This essay consists of three chapters. Chapter one extends Allen and Gale’s (2000) model to a core-periphery network structure. We identify that the financial contagion in core-periphery structure is different to Allen and Gale (2000) in two aspects. Firstly, the shocks to the periphery bank and to the core bank have different contagion processes. Secondly, contagion not only depends on the amount of claims a bank has on a failed bank, but also on the number of links the failed neighbour has. Chapter two studies the policy effect on financial network formation when the government has time-inconsistency problem on bailing out systemically important bank. We show that if interbank deposits are guaranteed, the equilibrium network structure is different from the one under market discipline. We show that under market discipline individual banks can collectively increase the component size using interbank intermediation in order to increases the severity of systemic risk and hence trigger the bailout. If interbank intermediation is costly the equilibrium network has core-periphery structure. Chapter three follows Acharya and Yorulmazer’s (2007) study of the "too many to fail" problem in a two-bank model. They argue that in order to reduce the social losses, the financial regulator finds it ex post optimal to bail out every troubled bank if they fail together, because the acquisition of liquidated assets by other investors result in a high misallocation cost. In contrast to their paper, we argue that there is no "too many to fail" bailout, unless banking capital is costly and market price sensitive. We argue that market price sensitive capital can induce banks herding and high social cost.