This paper examines the following wireless data access scenario: a number of clients are interested in a set of data items kept at the server. A client sends a query request to inform the server of its desired data item. The server replies in the common broadcast channel. We first define a utility function that considers client?s power consumption in transmit, receive and idle modes. Specifically, utility is expressed as the number of queries that can be completed given a fixed energy source. Based on the utility function, we formulate our power aware wireless data access scheme as a non-cooperative game, called the WDA game. From our theoretical analysis, we show that clients are not always necessary to send query requests to the server. Instead, each client determines the request probability without any explicit communication with one another. Furthermore, we design and evaluate the server and client algorithms for the WDA game. Simulation results confirm that our proposed scheme, comparing with a simple always-request one, increases the utility and lifetime of every client while reducing the number of requests sent, at the cost of a slightly larger average query delay.