  In this paper, we aim to design a distributed approximate algorithm for
seeking Nash equilibria of an aggregative game. Due to the local set
constraints of each player, projectionbased algorithms have been widely
employed for solving such problems actually. Since it may be quite hard to get
the exact projection in practice, we utilize inscribed polyhedrons to
approximate local set constraints, which yields a related approximate game
model. We first prove that the Nash equilibrium of the approximate game is the
$\epsilon$-Nash equilibrium of the original game, and then propose a
distributed algorithm to seek the $\epsilon$-Nash equilibrium, where the
projection is then of a standard form in quadratic programming. With the help
of the existing developed methods for solving quadratic programming, we show
the convergence of the proposed algorithm, and also discuss the computational
cost issue related to the approximation. Furthermore, based on the exponential
convergence of the algorithm, we estimate the approximation accuracy related to
$\epsilon$. Additionally, we investigate the computational cost saved by
approximation on numerical examples.
