Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization

Francesco Caruso (), M. Beatrice Lignola () and Jacqueline Morgan
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Francesco Caruso: Università di Napoli Federico II
M. Beatrice Lignola: Università di Napoli Federico II

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: In a two-stage Stackelberg game, depending on the leader's information about the choice of the follower among his optimal responses, one can associate different types of mathematical problems. We present formulations and solution concepts for such problems, together with their possible connections in bilevel optimization, and we illustrate the crucial issues concerning these solution concepts. Then, we discuss which of these issues can be positively or negatively answered and how managing the latter ones by means of two widely used approaches: regularizing the set of optimal responses of the follower, via different types of approximate solutions, or regularizing the follower's payoff function, via the Tikhonov or the proximal regularizations. The first approach allows to obviate the lack of existence and/or stability through approximating problems, whose solutions exist under not restrictive conditions and enable to construct a surrogate solution to the original problem. The second approach permits to overcome the non-uniqueness of the follower's optimal response, by constructing sequences of Stackelberg games with a unique second-stage solution which approximate in some sense the original game, and to select among the solutions by using a constructive method with behavioural motivations.

Keywords: Two-stage Stackelberg game; bilevel optimization; pessimistic and optimistic problem; intermediate Stackelberg problem; subgame perfect Nash equilibrium; existence and stability of solutions; constructive selection method; follower's optimal reaction set approximation; approximate solution; viscosity solution; follower's payoff function approximation; Tikhonov method; proximal regularization; cost-to-move. (search for similar items in EconPapers)
Date: 2019-09-16, Revised 2020-09-18
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (2)

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Chapter: Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization (2020)
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