Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs

Elena Parilina () and Georges Zaccour ()
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Georges Zaccour: GERAD, HEC Montréal

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 1, No 4, 92-120

Abstract: Abstract We built a time-consistent cooperative solution for the class of dynamic games played over event trees in the context where the tree structure is given, but the players have different beliefs about the transition probabilities between nodes. Our three-step approach is as follows. First, we consider three alternative methods for aggregating the players’ beliefs and assume that the players agree to adopt one of them if they decide to cooperate. Second, we determine the Nash bargaining outcomes for the whole duration of the game. Finally, to insure sustainability of cooperation throughout the whole duration of the game, we propose two time-consistent decompositions over nodes of each player’s cooperative share, namely a proportion-consistent and a node-consistent allocation schemes. We illustrate our results with a simple Cournot oligopoly with capacity constraints.

Keywords: Stochastic games; Event tree; S-adapted strategies; Asymmetric information; Belief aggregation; Nash bargaining solution; 91A25; 91A15; 91A12 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02010-5

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