Seminar by Sobhan Babu
Nash Equilibria in Fisher Market
Sobhan Babu
IIT Bombay
Date: Monday, October 26, 2009
Time: 11:00 AM
Venue: CS101.Abstract:
In the Fisher market model, each buyer reveals her preferences over the available goods in terms of a linear utility function. These utility functions crucially influence market equilibrium and consequently the payoffs to the buyers. Motivated by the observation that a buyer may derive a better payoff by feigning her utility function and thereby manipulating the market equilibrium, we formulate the Fisher market game in which buyers strategize by posing different utility functions while their payoffs are determined with respect to their true utility functions. We study all Nash equilibria of one shot Fisher market game with two buyers and an arbitrary number of goods and provide a complete polyhedral characterization of the same. We also analyze how the payoffs to the buyers change with varying Nash equilibria and show that these payoffs constitute a piecewise linear concave curve, albeit, polarized. We also study the correlated equilibria of a related game and show that third-party mediation in this game does not help to achieve better payoffs than Nash equilibria payoffs.