1st International Conference on Game Theory for Networks

Research Article

Oblivious equilibrium: An approximation to large population dynamic games with concave utility

  • @INPROCEEDINGS{10.1109/GAMENETS.2009.5137384,
        author={Sachin  Adlakha and Ramesh   Johari and Gabriel   Weintraub and Andrea  Goldsmith},
        title={Oblivious equilibrium: An approximation to large population dynamic games with concave utility},
        proceedings={1st International Conference on Game Theory for Networks},
        publisher={IEEE},
        proceedings_a={GAMENETS},
        year={2009},
        month={6},
        keywords={},
        doi={10.1109/GAMENETS.2009.5137384}
    }
    
  • Sachin Adlakha
    Ramesh Johari
    Gabriel Weintraub
    Andrea Goldsmith
    Year: 2009
    Oblivious equilibrium: An approximation to large population dynamic games with concave utility
    GAMENETS
    IEEE
    DOI: 10.1109/GAMENETS.2009.5137384
Sachin Adlakha1, Ramesh Johari1, Gabriel Weintraub1, Andrea Goldsmith1
  • 1: Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA

Abstract

We study stochastic games with a large number of players, where players are coupled via their payoff functions. A standard solution concept for such games is Markov perfect equilibrium (MPE). It is well known that the computation of MPE suffers from the ldquocurse of dimensionality.rdquo Recently an approximate solution concept called ldquooblivious equilibriumrdquo (OE) was developed by Weintraub et al., where each player reacts to only the average behavior of other players. In this work, we characterize a set of games in which OE approximates MPE. Specifically, we show that if system dynamics and payoff functions are concave in state and action and have decreasing differences in state and action, then an oblivious equilibrium of such a game approximates MPE. These exogenous conditions on model primitives allow us to characterize a set of games where OE can be used as an approximate solution concept.