Minimax Theory and its Applications 09 (2024), No. 1, 129--141
Copyright Heldermann Verlag 2024
Multi-Leader-Common-Follower Games with Pessimistic Leaders: Approximate and Viscosity Solutions
M. Beatrice Lignola
Dept. of Mathematics and Applications R. Caccioppoli, University of Naples Federico II, Naples, Italy
lignola@unina.it
Jacqueline Morgan
Department of Economics and Statistics, and: Centre for Studies in Economics and Finance, University of Naples Federico II, Naples, Italy
morgan@unina.it
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.
Keywords: Two-stage game, weighted potential game, pessimistic behavior, viscosity solution, lower semicontinuous set-valued map.
MSC: 91A10, 91A14, 49J45, 49J53.
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