Potential, value, and coalition formation

Laruelle, Annick; Valenciano, Federico

doi:10.1007/s11750-007-0035-y

Cited by 6 publications

(6 citation statements)

References 18 publications

(49 reference statements)

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“…We thus depart from most of the previous literature in two respects: first, similar to Laruelle and Valenciano (2008a), we explicitly consider probabilistic games (N , v, P) where (N , v) is a standard TU game and P is a probability distribution on N 's power set 2 N . Second, we introduce a new value that reflects the difference between two conditional expectations.…”

Section: Unfortunately the Expectation E P I [V(s ∪ I) − V(s)]mentioning

confidence: 99%

“…Knowing this might imply that j cannot (or must) be amongst the members of the coalition. This may have ramifications 9 Laruelle and Valenciano (2008a) refer to + i (N , v, P) as player i's "interim expected marginal contribution" and identify its relations with different classes of probabilistic values. 10 Note that the respective distributions P which need to be assumed in order to obtain the Shapley value as a conditional expected marginal contribution in (16) and (17) differ.…”

Section: The Prediction Valuementioning

confidence: 99%

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The prediction value

Koster¹,

Kurz²,

Lindner³

et al. 2016

Soc Choice Welf

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We introduce the prediction value (PV) of player i as the difference between the conditional expectations of v(S) when i cooperates or not in a probabilistic TU game. The latter combines a standard TU game and a probability distribution over the set of coalitions. The PV reflects the importance of information about a given player's behavior for predicting, e.g., committee decisions that are subject to opinion interdependencies. The PV is characterized by anonymity, linearity, a consistency requirement and two normalization conditions. Every multinomial probabilistic value, hence every binomial semivalue, coincides with the PV for a particular family of probability distributions. So the PV can be regarded as a power index in specific cases. Conversely, some semivalues-including the Banzhaf but not the Shapley value-can be interpreted in terms of informational importance.

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Section: Unfortunately the Expectation E P I [V(s ∪ I) − V(s)]mentioning

confidence: 99%

Section: The Prediction Valuementioning

confidence: 99%

The prediction value

Koster¹,

Kurz²,

Lindner³

et al. 2016

Soc Choice Welf

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“…A semivalue on G is a function that for each n restricts to a semivalue on X n . In [3] it was shown that in addition to the explicit form (5), the recursion…”

Section: Individual Measuresmentioning

confidence: 99%

“…Coalition formation. Consider the following model of coalition formation [5]. We assume that each possible coalition (subset S of X) forms with probability p(S), and that only one coalition S will form.…”

Section: Interpretation Of the Measuresmentioning

confidence: 99%

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Power measures derived from the sequential query process

Pritchard

Reyhani

2013

Mathematical Social Sciences

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We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual power in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. In particular, the individual measures include all weighted semivalues. We single out the simplest measure in our family for more investigation, as it is new to the literature as far as we know. Although it is very different from the Shapley value, it is closely related in several ways, and is the natural analogue of the Shapley value under a nonstandard, but natural, definition of simple game. We illustrate this new measure by calculating its values on some standard examples.Comment: 13 pages, to appear in Mathematical Social Science

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