A study of general and security Stackelberg game formulations

Casorrán, Carlos; Fortz, Bernard; Labbé, Martine; Ordóñez, Fernando

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.ejor.2019.05.012

Title :

A study of general and security Stackelberg game formulations

Author(s) :

Casorrán, Carlos [Auteur]
Integrated Optimization with Complex Structure [INOCS]
Fortz, Bernard [Auteur]
Graphes et Optimisation Mathématique [Bruxelles] [GOM]
Labbé, Martine [Auteur]
Integrated Optimization with Complex Structure [INOCS]
Ordóñez, Fernando [Auteur]
Departamento de Ingenieria Industrial [Santiago] [DII]

Journal title :

European Journal of Operational Research

Pages :

855 - 868

Publisher :

Elsevier

Publication date :

2019

ISSN :

0377-2217

English keyword(s) :

Integer programming
discrete optimization
game theory
bilevel optimization

HAL domain(s) :

Computer Science [cs]/Operations Research [math.OC]

English abstract : [en]

In this paper, we analyze different mathematical formulations for general Stackelberg games (GSGs) and Stackelberg security games (SSGs). We consider GSGs in which a single leader commits to a utility maximizing strategy ...
Show more >In this paper, we analyze different mathematical formulations for general Stackelberg games (GSGs) and Stackelberg security games (SSGs). We consider GSGs in which a single leader commits to a utility maximizing strategy knowing that one of p possible followers optimizes its own utility taking this leader strategy into account. SSGs are a type of GSG that arise in security applications where the strategies of the leader consist in protecting subsets of targets and the strategies of the p followers consist in attacking a single target. We compare existing mixed integer linear programming (MILP) formulations for GSGs, sorting them according to the tightness of their linear programming (LP) relaxations. We show that SSG formulations are projections of GSG formulations and exploit this link to derive a new SSG MILP formulation that i) has the tightest LP relaxation known among SSG MILP formulations and ii) its LP relaxation coincides with the convex hull of feasible solutions in the case of a single follower. We present computational experiments empirically comparing the difficulty of solving the formulations in the general and security settings. The new SSG MILP formulation is computationally efficient, in particular as the problem size increases.Show less >

Language :

Anglais

Popular science :

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