This dissertation studies dynamic matching and bargaining games with two-sided private information bargaining. There is a market in which a large number of heterogeneous buyers and sellers search for trading partners to trade with. Traders in the market are randomly matched pairwise. Once a buyer and a seller meet, they bargain following the randomproposer protocol: either the buyer or the seller (randomly chosen) makes a take-it-orleave-it offer to the other party. The traders leave once they successfully trade, and the market is continuously replenished with new-born buyers and sellers who voluntarily choose to enter. We study the steady state with positive entry. There are (except the asymmetric information) two kinds of frictions: time discounting and explicit search costs. Chapter 2 addresses existence and uniqueness of equilibrium. It provides a simple necessary and sufficient condition for the existence of a nontrivial steady-state equilibrium. The equilibrium is unique if the discount rate is small relative to the search costs. This chapter also analyzes how the composition of frictions affects the patterns of equilibria. It shows that if the discount rate is small relative to the search costs, in equilibrium every meeting results in trade. If the discount rate is relatively large, some meetings do not result in trade. Chapter 3 shows that private information typically deters entry. Because of search externalities, this entry-deterring effect may be socially desirable or undesirable. We provide and interpret a simple condition under which private information improves welfare. Chapter 4 studies the convergence properties of equilibria as frictions vanish. It not only shows that, as frictions vanish, the equilibrium price range collapses to the Walrasian price and the equilibrium welfare converges to the Walrasian welfare level, but also provides the rate of convergence. Under random-proposer bargaining, welfare converges at the fastest possible rate among all bargaining mechanisms. If we assume double auction instead of random-proposer bargaining, equilibria might converge at a slower rate or even not converge at all. These results also hold under full information bargaining. It suggests that private information does not affect asymptotic efficiency, but bargaining protocol might.