On the selection of leader in Stackelberg games with parameter uncertainty

Abstract

In leader-follower Stackelberg games, the leader determines and announces its strategy first by anticipating the follower’s reaction function, and the follower determines its strategy as a best response to the leader’s strategy. Thus, there is a perceived advantage in assuming the role of leader in a Stackelberg game. When the roles of the players are not determined a priori, both players must mutually agree on the selection of the leader. Such an agreement is possible only if the players realise that they are both better off with the agreed selection of leader as compared to when the other player is selected as leader. In games with parameter uncertainty, the availability of this option depends on the parameter space over which the game is defined. In this paper, we describe the partitioning of the parameter space to characterise when a Stackelberg solution based on an agreed leader selection exists and when it does not. The resulting partition can then be used to determine the probability of occurrence of all possible games where agreement can and cannot be reached. We illustrate the results using two examples.

KEYWORDS:

• Game theory
• Stackelberg games
• leader-follower
• selection of Stackelberg leader

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The preference can be either based on a cardinal ranking of the choices available to each player according to an objective function or on an ordinal ranking of the choices based on each players’ subjective preferences (Cruz & Simaan, 2000).

Additional information

Notes on contributors

Raaed S. Al-Azzawi

Raaed S. Al-Azzawi is a faculty member in Control and Systems Engineering department at University of Technology in Baghdad, Iraq. He received his B.Sc. degree in Control and Systems Engineering and his M.Sc. degree in Mechatronics Engineering from the University of Technology Baghdad, Iraq, in 2002 and 2007 respectively. He is currently a Ph.D. candidate in Electrical Engineering at the University of Central Florida, Orlando, USA. His research interests include Cooperative/Non-cooperative Game Theory, Control, Optimal Control, Optimization, Robotics and Automation.

Marwan A. Simaan

Marwan A. Simaan is the Florida 21st Century Chair and Distinguished Professor of EE and CS at the University of Central Florida. He served on the EE faculty at the University of Pittsburgh from 1976 to 2008. He received his Ph.D. in EE from the University of Illinois at Urbana Champaign in 1972. His research covers a wide range of topics in game theory, control, optimization, and signal processing and has published extensively in these areas. He is a member of US National Academy of Engineering (NAE), a Life Fellow of the IEEE and ASEE, and a Fellow of AAAS, AIMBE and NAI.