Subgame Consistent Cooperative Behavior in an Extensive form Game with Chance Moves

Denis Kuzyutin and Nadezhda Smirnova
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Denis Kuzyutin: Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia
Nadezhda Smirnova: Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia

Mathematics, 2020, vol. 8, issue 7, 1-20

Abstract: We design a mechanism of the players’ sustainable cooperation in multistage n -person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players’ rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal bundle of cooperative strategies satisfies time consistency, that is, at every subgame along the optimal game evolution a part of each original cooperative trajectory belongs to the subgame optimal bundle. We propose a refinement of the backwards induction procedure based on the players’ attitude vectors to find a unique subgame perfect equilibrium and use this algorithm to calculate a characteristic function. Finally, to ensure the sustainability of the cooperative agreement in a multistage game we employ the imputation distribution procedure (IDP) based approach, that is, we design an appropriate payment schedule to redistribute each player’s optimal payoff along the optimal bundle of cooperative trajectories. We extend the subgame consistency notion to extensive-form games with chance moves and prove that incremental IDP satisfies subgame consistency, subgame efficiency and balance condition. An example of a 3-person multistage game is provided to illustrate the proposed cooperation mechanism.

Keywords: time consistency; multistage game; chance moves; subgame perfect equilibria; cooperative trajectory; imputation distribution procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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