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Pure Mathematics 2023
闭环动态古诺垄断博弈的γ-核
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Abstract:
本文研究具有闭环(无记忆)信息的效用可转移动态古诺垄断博弈的γ-核心解。基于合作微分博弈框架，运用Pontryagin极大值原理，获得了闭环信息的γ-特征函数，并进一步证明γ-核非空。数值例子表明，与开环信息相比，闭环信息不能带来真子联盟γ-特征函数值的一致严格变大或变小；但闭环信息对γ-核存在性的影响是鲁棒的。
This paper investigates the γ-core for the transferable-utility dynamic Cournot oligopoly game with closed-loop (memoryless) information. Based on the cooperative differential game and the Pontryagin maximum principle, we obtain the γ-characteristic function and further prove the non-emptiness of γ-core. Numerical example shows that compared to the open-loop information, the closed-loop information cannot bring the γ-characteristic function values of any proper coalition uniformly increasing or decreasing. But the impact of closed-loop information is robust for the non-emptiness of γ-core.
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