Abstract
The paper is devoted to inverse Stackelberg games with many players. We consider both static and differential games. The main assumption of the paper is the compactness of the strategy sets. We obtain the characterization of inverse Stackelberg solutions and under additional concavity conditions, establish the existence theorem.
Highlights
The paper is concerned with the inverse Stackelberg game, known as the incentive problem
The inverse Stackelberg games appear in several models
If the strategy sets are normed space, the incentive strategy can be constructed in the affine form (Ref. [11] for static games and Ref. [12] for differential games)
Summary
The paper is concerned with the inverse Stackelberg game, known as the incentive problem. The inverse Stackelberg solutions of two-person differential games were studied via punishment strategies in the paper by Kleimonov [14]. Note that the incentive strategies considered in the paper by Kleimonov [14] use full memory, i.e., the leader plays with the nonanticipating strategies proposed in the papers by Elliot and Kalton [15] and Varaiya and Lin [16] for zero-sum differential games. Punishment strategies are applied to static inverse Stackelberg games and to differential inverse Stackelberg games with many followers.
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