Abstract
The paper proposes a game model with an additive convolution of two criteria, describing public and personal interests. The first (general) criterion depends on strategies of all players and represents losses from the intensity of their activity. The second (particular) criterion for each player is a function of his strategy and reflects the income from his activities. The negative definite quadratic form is taken as a general criterion. The particular criterion of each player is linear, which is quite natural for the formalization of the income function. It turns out that the resulting game with linear-quadratic payoff functions has good properties, in particular, the independence of the leader’s strategy in the Stackelberg equilibrium from the parameters of the follower’s linear functions (in contrast to the Nash equilibrium). This property means that the leader does not need accurate information about the follower’s objective function, and his strategy has the property of robustness.
The work was carried out within the framework of the project No. AAAA-A20-120122190034-9.
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Gorelik, V., Zolotova, T. (2021). Stackelberg and Nash Equilibria in Games with Linear-Quadratic Payoff Functions as Models of Public Goods. In: Olenev, N.N., Evtushenko, Y.G., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2021. Lecture Notes in Computer Science(), vol 13078. Springer, Cham. https://doi.org/10.1007/978-3-030-91059-4_20
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