of what if everything goes right, they would have been happily together. But the reality is, success and love often do not go hand in hand; you must pick one. The ending reminds me of the movie Cafe Society.

Flora and I much enjoyed the movie. We both agree that the first half of musicals is a bit overdone.  I am not a big fan of musicals, and LA is never that fairy land like; you have to pick and choose carefully to get those beautiful shots. The second half is however substantial. It tells that love and dream may not be computability. Had they stick together, they would get neither love nor dream. Sad as it is, the real outcome is perhaps the best they can do.

Besides the plot, music, and the characters, I also find the cinematography amazing. From start it has the quality of fluid, dynamic, and nostalgia. For example, the penning scene of LA highway dancing, and the pool party scene (shifting the perspective from a girl jumping into the water to the band).

la la land

Writing 6.359: movie review, La La Land, 8/10

Writing 5.360: book review, economics rules, 10/10

As an established economist, Rodrik gives the best account of the strength and weakness of economics. He argues that a main strength of economics comes from its reliance on math modeling. Indeed, the modeling approach provides a universal language for the profession. Models link assumptions to their implications by logic. The persuasive power of a theory, then, derives not from the status of the authors, but the cogency of its logic. This approach leaves little room for BS to hide.

Much of the critics on economics is due to  the poor understanding of modeling. Economics does not claim universal truth, a unattainable goal in the ever-changing social world. In contrast, economics offer a collection of models that apply to specific situations. As such, the conclusions are not pre-ordained. Rather, they rely on model users’ ability to apply the right tool/model for the question at hand. In other word, it is the wrong application, rather than the model itself, to blame. This is the case for applying black-shoe model indiscriminarily in financial industry, which contributed to the 2008 financial meltdown.

I may be cynical, but part of the reason that other social disciplines hate economics is because they are not mature enough to understand math. If you truly want to know the reach and limitation of economics, this book is for you.

To read:

Credible words, capacities and mechanisms
The Changing Face of Mainstream Economics
Economic Fables, by Ariel Rubinstein

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Writing 5.360: book review, economics rules, 10/10

Writing 4.361: Games We Play

People tend to believe the world is a fair and just place, until hitting the harsh reality.

Here is a case in mind. Our administrators have been enjoying the wild ride for quite a while. They do what they please, reward their cronies, penalize who dare to challenge. The violations go one without real check. Last year, one faculty who cannot speak just got promotion, because he is their guy. This allows him to continue ruin students. Another faculty who has published zero got all the goodies and stayed for eight years, wasting taxpayers over a million of dollars. 

But they are running out of luck. Last year, we elected a new faculty chair, a seemingly harmless Asian guy. He turns out to be the show stopper. Two months into his tenure, he organized the faculty coupe to outer the provost. The provost tried several measurers, but eventually sees the inevitability. To avoid immediate embarrassment, he choose to step down by the end of June.

These dramas are at the university level, and should have not affected our school much. But in his final attempt to stay in power, the provost finally appointed a committee to investigate our dean. We have doubted that the committee is just another token show.

But now it seems all real: the provost intends to sacrifice our dean to save himself. This week, our dean eliminated two directors in the graduate office—they know too much of his fishy deals. One of them is a competent Polish guy, who sincerely cares about students.  Unfortunately, no one is real safe in this politicized place. His layoff is neither expected, nor preventable: the election of new faculty chair eventually leads to his layoff.

So, get real: the world is never a fair and just place. You got to watch out for yourself.



Writing 4.361: Games We Play

Writing 3.362: DSM, reading notes

G16 is an essential reading. It provides a starting point for our model. The main complication is that, the agent has nonlinear utility over the payment. So how the payments are distributed over time matters a great deal. As a consequence, we cannot reduce the firm’s payoff to the function of virtual surplus—we must account of the non-transferability of the the firm’s cost to the agent.

Technically, we need to derive two conditions to guarantee IC and IR constraints: envelope and monotonicity. The envelope condition shows that each type should derive the premium beyond the low type for truthtelling. The premium consists of two terms: the weighted rents for his information advantage, and the gap to ensure within-period truthtelling. The monotonicity condition ensures that the net present value of the cash flow increases in the current type. The envelope condition puts constraints the payment scheme, while the monotonicity condition restricts the cash flow policy.

Once these two conditions are in place, we can apply the variational approach to derive sharp insights. In particular, we focus on the inefficiency loss, i.e., the distortion from the first best. The dynamics of the distortion depends on the interplay of risk aversion and market volatility. Depending on how they play out, the distortion can go either way. This property allows us to explain a wide range of salesforce practices.

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Writing 3.362: DSM, reading notes