51. Bilevel Programming Approaches to the Computation of Optimistic and Pessimistic Single-Leader-Multi-Follower Equilibria
- Author
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Basilico, Nicola, Coniglio, Stefano, Gatti, Nicola, Marchesi, Alberto, Iliopoulos, Costas S., Pissis, Solon P., Puglisi, Simon J., and Raman, Rajeev
- Subjects
TheoryofComputation_MISCELLANEOUS ,Computer Science::Computer Science and Game Theory ,Stackelberg games ,Nash equilibria ,Game theory ,Bilevel and nonlinear programming ,Branch-and-bound ,000 Computer science, knowledge, general works ,Settore INF/01 - Informatica ,020209 energy ,TheoryofComputation_GENERAL ,02 engineering and technology ,Computer Science ,0202 electrical engineering, electronic engineering, information engineering ,Settore MAT/09 - Ricerca Operativa - Abstract
We study the problem of computing an equilibrium in leader-follower games with a single leader and multiple followers where, after the leader’s commitment to a mixed strategy, the followers play simultaneously in a noncooperative way, reaching a Nash equilibrium. We tackle the problem from a bilevel programming perspective. Since, given the leader’s strategy, the followers’ subgame may admit multiple Nash equilibria, we consider the cases where the followers play either the best (optimistic) or the worst (pessimistic) Nash equilibrium in terms of the leader’s utility. For the optimistic case, we propose three formulations which cast the problem into a single level mixed-integer nonconvex program. For the pessimistic case, which, as we show, may admit a supremum but not a maximum, we develop an ad hoc branch-and-bound algorithm. Computational results are reported and illustrated.
- Published
- 2017