On the consistency of leaders' conjectures in hierarchical games

Ankur A. Kulkarni, Uday V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations


In multi-leader multi-follower games, a set of leaders compete in a Nash game, while anticipating the equilibrium arising from a game between a set of followers. Conventional formulations are complicated by several concerns. First, since follower equilibria need not be unique, conjectures made by leaders regarding follower equilibria may not be consistent at equilibrium. When the follower equilibrium is a physical quantity to be exchanged, one is led to ask whether an equilibrium without consistent conjectures is even sensible. Second, these games are often irregular and nonconvex and no general sufficiency conditions for existence of equilibria are known. Third, no globally convergent algorithms for computing equilibria are known. We show that these concerns are addressed en masse by a modified model we introduce in this paper. In this model each leader makes conjectures while also requiring that his conjectures are consistent with those made by other leaders. If leader payoff functions admit a potential function, then under mild conditions, this model admits an equilibrium. At equilibrium, the conjectures of leaders are necessarily consistent, and when there is a unique follower equilibrium, the equilibria of the original model are equilibria of the new model. Preliminary empirical evidence suggests that such equilibria are also significantly easier to compute.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781467357173
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other52nd IEEE Conference on Decision and Control, CDC 2013

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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