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.

Class #22 Highlights

A War of Attrition

This class completed our auction unit. There were two key highlights:

1. N is a big deal. More than anything else, the number of bidders is the key variable in constructing a successful auction. We illustrated this in two ways. First, a quick case about the failure of the German 3g auctions owing to the fact that the number of licenses equaled the number of large players in the industry. Second, we showed that the worst auction beats the best negotiation if it attracts one additional bidder. This latter result is important in thinking about M&A.

2. How to think about wars of attrition. Wars of attrition arise in many business situations. In strategy, both the bitter competition and Ryanair cases are about anticipating wars of attrition.

An Update from the Penny Auction Front

The auction unit seemed to inspire a burst of interactivity on your part. I got a number of comments about penny auctions and slot auctions. Here are some highlights:

Leigh Fiske writes:

Quibids (http://www.quibids.com/) is a new "penny auction" site in the model of swoopo.com. Each bid costs $0.60 to make, and in the last few minutes of the auction, each new bid extends the remaining time by a certain amount. It's pretty interesting. They must think that their business model has a higher likelihood of success than their predecessors'!

Rosie Wang notes the demise of Swoopo and finds the effective markups on penny auctions rather yucky:

Thought you'd be interested to note that Swoopo has recently filed for bankruptcy. (http://technologizer.com/2011/03/25/swoopo-quietly-files-for-bankruptcy/) I was originally going to write you and let you know about another site called "oohilove" that had a very similar penny auction but for luxury handbags and accessories, only to find the site shuttered and that it's owned by the same company as Swoopo. I once did a calculation on oohilove though to see how much money they were making (since each bid is also $1 and bids go up in $0.02 increments), and was a bit disgusted by the multiple they were getting on the actual value of the product.

Gwyn Jones notes the burgeoning academic literature on position auctions. Here is a piece by Google's Chief Economist (and Berkeley Professor) Hal Varian title "Position Auctions" Here is a broad survey on Google style auctions from the source of all knowledge, Wikipedia.

Finally, a piece about waiting in line to see Star Wars.

Happy reading!

The Two Principles

Our auctions unit highlighted two principles: The Revenue Equivalence Principle and The Linkage Principle. The Revenue Equivalence Principle is a handy result allowing us to compare all sorts of auctions. It roughly says this:

Any auction where: (1) High bidder wins; (2) Free opt-out; (3) Bidders are similar; and (4) Bids are for cash yields the same expected revenue as a Vickrey auction. In fact, it says something a little stronger. It says that the expected payment for a bidder with value v is the same across auction forms. This auction pulls together a lot of non-auction settings such as price wars, R&D races, waiting times in line, and so on. It should be viewed as a first step and not a final answer. For instance, risk aversion will "break" the result. Bidders who differ a lot (i.e. one bidder known to be high value with a competitive fringe surrounding) will break the result. Multiple units that differ from one another (i.e. the slot auction) will break the result. But it's an essential starting point.

Our second principle was linkage. This roughly states that the more linked a bidder's payment is to value, the more revenues the auctioneer earns. We saw this sharply in comparing debt to equity. Since equity has linkage, it yields more money. It can also be used for disclosure strategies when values are correlated. For instance, suppose that an auctioneer is selling rights to an oil tract. Here, bidders have a common value for the tract (equal to the amount of oil under it). The linkage principle says that the auctioneer is better off, on average, if it reveals information about the value of the tract (i.e. seismological studies) than when it does not. In other words, disclosure is the best policy even if it means sometimes disclosing unfavorable information.

Class #21 Highlights

This class featured guest speaker Elizabeth Churchill talking about the evolving experience of shopping. Her slides are now posted up on the course website. More importantly, here is Elizabeth's light-hearted blog post about the topic:

Rat, Rational or Seething Cauldron of Desire: Designing the Shopper

Class # 19 Highlights

Structuring a deal

This is the first part of a two part class on structuring deals through auctions. In the experiment, we considered two dimensions of a deal: the degree of transparency and debt versus equity. Deals made via auction can be transparent, as in an English auction. Here, the auctioneer discloses the leading bid along the path to getting to a final deal. Deals can also be secret. Here, the auctioneer asks for sealed bids and the results are revealed only at the end. Each type of deal has advantages, which we will flesh out in class #20.

Class # 18 highlights

The Road not Taken

The highlight of this class was to introduce the Nash Bargaining Solution. This suggests that surplus should be allocated to maximize the product of the happiness of the two sides. The solution follows as a consequence of 4 principles: symmetry, no money left on the tables, frames don't matter, and the road not taken. It is the only rule satisfying these principles.