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Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility

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Abstract

In this paper, we study the time consistency of cooperative agreements in dynamic games with non-transferable utility. An agreement designed at the outset of a game is time-consistent (or sustainable) if it remains in place for the entire duration of the game, that is, if the players would not benefit from switching to their non-cooperative strategies. The literature has highlighted that, since side payments are not allowed, the design of such an agreement is very challenging. To address this issue, we introduce different notions for the temporal stability of an agreement and determine endogenously the duration of the agreement. We illustrate our general results with a linear-quadratic difference game and show that an agreement’s duration can be easily assessed using the problem data. We also study the effect of information structure on the endogenous duration of the agreement. We illustrate our results with a numerical example.

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Notes

  1. That is, an outcome of the game when players can communicate.

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Acknowledgements

The first author’s research is supported by Saint Petersburg State University, Grant No. 41128961. This research was partially conducted during the research stay of the first author at GERAD, HEC Montreal, Canada.The second author’s research is supported by the IIT Madras, New Faculty Initiative Grant ELE1718849NFIGPUVR. The third author’s research is supported by NSERC Canada, Grant RGPIN-2016-04975. He also thanks the Department of Electrical Engineering, IIT Madras, India, for its hospitality.

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Authors and Affiliations

  1. Saint Petersburg State University, Saint Petersburg, Russia

    Elena M. Parilina

  2. Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

    Puduru Viswanadha Reddy

  3. GERAD and HEC Montréal, Montréal, Canada

    Georges Zaccour

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  1. Elena M. Parilina
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  3. Georges Zaccour
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Correspondence to Georges Zaccour.

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Communicated by Mauro Pontani.

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Parilina, E.M., Reddy, P.V. & Zaccour, G. Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility. J Optim Theory Appl 195, 808–836 (2022). https://doi.org/10.1007/s10957-022-02109-9

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