Existence and computations of best affine strategies for multilevel reverse Stackelberg games

Seyfe Belete Worku (), Birilew Belayneh Tsegaw () and Semu Mitiku Kassa ()
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Seyfe Belete Worku: Bahir Dar University
Birilew Belayneh Tsegaw: Bahir Dar University
Semu Mitiku Kassa: Botswana International University of Science and Technology

Mathematical Methods of Operations Research, 2023, vol. 97, issue 3, No 3, 339-366

Abstract: Abstract The multilevel reverse Stackelberg game is considered. In this game, the leader controls the outcome by announcing a strategy as a function of decision variables of the followers to his/her own decision space. Corresponding to the leader’s strategy, the player in the next level presents his/her strategy as a function of decision variables of the remaining players. This procedure is repeated until it is the turn of the bottom level player in the hierarchy, who reacts by determining his/her optimal decision variables. The structure of this game can be adopted in decentralized multilevel decision making like resource allocation, energy market pricing, problems with hierarchical controls. In this paper conditions for existence and construction of affine leader reverse Stackelberg strategies are developed for such problems. As an extension to the existing literature, we considered nonconvex sublevel sets of objective functions of followers. Moreover, a method to construct multiple reverse Stackelberg strategies for the leader is also presented.

Keywords: Multilevel game; Hierarchical decision; Stackelberg strategy; Reverse Stackelberg strategy; Team solution; Desired equilibrium; 90B50; 90C25; 90C30; 90C31 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00820-5

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