Infinite games with incomplete information are common in practice. First-price, sealed-bid auctions are a prototypical example. To solve this kind of infinite game, a heuristic approach is to discretise the strategy spaces and enumerate to approximate the equilibrium strategies. However, an approximate algorithm might not be guaranteed to converge. This paper discusses the utilisation of a best response algorithm in solving infinite games with incomplete information. We show the constraints of the valuation distributions define the necessary conditions of the convergence of the best response algorithm for several classes of infinite games, including auctions. A salient feature of the necessary convergence conditions lies in that they can be employed to compute the exact Nash equilibria without discretising the strategy space if the best response algorithm converges.