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Milind Sohoni

  1. Rank-1 Bi-matrix Games: A Homeomorphism and a Polynomial Time Algorithm.

    Mon, 10/18/2010 - 15:01 — SomNambul
    Authors: Bharat Adsul, Jugal Garg, Ruta Mehta, Milind Sohoni
    Subjects: Computer Science and Game Theory
    Abstract

    Given a rank-1 bimatrix game (A,B), i.e., where rank(A+B)=1, we construct a
    suitable linear subspace of the rank-1 game space and show that this subspace
    is homeomorphic to its Nash equilibrium correspondence. Using this
    homeomorphism, we give the first polynomial time algorithm for computing an
    exact Nash equilibrium of a rank-1 bimatrix game. In addition, we give a novel
    algorithm to enumerate all the Nash equilibria of a rank-1 game and show that a
    similar technique may also be applied for finding a Nash equilibrium of any
    bimatrix game.

  2. Nash equilibria in Fisher market.

    Fri, 02/26/2010 - 16:01 — SomNambul
    Authors: Bharat Adsul, Ch. Sobhan Babu, Jugal Garg, Ruta Mehta, Milind Sohoni
    Subjects: Computer Science and Game Theory
    Abstract

    In the Fisher market model, every 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 {\em Fisher market game} in which buyers strategize by posing
    different utility functions while their payoffs are determined with respect to
    their true utility functions.

Math-arch

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