Final Project Deadline

Final projects are due on May 16 at 1159pm Hawaii time. Please send as a PDF.

Mixed Strategies Highlights

Choosing the Right Strategy?

In our section on mixed strategies, we studied games that had no set of deterministic best responses. For instance, in soccer penalty kicks, the best response to a keeper who defends left is to kick right, but then the keeper's best response is to defend to the right, which leads to kicking to the left as being optimal and we end up going in a circle. The solution to the "circle" problem is to study mixed strategy equilibria. These strategies can be understood literally as using randomization schemes to determine which strategy to play.

Signaling Highlights

Please find the results of the value of education experiment here.

We studied signaling through the value of education game. In signaling games, the key parameter in the mental model are the beliefs of employers about a worker's type following each signal. In a separating equilibrium, different signals produce different beliefs. In our game, we saw that a separating equilibrium consisted of believing that grade school (or BS) were associated with low types while MBA was associated with being a high type. In that case, a low type could not gain by pretending to be a high type and, therefore, these beliefs are confirmed by actions. We also saw that one could not sustain a separating equilibrium by believing that low types choose grade school while high types choose BS or MBA. The reason is that the marginal benefit to a low type from imitating a high type and getting a BS was 100k while the marginal cost was only 80k; therefore, low types will "invade" the BS population and thereby destroy the signal.

Let us reflect on this for a moment. 20-30 years ago, an MBA was unnecessary to climb to the highest levels in business whereas now it more or less is required. What has changed over that time is undergraduate enrollments. 20-30 years ago, many people ended their education with a high school degree. Now, there are strong incentives to proceed to get an undergraduate degree and many subsidies and loans to make this affordable. In a sense, an undergraduate education is now too cheap to offer a useful signal. In our game, this signal inflation was altogether a bad thing since there were no gains to human capital from signaling. Of course, the reality is that there are some human capital gains. Nonetheless, the results of the game indicate that there is an incentive to overinvest in education purely for the signaling aspect. In other words, the problem might be too much education rather than too little.

Preso Order

Here is my best reconstruction of the preso order on the basis of your cards from last class. Please alert me if any of this is screwed up.
Class #28 (Weds)
1. YNK
2. MAX
3. AGT
4. WSID
5. NAS
6. F
7. HAZ

Class #29 (Mon)
1. REPS
2. H8
3. MOAB
4. RDR
5. MOTN
6. BNT
7. SEA
8. PLAYA

Aside: Photos, creativity, and conversations

I was delighted to get a comment after class on the photos on the blog. When I'm not professoring, I'm an amateur photographer. Indeed, other than working on game theory, photography is my other great passion. I mentioned creativity in an earlier aside and I do think this is perhaps the most important thing to gain from an MBA education. To me, both game theory and photography offer a chance to "see the world differently," which is the essence of creativity in my view.

Class # 23 Highlights

Surviving the War of Attrition

We closed the auction unit with a cautionary tale about modeling behavior. The key to fighting a war of attrition is to determine the hazard rate of concessions. Now, there is a tendency toward overoptimism in estimating this hazard rate and, as a consequence, the war tends to lost longer than expected. We saw this vividly in the $20 bill auction where the total spend exceeded the value of the bill by $7. This also illustrates that the revenue equivalence theorem is a starting point rather than an ending point. Accounting for behavioral factors, risk preferences, framing and so on is essential in developing good mental models.

Mid-Semester Projects

I've now added links for all the mid-semester projects, so you can read what your colleagues have written. I would especially call your attention to MOAB's mid-semester project. This is by far the nicest mid-semester project I've seen since running game theory. They study the NYSE/Euronext acquisition. Notice how they pin down 4 key bidding points in the negotiation based on the inside versus outside option equalization in second price auctions. Notice also the care in devising what these valuations are. They are facing a potentially super-complicated game, but used the tools of game theory to isolate and analyze the key aspects.

Check it out here.