A novel class of multi-period multi-player competitive stopping games with redistribution of payoffs is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single-period case is shown to be weakly unilaterally competitive under some assumptions on redistribution of payoffs. We present an explicit construction of the unique value at which Nash and optimal equilibria are attained. The multi-period stochastic extension of the game is also studied and solved by the backward induction. The game has interpretations in economic and financial contexts, for example, as a consumption model with bounded resources or a starting point to the construction of multi-person financial game options. Deterministic multi-period quitting games are also examined as an alternative to stopping games.
|Title of host publication||Arbitrage, Credit and Informational Risks|
|Editors||Caroline Hillairet, Monique Jeanblanc, Ying Jiao|
|Place of Publication||Singapore|
|Publisher||World Scientific Publishing|
|Number of pages||36|
|Publication status||Published - 2014|
|Name||Peking University Series in Mathematics|