Thursday, August 28, 2014

Class #2 Highlights

The theme of class #2 was look forward, reason back (LFRB), a fundamental idea in game theory. The point of LFRB is to look ahead to the end of the game, anticipate what future moves will be, and then respond accordingly. Anticipation, as we discussed, requires two ingredients:

  1. What are the possibilities? What strategies are possible in reaction to my move?
  2. What are the preferences? What do the other players value? Do they care about money, reputation, ego, social justice, or something else entirely?
The combination of what is possible and how these possibilities are valued, allows one to anticipate the future (almost like looking into a crystal ball) and react (or pro-act) accordingly.

To get a sense of how this works, we studied two common dilemmas: The trust dilemma and the reputation dilemma. The trust dilemma describes poverty and underinvestment in many places. Here, we considered a situation between an investor and an entrepreneur. The entrepreneur creates a high expected return from the capital investment, but legal institutions are such that contracts cannot be enforced. Faced with a one-off situation, we saw that, no matter how profitable the opportunity, the investor would not commit capital since it would anticipate being expropriated (cheated). Solving this dilemma has preoccupied academics, NGOs, and, of course, banks and other investors, for many years. A common solution is repeated interaction even across generations. The keiretsu system of "family" investment in Asia occurred in large part as a response to this LFRB dilemma. Grameen banks, which use the community sanctions to enforce contracts, represent a more recent response.

Apart from the developing world, versions of this dilemma occur all the time within firms. For instance, one needs help from an expert from another team on a given project. But there is no formal contract for repayment of this service existing within the firm. Depending on the nature of the relationship with the other team or the expert, many times such synergies fail to be realized as the expert, or his team, fear that the project manager will take all the credit for solving the problem without "repaying" the expert.

If you have other examples of the trust dilemma, please share them either in the comment section or by writing me directly.

A more subtle LFRB situation is the reputation dilemma. In this situation, a "long-term" player confronts a succession of n short-term (one-shot) players. The short term player can choose to challenge the long-term player or not and the long-term player must decide whether to fight, which is costly to both, or accommodate. Early in the game, reputation is obviously important, so the long-term player would seem to want to fight (or at least have that reputation). Near the end, however, both players realize that reputation is no longer valuable, so accommodation will be anticipated correctly. Here, we see the power of LFRB--there is no credible way for the long-run player to gain a fighting reputation if she is rational. In effect, the resolve of the player unravels. If the long-run player won't fight the last player, then the penultimate short-run player need not fear either, since there is no reason to fight to maintain a worthless reputation. But now the same is true of the short run player third from the end, and so on...all the way to the beginning.

How can the long-run player solve this situation? Paradoxically, it is her very rationality that is the cause of the problem. If the long-run player were crazy, reputation could easily be maintained, and challenges deterred. The precise way in which this happens is the subject of our next class.

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