  We prove the existence of Bayesian Nash Equilibrium (BNE) of general-sum
Bayesian games with continuous types and finite actions under the conditions
that the utility functions and the prior type distributions are continuous
concerning the players' types. Moreover, there exists a sequence of discretized
Bayesian games whose BNE strategies converge weakly to a BNE strategy of the
infinite Bayesian game. Our proof establishes a connection between the
equilibria of the infinite Bayesian game and those of finite approximations,
which leads to an algorithm to construct $\varepsilon$-BNE of infinite Bayesian
games by discretizing players' type spaces.
