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Dynamic linear programming games with risk-averse players

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Abstract

Motivated by situations in which independent agents wish to cooperate in some uncertain endeavor over time, we study dynamic linear programming games, which generalize classical linear production games to multi-period settings under uncertainty. We specifically consider that players may have risk-averse attitudes towards uncertainty, and model this risk aversion using coherent conditional risk measures. For this setting, we study the strong sequential core, a natural extension of the core to dynamic settings. We characterize the strong sequential core as the set of allocations that satisfy a particular finite set of inequalities that depend on an auxiliary optimization model, and then leverage this characterization to establish sufficient conditions for emptiness and non-emptiness. Qualitatively, whereas the strong sequential core is always non-empty when players are risk-neutral, our results indicate that cooperation in the presence of risk aversion is much more difficult. We illustrate this with an application to cooperative newsvendor games, where we find that cooperation is possible when it least benefits players, and may be impossible when it offers more benefit.

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Acknowledgments

The authors’ work was partially supported by the National Science Foundation via Grant CMMI 1265616.

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  1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Alejandro Toriello

  2. Mathematics Department, United States Naval Academy, Annapolis, MD, 21402, USA

    Nelson A. Uhan

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  1. Alejandro Toriello
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  2. Nelson A. Uhan
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Toriello, A., Uhan, N.A. Dynamic linear programming games with risk-averse players. Math. Program. 163, 25–56 (2017). https://doi.org/10.1007/s10107-016-1054-y

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