Coalition formation in general apex games under monotonic power indices

Karos, Dominik

doi:10.1016/j.geb.2014.05.011

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…This has been elaborated for instance in Karos (2014). The next theorem characterizes the class of simple games that have the property described in Lemma 2.…”

Section: Lemma 2 Let ϕ Be a Monotonic Power Index And Let V Be A Simpmentioning

confidence: 99%

A note on monotonic power indices, smaller coalitions, and new members

Karos

2016

Theory Decis

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Brams' paradox of new members and Shenoy's paradox of smaller coalitions are, in a sense, equivalent. They are both implied by the monotonicity of a power index: while the first is exhibited on every simple game that is not strong, the latter can be observed on every simple game in which players are not almost symmetric. For the Shapley-Shubik index, this symmetry condition is not only necessary but also sufficient to avoid the paradox of smaller coalitions.

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“…This has been elaborated for instance in Karos (2014). The next theorem characterizes the class of simple games that have the property described in Lemma 2.…”

Section: Lemma 2 Let ϕ Be a Monotonic Power Index And Let V Be A Simpmentioning

confidence: 99%

A note on monotonic power indices, smaller coalitions, and new members

Karos

2016

Theory Decis

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“…We assume that W is such that, if S is winning, N \S is not winning. Furthermore, if S ∈ W , then T ∈ W for all 6 A recent paper by Karos [12] analyses coalition formation in apex games using core stability under a fixed pay-off division rule as a solution concept. 7 The seat distribution in the German Bundestag often corresponds to an apex game.…”

Section: The Modelmentioning

confidence: 99%

“…A proposal to form a protocoalition S with k∈S y k < 1 is always accepted, because the expected pay-off from accepting the proposal, y j + θ S j (1 − k∈S y k ), is strictly greater than the expected pay-off from rejecting it, y j , for all j ∈ N . 12 Consider the situation of i as the formateur. There is always a coalition that i can propose with 1 > k∈S y k .…”

Section: The Equilibrium Of the Gamementioning

confidence: 99%

“…This is because N \{j} is winning for all j; thus, player i can propose any N \{j} where j is such that y j > 0. The only case in which this would not be possible is if y i = 1, but clearly, this cannot happen in equilibrium, 12 Notice that equilibria in which several responders reject just because S is going to be rejected anyhow are ruled out by the fact that the players in S respond sequentially.…”

Section: The Equilibrium Of the Gamementioning

confidence: 99%

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A Model of Protocoalition Bargaining with Breakdown Probability

Montero

2015

Games

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This paper analyses a model of legislative bargaining in which parties form tentative coalitions (protocoalitions) before deciding on the allocation of a resource. Protocoalitions may fail to reach an agreement, in which case they may be dissolved (breakdown) and a new protocoalition may form. We show that agreement is immediate in equilibrium, and the proposer advantage disappears as the breakdown probability goes to zero. We then turn to the special case of apex games and explore the consequences of varying the probabilities that govern the selection of formateurs and proposers. Letting the breakdown probability go to zero, most of the probabilities considered lead to the same ex post pay-off division. Ex ante expected pay-offs may follow a counterintuitive pattern: as the bargaining power of weak players within a protocoalition increases, the weak players may expect a lower pay-off ex ante.

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“…The special case of ordinal games that are derived from payoff configurations has first been considered by Shenoy (1979) and more recently by Dimitrov and Haake (2008) and Karos (2014). But neither of the authors presented a necessary and sufficient condition for the existence of core stable partitions.…”

Section: Further Related Literaturementioning

confidence: 99%

Stable partitions for games with non-transferable utility and externalities

Karos

2015

Int J Game Theory

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I propose a model of coalitional bargaining with claims in order to find solutions for games with non-transferable utility and externalities. I show that, for each such game, payoff configurations exist which will not be renegotiated. In the ordinal game derived from these payoff configurations, a core stable partition can be found, i.e. a partition in which no group of players has an incentive to jointly change their coalitions.

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Coalition formation in general apex games under monotonic power indices

Cited by 6 publications

References 15 publications

A note on monotonic power indices, smaller coalitions, and new members

A note on monotonic power indices, smaller coalitions, and new members

A Model of Protocoalition Bargaining with Breakdown Probability

Stable partitions for games with non-transferable utility and externalities

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