Endogenous Stackelberg Leadership

Damme, Eric van; Hurkens, Sjaak

doi:10.1006/game.1998.0687

Cited by 161 publications

(72 citation statements)

References 11 publications

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“…These risk dominance relationships play also an important role in evolutionary game theory. The linear tracing procedure is also used in other theories of equilibrium selection that are usually closely related to the ideas of Harsanyi and Selten (198ti) and that are applied to several interesting economic models, see for instance , and van Damme and Hurkens (1996).…”

Section: Introductionmentioning

confidence: 99%

Two simple proofs of the feasibility of the linear tracing procedure

Herings

2000

Economic Theory

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They show by means of heavy mathematical machinery that the so-called logarithmic tracing procedure selects a unique Nash equilibrium for every game. Using that result it can be shown by means of a straightforward lunrt argument that the linear tracing procedure is feasible. In this paper we give two direct., simple proofs of the feasibility of the linear tracing procedure. The first one utilizes a result that is related to Kakutani's fixed point theorem and that is an extension of 13rowdcr's fixed point theorem. The second proof shows that it is even possiblc to avoid the use of correspondences.Keywords: Non-cooperative game theory, tracing procedure, equilibrium selection, Brow- Herings has been made possible by a fellowship of the Royal Netherlands Acadetny of Arts and Sciences.

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Section: Introductionmentioning

confidence: 99%

Two simple proofs of the feasibility of the linear tracing procedure

Herings

2000

Economic Theory

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“…That is, the great fitness boost to the weaker player of moving first more than compensates for the direct fitness cost to the stronger player of moving second. In an interesting parallel, several economic models of duopoly competition predict that firms that are less cost-efficient, or have a higher variance in cost, will emerge as the endogenous leaders (Albaek 1990;Amir & Grilo 1999;van Damme & Hurkens 2004; but see van Damme & Hurkens 1999 for a counterexample). In these cases, stronger firms benefit from acting as follower, because this affords them reduced uncertainty about their opponent's costs and actions.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, however, economic theorists have focused on games in which both players prefer to adopt sequential roles rather than engage in simultaneous competition, and there is no conflict over who moves first. Such games are said to exhibit endogenous timing (ET) or 'endogenous leadership' because the roles of first and second mover emerge spontaneously as a consequence of each player attempting to maximize its rewards, rather than being assigned exogenously (Albaek 1990;Hamilton & Slutsky 1990;Amir & Grilo 1999;van Damme & Hurkens 1999.…”

Section: Introductionmentioning

confidence: 99%

Endogenous timing in competitive interactions among relatives

Cant

Shen

2005

Proc. R. Soc. B.

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Most evolutionary game theory models solve for equilibrium levels of some behaviour on the restrictive assumptions that players choose their actions simultaneously, and that a player cannot change its action after observing that of its opponent. An alternative framework is provided by sequential or 'Stackelberg' games in which one player commits to a 'first move' and the other has an opportunity to observe this move before choosing its response. Recent interest in the economic literature has focused on Stackelberg games which exhibit 'endogenous timing', i.e. games in which a leader and a follower arise spontaneously as a consequence of each player attempting to maximize its reward. Here, we provide the first demonstration of endogenous timing in an evolutionary context using a simple model of resource competition (the 'tugof-war' model). We show that whenever two related individuals compete for a share of communal resources, both do best to adopt distinct roles in a sequential game rather than engage in simultaneous competition. Somewhat counterintuitively, the stable solution is for the weaker individual to act as leader and commit to a first move, because this arrangement leads to a lower total effort invested in competition. Endogenous timing offers a new explanation for the spontaneous emergence of leaders and followers in social groups, and highlights the benefits of commitment in social interaction.

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“…+ the residual demand of firm i in all three games 4 , which 'almost' equals the demand of firm i if it is 'just' undercut by its opponent j. In particular, in the sequential games D r 1 (p) simply equals the demand firm 1 faces if firm 2 matches firm 1's price, whereas in any other case we have…”

Section: The Frameworkmentioning

confidence: 99%