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Péter Csóka

is an Associate Professor at the Corvinus University of Budapest, Department of Finance and a senior research fellow at the game theory research group of the Hungarian Academy of Sciences. He received his Ph.D. in economics from Maastricht University in 2008. His research topics include risk measures, risk capital allocation, various aspects of liquidity, and financial networks. He has papers published in journals like Management Science, European Journal of Operational Research, Games and Economic Behaviour, and Journal of Banking and Finance.

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Péter Csóka, P. Jean-Jacques Herings: Liability games

A firm has liabilities towards a group of creditors. We analyze the question of how to distribute the asset value of the firm among the creditors and the firm itself. Compared to standard bankruptcy games, on top of the creditors, we introduce the firm as an explicit player and define a new class of cooperative games called liability games. Liability games are superadditive, constant sum, partially convex, and partially concave. 

We analyze the nucleolus of the game and show that allocating the asset value of the firm using the nucleolus satisfies efficiency, non-negativity and liabilities boundedness. We prove that at the nucleolus, the firm gets a strictly higher amount than its equity if and only if the firm is insolvent and has multiple liabilities. Thus the firm can use the threat to pay others to gain equity and get debt forgiveness, resulting in legally binding lower liabilities. This "threat to pay others"' possibility is also necessary and sufficient for the core of the game to be empty. Finally, we provide conditions under which the nucleolus coincides with a generalized truncated proportional rule, assigning a non-negative payment to the firm and distributing the rest in proportional to the liabilities, truncated by the asset value of the firm.

Last modified: 2018.11.30.