Tuesday, April 24, 2012
Class 23 & 24 Results
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.
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.