A mathematical programming model of decentralized multi-level systems. (English) Zbl 0657.90061

In decentralized systems, the objective at the different levels often differ. Each level controls only a subset of the decision variables but is affected by the decision made at the other levels. Recent methods in bi-level linear programming solve such systems better than decomposition methods. Here, the bi-level LP is extended to a bi-level system with many decision-makers at the lower level, and a tri-level system with one decision-maker at each level. In both of these cases, the higher level acts as the leader and the lower level as the follower in the Stackelberg game. The resulting techniques are illustrated with simple numerical examples.


90C05 Linear programming
91A80 Applications of game theory
93A13 Hierarchical systems
91B24 Microeconomic theory (price theory and economic markets)
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