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The index coding problem includes a server, a group of clients, and a set of data chunks. While each client wants a subset of the data chunks and already has another subset as its side information, the server transmits some uncoded data chunks or coded data chunks to the clients over a noiseless broadcast channel. The objective of the problem is to satisfy the demands of all clients with the minimum number of transmissions. In this paper, we investigate the index coding setting from a game-theoretical perspective. We consider selfish clients, where each selfish client has private side information and a private valuation of each data chunk it wants. In this context, our objectives are following: 1) to motivate each selfish client to reveal the correct side information and true valuation of each data chunk it wants; 2) to maximize the social welfare, i.e., the total valuation of the data chunks recovered by the clients minus the total cost incurred by the transmissions from the server. Our main contribution is to jointly develop coding schemes and incentive schemes for achieving the first objective perfectly and achieving the second objective optimally or approximately with guaranteed approximation ratios (potentially within some restricted sets of coding matrices).