Mini-max incentive strategy for leader–follower games under uncertain dynamics

Celeste Rodríguez-Carreón, Manuel Jiménez-Lizárraga, César Emilio Villarreal and Ignacio Quiroz-Vázquez

International Journal of Systems Science, 2021, vol. 52, issue 15, 3159-3175

Abstract: This paper studies the problem of designing an incentive strategy for a leader–follower dynamic game affected by some sort of uncertainties. As is traditionally understood in the standard theory of incentives, the leader has complete knowledge of the game parameters, including the follower's performance index. So then he can compute the strategy that will lead the game to the global optimum that is favourable for him. Most of the current work is devoted to this situation. Nevertheless, such an assumption is unrealistic. This paper proposes an incentive scheme in which the game's dynamic depends on an unknown value that belongs to a finite set. The solution of the incentive strategy is computed in terms of the worst-case scenario, of the team's optimal solution. Based on the Robust Maximum Principle, the new incentive is presented in the form of a mini-max feedback control. Two numerical examples illustrate the effectiveness of the approach.

Date: 2021
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DOI: 10.1080/00207721.2021.1922951

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