Abstract
Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers. Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower (or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse Stackelberg concept. As a side issue, expressions like “two captains on a ship” and “divide and conquer” are given a mathematical foundation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Başar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory. SIAM, Philadelphia (1999)
Ho, Y.-C., Luh, P.B., Olsder, G.J.: A control-theoretic view on incentives. Automatica 18, 167–179 (1982)
Bernhard, P.: A robust control approach to option pricing including transaction costs. In: Nowak, A. (ed.) Advances in Dynamic Gases. Annals of the ISDG, vol. 7, pp. 391–416. Birkhäuser, Basel (2002)
Olsder, G.J.: Differential game-theoretic thoughts on option pricing and transaction costs. Int. Game Theory Rev. 2, 209–228 (2000)
Kuczma, M.: Functional Equations in a Single Variable. Polish Sci., Warsaw (1968)
Cruz Jr, J.B., Drakunov, S.V., Sikora, M.A.: Leader-follower strategy via a sliding mode approach. J. Optim. Theory Optim. 88(2), 267–295 (1996)
von Stackelberg, H.: Marktform und Gleichgewicht. Springer, Vienna (1934) (English translation: The Theory of the Market Economy. Oxford University Press, Oxford (1952))
Simaan, M., Cruz Jr., J.B.: On the Stackelberg strategy in nonzero sum games. J. Optim. Theory Optim. 11, 533–555 (1973)
Simaan, M., Cruz Jr., J.B.: Additional aspects of the Stackelberg strategy in nonzero sum games. J. Optim. Theory Optim. 11, 613–626 (1973)
Epstein, G.S., Hefeker, C.: Lobbying and concessions: comparing Nash to Stackelberg games. Public Choice 109(1–2), 175–181 (2001)
Roughgarden, T.: Stackelberg scheduling strategies. SIAM J. Comput. 33(2), 332–350 (2004)
Stan̆ková, K., Olsder, G.J., Bliemer, M.C.J.: Bilevel optimal toll design problem solved by the inverse Stackelberg games approach. Urban Transp. 12, 871–880 (2006)
Selanie, B.: The Economics of Contracts. MIT Press, Cambridge (2000)
Olsder, G.J.: Phenomena in inverse Stackelberg games, part 2: Dynamic problems. J. Optim. Theory Optim. (2009). doi:10.1007/s10957-009-9572-x
van Eck, T.: A New Balance for the Energy Sector. Industrielinqs Pers en Platform, Amsterdam (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Y.-C. Ho.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Olsder, G.J. Phenomena in Inverse Stackelberg Games, Part 1: Static Problems. J Optim Theory Appl 143, 589–600 (2009). https://doi.org/10.1007/s10957-009-9573-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-009-9573-9