Thoughts on Life, Work, and School
I know I know… I said i would be more prolific, but i got bogged down in papers and finals!
While you’re waiting for me to emerge from the fog of war go listen to Shoemoney’s new show ‘Net Income’! It’s on Webmasterradio.fm Tue nights 5p CST. He knows a LOT about making Coin online and I’m sure you’ll learn something valuable…
Jason
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At the end of my post about Nash Equilibriums I teased that I may discuss how collusive optimums could possibly be stabilized. Well I decided I would all of my loyal readers… (NOTE: this discussion assumes a multi shot game, which I haven’t really discussed yet. I will though, eventually 
)
First, I will talk about why collusive optimums are typically unstable in the first place. Then I will illustrate one of my favorite examples of how to make them rock solid
Collusive optimums are typically unstable because there is a LARGE incentive to cheat, and we all know that everyone is a cheater… Notice, in our example from before, that if Sav-on and Walgreen’s got together and decided that they would both price HIGH that both parties would be better off than in the Nash Equilibrium. However, also notice that if, instead, either party (but not both) agreed to the higher pricing and then cheated by setting a low price they would actually make out better. This is the incentive to cheat.
How do we overcome this? Well first there is a problem of credibility. Walgreen’s can tell Sav-On that if they lower their price we will immediately lower ours, but there is a problem with this threat; it’s not credible. Walgreen’s would MUCH rather forgive Sav-On for being so scandalous and reinstate the high price agreement because they would make more money that way. This often happens in collusive oligopolies (or cartels), such as OPEC. They get together and decide on a production ceiling that each country will not produce beyond. In a free market this sets price… Inevitably what happens, though, is that each country has an incentive to produce just a liiitttle more . That way they enjoy the extra profits from the added volume at the expense of their associates. Then the other countries come and slap their wrist and sit down to agree to another farcical production ceiling.
Ok… so we need a credible threat. Threats could be made credible by prior history of enforcement. For example, the airline industry has time and time again instituted a fare war, incurring massive losses, in order to dissuade firms from lowering prices. Another credible threat would be an advertised promise to follow through with a price reduction. This is the all to familiar ‘lowest price guarantee’ See you ignorant consumer… you thought that was actually something that would be in your benefit didn’t you? Oh Contraire! Empirical evidence shows that prices, in fact, rise when these policies are put in place. Let’s use our Sav-On example to illustrate…
If both Sav-On and Walgreen’s announce that they will match any LOW move made by its opponent prior to making their move it then makes it possible for both players to price HIGH. It would now be disadvantageous for either firm to price LOW because it KNOWS its opponent will price LOW as well. We’ve now removed the incentive to cheat by making a credible threat and in so doing we’ve created a stable collusive equilibrium. We’ve also modified the Normal form of our game, by removing both the (HIGH,LOW) and (LOW,HIGH) states we are left with only (HIGH,HIGH) and (LOW,LOW). Faced with only these two states both companies will choose to price HIGH.
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Seth Godin recently wrote a post on how large companies hate that people use search on the net to find what they’re looking for… I say, boo f’ing hoo…
What are they whining about? I understand that they may have liked the good old days when people just mindlessly entered the first major company that entered their mind into the URI field, but they should easily be able to compete in the relatively inexpensive industry that is SEARCH. I guess it is just the usual complaining that they must improve their offering so that they actually deserve that user traffic…
My suggestion? Hire an SEO consultant, create an affiliate program to attract more creative minds than they obviously possess, or get out of the industry and stop complaining that you were beaten w/o even trying…
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When I decided to go back to school, I decided I would be commuting, rather than moving back to LA. I would be driving 120miles each day, round trip… This presented a couple of monetary and logistical problems. First, with gasoline at it outrageously high price I would be spending around $15 per day if I continued to drive my Toyota Tacoma. Second, without using the carpool lane the drive could eat up as much as 5 hours per day, not so cool…
In order to address both of these issues I began to consider an alternative fueled vehicle. Why not a Hybrid? Because it still didn’t solve problem one, and I believe they aren’t really the awesome inventions everyone thinks they are. They cost a LOT and they have this gigantic, expensive, environmentally hazardous battery in them. My neighbor down the street introduced me the Honda Civic GX Natural Gas Vehicle. He loves his, and it solves both of my issues AND only costs around $16K, used. The gas only costs $1.5/gal and these things were first to get carpool lane access. So, it’s a tremendous solution to my commuting issues, plus it’s a Honda, which I’ve heard, are pretty good quality.
I was sold, now I had to find one. I didn’t really want to get a new one. They’re around $22K new and I figured since I was going to be driving it to DEATH that I should just get a used one and save some cash. I started my search about three month before school started because these things aren’t that easy to pick up on the used market. After searching high and low I got lucky and found one for sale from EV Rentals. It was a 2004 model with 21K miles for $16K, great deal. I test drove it, took it to the dealer for a checkup, and then bought it.
I also considered getting Phill, but at $1500 it didn’t seem like it would ever pay for itself, and it isn’t THAT inconvienant filling every day.
Now that I’ve been driving it for the past seven months I just wanted to write about my thoughts. It’s great! I think more people should be buying these things over the stupid Hybrids. It certainly does have its drawbacks, though, none really major. First, the gas tank takes up most of the trunk space, so there is a very small trunk (sports car size). Second, it lacking a bit in range; I get around 200 miles to the tank. With school being 120 miles round trip I need to fill up every day. Lastly, there aren’t that many gas stations. If you wanted to drive country it may be a little tough, but it is TREMENDOUS as a commuter vehicle, and it truly is environmentally friendly (not that that really had an impact on my decision).
BTW: The 2005 model has an eight gallon tank which should increase its range to around 300 miles.
I’m going to my first ever focus group next week. It’s concerning ‘alternative fueled’ vehicles, should be interesting. I’ll keep you all posted
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Leveraging my discussion of NPV calculations in a previous post, I’m going to discuss the concept of Customer lifetime value (CLTV).
This analysis is critical for many businesses, especially membership type services like netflix because it helps the firm balance customer acquisition costs with customer retention costs. Most often firms are too heavily focused on acquiring new customers and often neglect their installed consumer base (remember the cell phone plans that would give steep discounts on phones, but only if you were a new client?).
There are four factors that impact the CLTV calculation.
A - Per customer acquisition costs, the costs incurred to turn a lead into a customer.
M – Maintenance costs, the costs incurred to keep a customer.
C – Gross profit revenues generated per customer per period.
r – Retention rate
i – Discount rate (I discussed this in the post on NPV calculations)
CLTV = SUM[ (C – M)*r^t/(1+i)^t ] – A
The way this works conceptually is that we follow a fictitious customer though time. Each period a smaller and smaller fraction of him exists until he is totally eliminated.
With a little math-magic we can simplify the above equation to:
CLTV = (C-M)*[ (1+i)/(1+i – r) ] - A => (C-M) * ‘Margin Multiplier’ – A
Now we can examine the impact that the margin multiplier (MM) has on profitability at different levels of i.
We can see that the marginal impact of increasing the retention rate (which impacts the MM) is far greater going from 90% -> 95% than it is even from going from 50% - 80%. This is profound!
From these types of calculations we can determine where our marketing dollars are best spent between customer retention and customer acquisition…
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Saw this post on Shoemoney’s blog this morning (Viral Marketing For The Win) and went over to check it out, after listening to the interview
Major props to this guy for finding a message that is deeply powerful to a large portion of our population, and getting that message out. Notice, from his comments, that he had very little traffic until April 5. This is perhaps when it was picked up by shoemoney, who has a decent, and influential, readership. I can’t help but suspect that the power of the online marketing community was thrown behind it
So the guy went from no traffic to over 2.5M in a little under 2 days. That is just amazing, but the other message I got was that he was having such a difficult time of monetizing this traffic flood.
He did set out with a different purpose, I understand, so from a marketing perspective he was a success. He set a goal and used his marketing skills to achieve that goal. Along the way to deciding he needed 2M hits, though, I wonder why he didn’t think of $$$. Perhaps that would have diluted the message. Indeed, if you read Shoemoney’s post, many people were a little skeptical when they saw the metrodate connection…
Anyway… I just would have liked to see him get the 3 way AND make a few million dollars in the process
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Ok… So I just said I wouldn’t talk about other classes. Now I’m about to talk about something that I learned about first by watching a movie then in more detail in economics. What is so striking about this topic, though, is that I then heard about it in finance, marketing, statistics, and decision theory, but it was invented by a mathematician… So when that old dude from the Nobel Committee tells John Nash that his theory has had an incredible impact on a vast array of subjects, he wasn’t kidding
Unless you were hibernating in a cave for all of 2001, you’ve proly heard of the movie ‘A Beautiful Mind’ and it’s main character John Nash (if you haven’t I highly recommend it). So you may have a flavor for what I’m about to lay out. In short John Nash figured out that Adam Smith’s ‘Invisible Hand’ was only partially optimal. Smith said that in a capitalist free market economy, the ‘Invisible Hand’ would guide the market to an optimal equilibrium. He called it the invisible hand because by the mere fact that all parties are acting for the sole purpose of profit maximization prices could be set and quantities determined. Inefficient firms would leave the market and overpriced markets would attract competition…
What Nash realized is that this is in-fact not always the best way… A firm should also take into account the actions of their competition. This is simple game theory… I will illustrate with a very simple example.
- First, we assume that all parties act rationally (I know this is a BIG assumption But mathematicians and economists are optimistic folks)
- Second, for this example, we will assume a simultaneous move one shot game. This means that both players move at the same time and there is only one move to the game. We can extrapolate this out to multi move games; then it gets even more interesting. (I’ll write that up in another post, I promise )
OK… Here we go…
We have two players Sav-On and Walgreen’s. They are located on the same corner of some street USA and each is trying to decide how to set prices on a new product. They can choose to set price either HIGH or LOW. The decisions are interdependent…
We represent the game in a matrix normal form:
From the matrix we see the various outcomes of total profits to each firm depending on the combination of moves by each player.
Now we’ll analyze the game from the perspective of Sav-On:
First we ask what is Sav-On’s best response if we think Walgreen’s will price HIGH? From the above diagram we see it is to price LOW.
Next we ask what is Sav-On’s best response if we believe Walgreen’s will price LOW? Again, we see that Sav-On should price LOW.
We see that no matter what Walgreen’s does, Sav-On’s best response is to price LOW. This represents a DOMINANT strategy for Sav-On.
Now we analyze the game from the perspective of Walgreen’s and we again see that there exists a dominant strategy, which is to price LOW.
A Nash Equilibrium exists that takes into account each player’s BEST response, which is for both firms to price LOW. This maximizes the expected profits assuming that neither player is allowed to collude.
We see that there is a better equilibrium that can only exist in the presence of some sort of collusion… These equilibriums tend to be unstable, but stabilization strategies do exist. Perhaps I will post on that sometime
OK… This was a very very simple example of a Nash equilibrium. A Nash equilibrium doesn’t necessarily have to exist, neither does a Dominant strategy. In these cases there are certain decision strategies that can be employed, but optimality is no longer guaranteed.
Here we have used game theory to set the optimal price for a new item. We can also use the same approach to determine if market entry would be profitable…
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Users on the web have VERY short attention spans… This is not a knew idea, but recently Seth points to a study that claims we don’t get the 3 seconds we once thought that we did; we get 50 milliseconds
While this number may sound unbelievable, one should recall the last time they used a search engine to find what they wanted. Presented with sometimes millions of results for your search, you set to work finding the best site. This is usually performed quite fast… I know that when I am sifting through the top results I am usually making snap judgments on the site’s quality, presentation, and focus. If it doesn’t look like it scores highly on those three things, in an instant, I am clicking the back button.
This is why it is paramount to present a well designed site; one that is well laid out and provides a natural eye path for the user to read down the page quickly and find what he is looking for. Equally important to your sites success, is knowing WHY a user is on the page he is on Users land on your site for different reasons (I know this is obvious). As a site designer it is important to architect the site in such a way that you serve the needs of those different users. Some want information on the product, some are researching for later purchase, and others are just looking for the quickest (and safest) way to buy. Each one of these people wants to see something slightly different, and if you don’t show it to them QUICKLY the potential customer may be lost forever…
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In Seth’s recent posts he explains the new product adoption lifecycle and explores how much traditional marketing has power over it. Some commenter’s seem to think that Seth is trying to contend the adoption cycle all together. I whole heartedly disagree…
You can’t market away the cycle. Even in his example when he removes price altogether there is still the power of ‘inertia’. And while it can be debated that new marketing tools could play a greater role than current mass marketing tools in speeding the cycle there is NO way to eliminate the process altogether. There will ALWAYS be a cost of switching. There will always be a few people who adopt early, middle, and late. All we can do is ‘squish’ the bell curve. And this is where the new, cheaper, tools of marketing come in. They reduce the barriers of information exchange and allow for trust network based diffusion, which WILL speed product adoption.
If price were to be re-included into this exercise it would only prove to make it more unlikely for the bell curve to disappear. It can be argued, as Rogers did, that this bell curve is like a queue where every person in the market is ordered by reservation price. There are people who MUST have the product now and if you engage in penetration pricing you will only be giving away consumer surplus to those who would have bought at the higher price. To argue that marketing could raise everyone’s reservation price to the point of the innovators is a little absurd, but perhaps there is an equilibrium price where we balance reservation price with profits, but that’s for a later economics discussion…
So, no, Seth is clearly not disputing the adoption cycle or the existence of Moore’s Chasm. In fact, if you read the punch line in part three he is challenging marketers to rethink their role. We need to realize that throwing money at the problem is not the solution. To answer his earlier question, marketers are not peddlers of lies they are the shepherds of the masses. They help to guide those who will benefit from an idea or product to the realization of that benefit. Couple this with the idea of Rogers’ consumer categories and it says we need to send the message in a different way for each class of consumer and potentially even change the product itself to meet changing needs as we cross each chasm to the next category.
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Frank Bass borrowed a model from immunology to describe how new products diffuse into a market. This model is very elegant, both simple and powerful. Using only three variables (coefficient of innovation, coefficient of imitation, and market size) it is able to fairly accurately model diffusion. It does this by recognizing that there are a few people in the market who act on their own and make decisions independently of others (the innovators) and a few people who are influenced by the installed base of adopters (the imitators), this is called an installed base effect. Bellow is the Bass equation in all its glory.
S(t) = [p + q(Y(t-1)/m)] * [m – Y(t-1)]
Where S(t) is the number of new adopters in time period t and Y(t-1) is the total number of adopters from the prior period. Essentially the first bracketed part of the equation is the probability of getting a sale, either through innovation or imitation. The second bracketed part is the remaining untapped market. Thus, if we multiply the probability of adoption by the number of people remaining we get the number of adopters for the current period.
Immediately one should ask, “Where do we get m, p, and q from?” Well, there are various methods for finding these numbers. First we can use analogy. By using p/q values from similar products we are able to infer a likely value for this new product. Second we can use historical data. Perhaps we have sales data from another, comparable, geographic region or early sales data from the product in question. Finding m is a little bit more of an art even than finding p and q. We want to try to start with the most inclusive market and systematically reduce it until we have found a best guess. For example, we could use the number of households in the US for the color TV market… Then we can perform sensitivity analyses on these data to see how affected our estimate is by error in our estimates of the values we arrived at for p, q, and m.
Once we have our values we can plug then into the bass model and estimate the diffusion process. One point to note is the point of inflection. This point represents maximum demand for the new product and is an important figure for production sizing. It also represents the point at which demand will begin decreasing.
A short example for Seth’s Squid Soup: I’m going to somewhat arbitrarily take our market size to be one million (I know it’s a big buffet). I will then take a slightly conservative value of p = 0.003 (Average value of p for all products studied is 0.03) and a slightly less conservative value for q = 0.7 (average value of q is 0.4). My reasoning for selecting these values is as follows: I have to imagine that squid soup will have a bit of a bad reputation from the get go (i.e. a lot of negative inertia) which is represented by the low value of p. However, assuming the soup actually does taste at least somewhat good, after those few innovators display their pleasure in eating squid soup it will have a strong influence on the remaining untapped market. (I chose to rely on taste for this example because this product suffers from observability issues. Meaning that Squid Soup is supposed to be healthy, and that is its benefit, but that feature is VERY hard for the untapped market to observe definitively, whereas people can readily observe and hear people’s enjoyment of the taste.)
S(t) is new adoptions for that year (We’re also simplifying the example by assuming that you only eat squid soup once, though the model can be modified to take into account repeat sales). Y(t) is total adoption up to that period. And “Trip” is what I am using for time period, i.e. trip to the buffet line.
NOTE: All sales figures are in thousands.
From the graph we can see this product starts very slowly but then once it reaches a “critical mass” of adopters the installed base effect takes over and growth is very rapid. Then we reach the inflection point (at trip11) where we have maximum demand for Squid Soup at 174,300 adopters. After the point of inflection demand begins to wane as the untapped market shrinks…
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