A Comment on Dehez and Tellone, “Data games: sharing public goods with exclusion”

• Author: Anna Khmelnitskaya,Theo Driessen
• Date: 01 February 2017
• Published date: 01 February 2017
• DOI: http://doi.org/10.1111/jpet.12228

Received: 20 September 2013 Accepted: 19 March 2015

DOI: 10.1111/jpet.12228

ARTICLE

A Comment on Dehez and Tellone,

“Data games: sharing public goods with exclusion”

Anna Khmelnitskaya1Theo Driessen2

1Saint-PetersburgState University

2Universityof Twente

Theauthors would like to thank the referees and

editorsfor their helpful comments and sugges-

tions.

This comment shows that the data cost game introduced in Dehez

and Tellone (Journal of Public Economic Theory,2013) coincides with

the nonadditive component of the library cost game studied in

Driessen, Khmelnitskaya, and Sales (TOP, 2012) where the core,

nucleolus, and Shapley value were also investigated.

Dehez and Tellone(2013) introduced and studied data games, which provide a cooperative game-theoretic model of

data sharing. We show that a data game coincides with the nonadditive component of a library game, introduced in

Sales (2002) and studied in Driessen, Khmelnitskaya, and Sales (2012). In Driessen et al. (2012), it is proved that the

nonadditive component of a library game belongs to the class of 1-concave games introduced in Driessen and Tijs

(1983) and Driessen (1985), and as a corollary to that and known properties of the solutions of 1-concave games it

is shown that the core of this game is always nonempty and has a regular simplex structure and that the nucleolus is

linear and coincides with the 𝜏-value and the barycenter of the core. Due to Proposition 1 below, these results can be

extendedstraightforwardly to the data games as well, which covers the results of sections 4 and 5 in Dehez and Tellone

(2013).

Library games model situations in which a university library consortium has to assign prices to its members to pay

for a joint subscription for electronic scientific journals. A library game is determined by a finite set Nof nuniversity

libraries (players),a finite set Gof melectronic journals (goods), a demand matrix D=(dij)i∈N

j∈G

, where dij ≥0 is the num-

ber of paper copies of the jth journal previously demanded by the ith university,a cost cj≥0percopyofjthjournal in

the prior demand, and a discount parameter 𝛼∈[0,1]forjournals that were not previously demanded. The character-

istic function of the library cost game is given by

cl(S)=

j∈G

i∈S

dij cj+

j∈G

i∈Sdij=0

𝛼cj,for all S⊆N.

The characteristic function clis a sum of an additive function and multiplied by𝛼nonadditive function ̄

clgiven by

̄

cl(S)= 

j∈G

i∈Sdij=0

cj,for all S⊆N.

Observe that if for everyj∈Gthere isi∈Nwith dij >0, then ̄

cl(N)=0.

A data-sharing game is determined by a finite set Nof nplayers, a finite set Gof data of mtypes (public goods), a

collection of sets Gi⊆G,i∈N, that specify the types of data held by each player,and a vector of costs cjof reproducing

Journal of Public Economic Theory 2017; 19: 264–265 wileyonlinelibrary.com/journal/jpet c

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