Wednesday, March 30, 2011
Class #18 Highlights
A Cake Cutting Problem?
In this class, we developed a framework for assessing bargaining situations. Bargaining is complex and messy. Moreover, the answers provided by game theory are often frustratingly sensitive to the exact form of the game tree. What is needed is a toolkit for assessing outcomes without having to write down the game. Here, we took a page from cooperative game theory.
Cooperative game theory is an older line of game theory that is less used. It mainly involves developing principles (axioms in formal language) and then applying these to predict payoffs in bargaining and coalition building situations. While this branch of game theory is interesting in its own right, scarce course time limits our coverage.
Our main tool for assessing bargaining is the Nash Bargaining Solution. This says that, given a payoff frontier and outside options for each party, choose the outcome that maximizes the product of the payoffs.
This odd suggestion derives from 4 simple principles: 1. Symmetry, 2. Frames don't matter, 3. No money left on the table, and 4. The road not taken. Agreeing to these 4 principles is the same as agreeing to the Nash Bargaining Solution.
The solution has several sensible predictions. First, better outside options produce more payoffs in a settlement. Second, more risk averse parties do worse than less risk averse ones.