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Multi-Leader-Common-Follower games with pessimistic leaders: approximate and viscosity solutions

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We consider a two-stage game with k leaders having pessimistic attitude and one follower common to all leaders. Such a game, called CF game, may fail to have pessimistic solutions, even if the leader payoffs are linear and the optimal reaction of the follower to the leaders strategies is unique. So, we introduce two classes of games, called weighted value-potential and weighted potential CF games, and we illustrate their inherent difficulties and properties. For the more tractable class of weighted potential CF games, suitable approximate and viscosity solutions are introduced and are proven to exist under appropriate conditions, in line with what done for one-leader-one-follower games.

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  • M. Beatrice Lignola & Jacqueline Morgan, 2022. "Multi-Leader-Common-Follower games with pessimistic leaders: approximate and viscosity solutions," CSEF Working Papers 639, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    • Handle: RePEc:sef:csefwp:639
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    Keywords

    Two-stage game; Weighted potential game; Pessimistic behavior; Viscosity solution; Lower semicontinuous set-valued map;
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