RETRACTED: Penalties and contagion in financial networks (Retracted Article)

Contagion and systemic risk, though in existence for quite a while, has seen increasing attention following the last Financial crises. In an attempt to contribute a little to the existing literature, this work focuses primarily on networks in which some paying-firms face systemic fragility through default cascade in specific settings where firms in cyclical connections defaults but defaults cascade without completing a cycle. To capture relevant dynamics to the equilibrium, this paper imposes a contractual system whereby firms who default incur an estimable amount of monetary penalties. Then it investigates under these conditions, the existence and dynamic properties of equilibrium. This paper investigates for strategic interactions between vulnerable Firms. Results show that in a setting where defaults do not feedback to source and where penalties are of considerable magnitude, there exists a unique, strictly dominant Nash equilibrium for Firms which depends on the Vulnerability index of Firms. A basic algorithm that computes the basic equilibrium decision of Firms is also proposed. Finally, the paper additionally analyses the role of the network of financial liabilities and systemic vulnerability on default decisions and on the free-riding behaviour as well as possible levels of payoffs for Firms involved. We find that when actions are limited, harsh penalties might harm some Firms that otherwise, would have achieved greater utility.