In this paper, we consider a resource allocation game with binary preferences and limited capacities over large scale networks and propose a novel randomized algorithm for searching its pure-strategy Nash equilibrium points. It is known that such games always admit a pure-strategy Nash equilibrium and benefit from having a low price of anarchy. However, the best known theoretical results only provide a quasi-polynomial constant approximation algorithm of the equilibrium points over general networks. Here, we search the state space of the resource allocation game for its equilibrium points. We use a random tree based search method to minimize a proper score function and direct the search toward the pure-strategy Nash equilibrium points of the system. We demonstrate efficiency of our algorithm through some empirical results.