Thursday, May 17, 2012

How to Win at Battleship

Battleship 1

I used to play Battleship with my son, but he doesn't want to play with me any more. He's often wondered how I can consistently win the game. He assumes (and he's right) that, since I'm a game theorist, I've probably figured out some sort of mind-reading trick to be able to intuit where his ships are located. Apart from mind reading, I also rely on an optimal search strategy. Anyway, here's an amusing piece in Slate about a Microsoft employee who has taken this idea to its logical extreme.

http://www.slate.com/blogs/browbeat/2012/05/16/_battleship_how_to_win_the_classic_board_game_every_time.html

Thursday, May 10, 2012

Happy Summer


Something to remember the class by. This photo courtesy of Alper.

Have a happy summer and a great career gamers. Please stay in touch and feel free to visit the game theory website and blog for a refresh of key learnings from the class. Also, if you find a need for more game theory in your organization, please reach out. In the past, I've done custom sessions at several companies looking for more outward thinking. Many of these requests came from Game Theory alumni.

Keep using your outward thinking and empathy to build mental models and figure out what course of action to take. Previous game theory alums have said that the tools in the class were essential to career management and successfully leading teams.

Tuesday, May 1, 2012

Judo in Action: The Pebble Watch

Ran across this piece speculating about the lack of VC support for the Pebble, which is basically a limited version of an iPhone packed into a wristwatch. 


Now this seems like a classic judo. The gizmo itself is underpowered compared to the iPhone, the form factor obviously limits its appeal somewhat. And thus we come to the key question--how should Apple respond? 

Is the Pebble really committed to staying small? How large is the potential consumer base for such a device? Since you need an iPhone to run the thing, is it really a threat to Apple? Of course, Apple can kill it by producing their own Pebble, or they can let the thing go. 

My own guess is that this requires no response from Apple since the iPhone is essential for the thing to work. Apple has, in the past, tolerated thrid party offerings that change the form factor of iPod, such as the many speakers, clock radios, etc. produced for it. These have not hurt iPod at all. I expect that they'll reason analogously in this case. 

Your thoughts?


Wednesday, April 25, 2012

Classes #25 and 26 Highlights

Pocket Aces
In our last unit of game theory, we studied signaling. The goal of a signal is to influence the beliefs of the rival about some payoff relevant characteristic. In our setting, that characteristic was the worker's productivity. In firm settings, the characteristic is typically the quality of the item or service. To work, a signal must be understood by the receiver of the signal. That is, the message must meaningfully convey some information about the characteristic.

Most of the time, a firm or individual is interested in separating their product or service from the competition. The key to a good signal is one that a firm possessing the characteristic can send but which cannot be sent by someone lacking this characteristic. Often, this boils down to a difference in the cost of sending the signal. For instance, a car manufacturer with a low probability of breakdown can issue a comprehensive warranty that lasts for a long time whereas an unreliable manufacturer will find such a warranty too expensive to issue.

An MBA has some of these same characteristics. While the monetary cost of the degree is the same regardless of the quality of an individual, a low type will struggle to get through the courses, and this extra work effort will be costly in terms of quality of life, balance, and so on. A high type will not have to work as hard to get through the curriculum and hence will find the experience more pleasant and less costly.

Even though a separating equilibrium exists, it may not be optimal for anyone. Recognizing this, industry groups might agree not to permit certain types of signaling thus leaving all members better off. For instance, the industry council of distilled spirits manufacturers agreed not to advertise on television for many years. This agreement amounts to the enforcement of a pooling equilibrium over this signal.

Key Learnings


1. A signal works by changing beliefs about a payoff relevant characteristic. Thus, it is only effective if thie connection is readily understood by its recipient.
2. Using a signal to differentiate requires that the signal cannot be easily imitated by low quality types. This may be because it is prohibitively costly for them to do so or because it is technologically infeasible.
3. A signal is not useful simply because it is costly to send. It must be differentially costly, i.e. cheaper for high types than for low types to send.

Tuesday, April 24, 2012

Class 23 & 24 Results

Yahtzee!

In these classes, we studied mixed strategy equilibria. While usually your strategy is designed to maximize your profits given your mental model of the rival, there are some situations where the optimal strategy is simply to jam the signals your rival gets about what you intend to do. The use case is a circumstance where you are competing for price sensitive customers who buy at the lowest price. This happens in e-retail as well as in procurement contexts. Clearly, if your rival can predict your bid/price, she will simply undercut you and win the business. Thus, your job is to make the job of prediction as difficult as possible. The way to do this is through strategic ambiguity--building enough randomness into your actions that prediction is difficult.

But it's not enough simply to be random, you have to be smart about your randomness. In the e-retail situation, this consisted of using hit and run pricing strategies. Either you want to maintain a high price so as not to sacrifice margin to loyals while giving yourself a chance to win or you wanted to go low to ensure a good chance of capturing shoppers. Less good (against experienced players) is pricing in the middle, which sacrifices margin while risking defeat should your rival offer a "sale" in this period.

This is another example of the distinction between inward and outward thinking. Inward thinking says that you offer promotions to gain share, acquire customers, or introduce new customers to your product. The thinking has nothing to do with rivals. Outward thinking shows that sales promotions are a key tool in maintaining strategic ambiguity and jamming the signals of the rival.

Class #24 formalized how to do this. Your goal was to choose randomness so as to leave the rival indifferent among her strategies. Your rival acts in the same fashion and hence, in equilibrium, both sides are randomizing such that neither side gains from choosing any particular pure strategy. We showed this in the Beautiful Game example.

This strategic randomness can also lead to unintended consequences. In the Kitty Genovese game, we showed how rational players acting optimally give rise to a sort of collective madness---the larger is the team, the less likely each individual is to work hard (help) and the more likely the team is to fail at its job. The lesson for managers is to be careful about adding more people, even really good people, to teams. The logic of mixed strategies helps to explain why things like Amazon's 2PT (2 pizza team) rule makes sense despite the complexity of many business decisions.

Key Learnings:

1. Analyze games to determine is signal jamming is called for.
2. Optimal signal jamming leaves the rival indifferent among strategies.
3. When both sides are indifferent, we've found a mixed strategy equilibrium.
4. The logic of indifference can lead to perverse consequences such as diffusion of responsibility and ultimately failure despite the fact that everyone personally and collectively benefits from helping.

Final Presentation Schedule

Here is the schedule for final presentations. The rules are 10 minutes for the presentation, 2 minutes for Q&A. Please send me the slides 2 hours in advance of class so I can preload them on my laptop.


Wednesday  5/2
Monday 5/7
Good Swimmers
Latin Gambits
Gameblers
Nashty Equilibrium
Swimsocks
Pokerface
4 Young Men
JM Hypnotherapist
Wysiwyg
Beautiful Minds
YMCA^2
4 Men & a Baby Mama


Value of Education Results

Shapes: Cube and Cylinder

 Your colleague Abhishek Singhal was kind enough to create a results sheet for the Value of Education experiment. Check it out here:

Value of Education Results