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685

Abstract

We parameterize commitment in leader-follower games by letting the leader publicly choose her action set from a menu of options. We fully characterize for a large class of settings the set of equilibrium outcomes obtained when varying the degree of commitment that the leader has. We identify conditions under which giving more commitment power to the leader could end up making her worse off. Moreover, with partial commitment, the follower might obtain a larger payoff than the leader even in settings where the latter possesses a first-mover advantage under full commitment. We explore the implications of our analysis for oligopolies. JEL: C72, D43, D82 Keywords: commitment, sequential games, Stackelberg competition, robustness

1 Introduction

The Stackelberg model of commitment (von Stackelberg (1934)) has had a formidable impact on the development of industrial organization, political economy, international trade, and other areas of economic theory. A part of this impact is arguably explained by the sheer simplicity of the model, which, in turn, can be traced back to the leader’s ability to commit exactly to the action of her choice. Yet this “full-commitment” assumption of the Stackelberg model lacks realism when, as often in applications, small adjustments to the leader’s initial

∗OsloMet, jacopo.bizzotto@oslomet.no. †University of Nottingham and CEPR, toomas@hinnosaar.net. ‡University of Nottingham, <adrien.vigier@nottingham.ac.uk>.

Abstract We parameterize commitment in leader-follower games by letting the leader publicly choose her action set from a menu of options. We fully characterize for a large class of settings the set of equilibrium outcomes obtained when varying the degree of commitment that the leader has. We identify conditions under which giving more commitment power to the leader could end up making her worse off. Moreover, with partial commitment, the follower might obtain a larger payoff than the leader even in settings where the latter possesses a first-mover advantage under full commitment. We explore the implications of our analysis for oligopolies. JEL: C72, D43, D82 Keywords: commitment, sequential games, Stackelberg competition, robustness 1 Introduction The Stackelberg model of commitment (von Stackelberg (1934)) has had a formidable impact on the development of industrial organization, political economy, international trade, and other areas of economic theory. A part of this impact is arguably explained by the sheer simplicity of the model, which, in turn, can be traced back to the leader’s ability to commit exactly to the action of her choice. Yet this “full-commitment” assumption of the Stackelberg model lacks realism when, as often in applications, small adjustments to the leader’s initial ∗OsloMet, jacopo.bizzotto@oslomet.no. †University of Nottingham and CEPR, toomas@hinnosaar.net. ‡University of Nottingham, adrien.vigier@nottingham.ac.uk.

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