Multi-Leader-Common-Follower Games with Pessimistic Leaders: Approximate and Viscosity Solutions
Keywords:
Two-stage game, weighted potential game, pessimistic behavior, viscosity solution, lower semicontinuous set-valued map.Abstract
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 by the authors
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