This article addresses information-based sensing point selection from a set of possible sensing locations. A potential game approach has been applied to addressing distributed decision making for cooperative sensor planning. For a large sensor network, the local utility function for an agent is difficult to compute, because the utility function depends on the other agents' decisions, while each sensing agent is inherently faced with limitations in both its communication and computational capabilities. Accordingly, we propose an approximation method for a local utility function to accommodate limitations in information gathering and processing, using only a part of the decisions of other agents. The error induced by the approximation is also analyzed, and to keep the error small, we propose a selection algorithm that chooses the neighbor set for each agent in a greedy way. The selection algorithm is based on the correlation between one agent's and the other agents' measurement selection. Furthermore, we show that a game with an approximate utility function has an epsilon - equilibrium and the set of the equilibria include the Nash equilibrium of the original potential game. We demonstrate the validity of our approximation method through two numerical examples on simplified weather forecasting and multi-target tracking.