Nontransferable Utility Cooperative Dynamic Games

Living reference work entry


Cooperation in an inter-temporal framework under nontransferable utility/payoffs (NTU) presents a highly challenging and extremely intriguing task to game theorists. This chapter provides a coherent analysis on NTU cooperative dynamic games. The formulations of NTU cooperative dynamic games in continuous time and in discrete time are provided. The issues of individual rationality, Pareto optimality, and an individual player’s payoff under cooperation are presented. Monitoring and threat strategies preventing the breakup of the cooperative scheme are presented. Maintaining the agreed-upon optimality principle in effect throughout the game horizon plays an important role in the sustainability of cooperative schemes. The notion of time (subgame optimal trajectory) consistency in NTU differential games is expounded. Subgame consistent solutions in NTU cooperative differential games and subgame consistent solutions via variable payoff weights in NTU cooperative dynamic games are provided.


Cooperative games Nontransferable utility Differential games Dynamic games Time consistency Group optimality Individual rationality Subgame consistency Variable weights Optimality principle 



Financial support by the Russian Science Foundation (grant 17-11-01079) is gratefully acknowledged.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Center of Game TheorySt Petersburg State University, PetrodivoretsSt PetersburgRussia
  2. 2.SRS Consortium for Advanced Study in Dynamic GamesHong Kong Shue Yan UniversityHong KongChina
  3. 3.Faculty of Applied Mathematics-Control ProcessesSt Petersburg State UniversitySt PetersburgRussia

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