M. Álvarez-Mozos a, F. Ferreira b, J.M. Alonso-Meijide c & A.A. Pinto d a Department of Statistics and Operations Research, Faculty of
|
|
- Caroline Hicks
- 5 years ago
- Views:
Transcription
1 Ths artcle was downloaded by: [b-on: Bbloteca do conhecmento onlne UP] On: 29 May 205, At: 02:46 Publsher: Taylor & Francs Informa Ltd Regstered n England and Wales Regstered Number: Regstered offce: Mortmer House, 37-4 Mortmer Street, London WT 3JH, UK Clck for updates Optmzaton: A Journal of Mathematcal Programmng and Operatons Research Publcaton detals, ncludng nstructons for authors and subscrpton nformaton: Characterzatons of power ndces based on null player free wnnng coaltons M. Álvarez-Mozos a, F. Ferrera b, J.M. Alonso-Mejde c & A.A. Pnto d a Department of Statstcs and Operatons Research, Faculty of Mathematcs, Unversty of Santago de Compostela, La Coruña, Span. b ESEIG, Polytechnc Insttute of Porto, Porto, Portugal. c Department of Statstcs and Operatons Research, Faculty of Scences of Lugo, Unversty of Santago de Compostela, La Coruña, Span. d LIAAD-INESC TEC, Departament of Mathematcs, Faculty of Scences, Unversty of Porto, Porto, Portugal. Publshed onlne: 22 Feb 203. To cte ths artcle: M. Álvarez-Mozos, F. Ferrera, J.M. Alonso-Mejde & A.A. Pnto (205) Characterzatons of power ndces based on null player free wnnng coaltons, Optmzaton: A Journal of Mathematcal Programmng and Operatons Research, 64:3, , DOI: 0.080/ To lnk to ths artcle: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francs makes every effort to ensure the accuracy of all the nformaton (the Content ) contaned n the publcatons on our platform. However, Taylor & Francs, our agents, and our lcensors make no representatons or warrantes whatsoever as to the accuracy, completeness, or sutablty for any purpose of the Content. Any opnons and vews expressed n ths publcaton are the opnons and vews of the authors, and are not the vews of or endorsed by Taylor & Francs. The accuracy of the Content should not be reled upon and should be ndependently verfed wth prmary sources of nformaton. Taylor and Francs shall not be lable for any losses, actons, clams, proceedngs, demands, costs, expenses, damages, and other labltes whatsoever or
2 Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 howsoever caused arsng drectly or ndrectly n connecton wth, n relaton to or arsng out of the use of the Content. Ths artcle may be used for research, teachng, and prvate study purposes. Any substantal or systematc reproducton, redstrbuton, resellng, loan, sub-lcensng, systematc supply, or dstrbuton n any form to anyone s expressly forbdden. Terms & Condtons of access and use can be found at
3 Optmzaton, 205 Vol. 64, No. 3, , Characterzatons of power ndces based on null player free wnnng coaltons M. Álvarez-Mozos a, F. Ferrera b, J.M. Alonso-Mejde c and A.A. Pnto d Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 a Department of Statstcs and Operatons Research, Faculty of Mathematcs, Unversty of Santago de Compostela, La Coruña, Span; b ESEIG, Polytechnc Insttute of Porto, Porto, Portugal; c Department of Statstcs and Operatons Research, Faculty of Scences of Lugo, Unversty of Santago de Compostela, La Coruña, Span; d LIAAD-INESC TEC, Departament of Mathematcs, Faculty of Scences, Unversty of Porto, Porto, Portugal (Receved 9 May 202; fnal verson receved 3 December 202) In ths paper, we characterze two power ndces ntroduced n [] usng two dfferent modfcatons of the monotoncty property frst stated by [2]. The sets of propertes are easly comparable among them and wth prevous characterzatons of other power ndces. Keywords: smple game; power ndex; characterzaton. Introducton In the last decades, the measurement of power n decson-makng bodes such as the European Unon Councl of Mnsters or the Internatonal Monetary Fund has been a man topc n poltcal scences and many work has been done n order to attan an approprate measure. However, there s stll a debate even on the defnton of power. Most of the tmes, the power s understood as the ablty of an agent to nfluence the outcome. But, even when the defnton of power s agreed, the choce of an appropate rule to represent t s stll an open queston. Among the most studed power ndces n the lterature, one can fnd the Shapley Shubk ndex [3], the Banzhaf ndex [4], the Deegan Packel ndex [5] and the Publc Good ndex [6]. All the above power ndces are evaluatons of an agent s relatve sgnfcance to each of the coaltons that mght be formed. In ths work, we wll frst of all revew some of the man results related to these four power ndces. Some of the aforementoned power ndces restrct ther attenton to some knds of coaltons that are partcularly mportant. Indeed, the Deegan Packel and Publc Good ndces only take nto account the so-called mnmal wnnng coaltons. A wnnng coalton, that s, a group of agents that can pass a bll on ther own, s a mnmal wnnng coalton when the removal of any of ts members would prevent the coalton from passng the bll. More recently, other nterestng power ndces have been ntroduced. The Publc help ndex [7] s based on the set of all wnnng coaltons, more precsely, the power of each agent s proportonal to the number of wnnng coaltons n whch he partcpates. The Shft power ndex [8] consders only a subset of the Correspondng author. Emal: mkel.alvarez@ub.edu 203 Taylor & Francs
4 676 M. Álvarez-Mozos et al. Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 mnmal wnnng coaltons, the so-called mnmal wnnng coaltons wthout any surplus, n a sense, these coaltons are the most effcent mnmal wnnng coaltons. In ths paper, we take up agan the two power ndces ntroduced n [], namely f np and g np, and study ther propertes. These power ndces are also based on a partcularly mportant set of coaltons, specfcally on the wnnng coaltons that do not contan null players. A null player s a player whose partcpaton n any coalton does not change the stuaton,.e. the coalton contnues beng ether wnnng or loosng. Such set of coaltons contans the set of mnmal wnnng coaltons and s contaned n the set of wnnng coaltons. A frst consequence of ths fact s that f np and g np do not consder mnmal wnnng coaltons as the only source of power. Ths s the case n many real stuatons for nstance, many tmes the adopted decsons are more stable the greater the wnnng coalton supportng t s. Hence, the nformaton set on whch the new power ndces are based s wder than the nformaton set on whch the Deegan Packel and Publc Good ndces are based. The modellng of decson-makng bodes and votng procedures has been tackled usng smple games. The axomatc characterzaton of power ndces s a man topc n the feld for at least two reasons. Frst, characterzng a rule by means of a set of propertes may be more appealng than just gvng ts explct defnton. Second, decdng on whether to use a rule or another n a partcular stuaton may be done more easly takng nto account the propertes that each rule satsfes. In fact, many power ndces have shown to have dfferent sets of propertes that determne them unquely. In ths document, we present parallel characterzatons of the two power ndces ntroduced n [] n lne wth the characterzaton of the Deegan Packel power ndex by [9] and the Publc Good ndex by [0]. In ths way, the comparson among these four power ndces s much easer snce the characterzatons only dffer n one property. Moreover, the property n each of the characterzatons s a type of monotoncty n the sense that t descrbes the way n whch the payoff of an agent changes when hs poston n the stuaton s mproved. The rest of the paper s organzed as follows. In Secton 2, we announce notaton and present some prelmnary defntons and results such as the defntons and characterzatons of the Shapley Shubk and Banzhaf power ndces. In Secton 3, the Deegan Packel and Publc Good power ndces are presented together wth a par of characterzatons of each one of them. In Secton 4, the man results of the paper are presented, that s, the new power ndces f np and g np are characterzed by means of smlar propertes to the ones used n the characterzatons presented n Secton 3. Fnally, Secton 5 dscusses some concludng remarks. 2. Prelmnares A cooperatve transferable utlty game (just game from now on) s a par (N,v), where N ={,...,n} s the (fnte) set of players and v : 2 N R s the characterstc functon of the game, whch satsfes v( ) = 0. In general, we nterpret v(s) as the beneft that S can obtan by ts own,.e. ndependent to the decsons of players n N \ S. To avod cumbersome notaton, braces wll be omtted whenever t does not lead to confuson; for example, we wll wrte v(s ) or v(s \ ) nstead of v(s {}) or v(s \{}). A player N s a null player n a game (N,v)when hs margnal contrbuton to every coalton s zero,.e. when for every S N \, v(s ) v(s) = 0. Two players, j N are symmetrc n a game (N,v)f ther margnal contrbutons to every coalton concde,.e.
5 Optmzaton 677 f for every S N \{, j}, v(s ) = v(s j). A game, (N,v), s called monotone f for every S, T 2 N wth S T, v(s) v(t ). Defnton 2. A smple game s a monotone game such that the worth of every coalton s ether 0 or and the worth of the grand coalton s. Formally, (N,v)s a smple game f and only f: Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 (N,v)s monotone, for every S 2 N, v(s) {0, }, and v(n) =. The class of all smple games s denoted by SG. In a smple game (N,v) SG, a coalton S N s wnnng f v(s) =, and losng f v(s) = 0. W (v) denotes the set of wnnng coaltons of the smple game (N,v) and, gven N, W (v) denotes the subset of W (v) formed by the coaltons contanng player,.e. W (v) ={S W (v) : S}. Gven a smple game (N,v) SG, a swng for a player N s a coalton S 2 N such that S, S s a wnnng coalton and S \ s a losng coalton. The set of all swngs for player N s denoted by η (v). Any smple game (N,v) SG may be descrbed by ts set of wnnng coaltons W (v). Gven a player set N and an arbtrary famly of coaltons W 2 N, the par (N, W ) determnes a smple game f: / W, N W and for every S T N,fS W, then T W. A wnnng coalton S W (v) s a mnmal wnnng coalton f every proper subset of S s a losng coalton; that s, S s a mnmal wnnng coalton n (N,v) f v(s) = and v(t ) = 0 for any T S. W m (v) denotes the set of mnmal wnnng coaltons of the game (N,v)and W m (v) the subset of W m (v) formed by coaltons contanng player,.e. W m (v) ={S W m (v) : S}. Smlar to the case of wnnng coaltons, a smple game may also be defned by ts set of mnmal wnnng coaltons W m (v). Gven a player set N and an arbtrary famly of coaltons W m 2 N, the par (N, W m ) determnes a smple game f: / W m, W m = and for every S, T W m, S T and T S. It s easy to obtan the set of mnmal wnnng coaltons from the set of wnnng coaltons and vce versa,.e. W m (v) ={S W (v) : T S, T / W (v)}, W (v) ={S 2 N : T S, T W m (v)}. By a power ndex we mean a map f that assgns a vector f(n,v) R N to every smple game (N,v) SG. In the defntons below, two of the most popular power ndces are presented.
6 678 M. Álvarez-Mozos et al. Defnton 2.2 The Shapley Shubk power ndex [3], SS, s the power ndex defned for every (N,v) SG and N by SS (N,v)= s!(n s )!, n! where n = N and s = S. S η (v) Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 Defnton 2.3 The Penrose Banzhaf Coleman power ndex [4,,2], PBC, s the power ndex defned for every (N,v) SG and N by PBC (N,v)= η (v) 2 n. In order to present characterzatons of SS and PBC formally, some propertes need to be presented. effa power ndex f satsfes effcency f for every (N,v) SG, f (N,v)=. N nppa power ndex f satsfes the null player property f for every (N,v) SG and each null player N n (N,v), f (N,v)= 0. sym A power ndex f satsfes symmetry f for every (N,v) SG and each par of symmetrc players, j N n (N, v), f (N,v)= f j (N,v). trp A power ndex f satsfes the transfer property f for every par of smple games (N,v),(N,w) SG, f(n,v)+ f(n,w)= f(n,v w) + f(n,v w), where (N,v w), (N,v w) SG are defned for all S N by (v w)(s) = max{v(s), w(s)} and (v w)(s) = mn{v(s), w(s)}. tpp A power ndex f satsfes the total power property f for every (N,v) SG, N f (N,v)= η (v) 2 n. N Next, n lne wth the characterzatons of the Shapley and Banzhaf values by [3], parallel characterzatons of SS and PBC are presented. Theorem 2.4 [4] The Shapley Shubk power ndex, SS, s the unque power ndex satsfyng eff, sym, npp and trp. Theorem 2.5 [5] The Penrose Banzhaf Coleman power ndex, PBC, s the unque power ndex satsfyng tpp, sym, npp and trp.
7 Optmzaton 679 The man dfference between the Shapley value and the Banzhaf value s that the former s effcent whle the later satsfes the total power property. The characterzatons above show that ths dfference s transferred when smple games are consdered. Hence, the man dfference between SS and PBC s that the former s effcent whle the latter satsfes the total power property. Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May Power ndces based on mnmal wnnng coaltons The Deegan Packel power ndex [5] s based on the dea that when t comes to measure the power of an agent, t should only be consdered hs partcpaton n mnmal wnnng coaltons. Moreover, t assumes the followng three facts: Only mnmal wnnng coaltons wll emerge vctorous. Each mnmal wnnng coalton has an equal probablty of formng. Players n mnmal wnnng coaltons dvde the spols equally. The condtons above seem reasonable n many stuatons. The frst condton s a consequence of havng ratonal players n the sense that they seek for maxmzng ther power and hence, they wll only partcpate n mnmal wnnng coaltons. In other words, f a wnnng coalton s not a mnmal wnnng coalton, t means that there are players whose partcpaton n the coalton s not needed. Hence, the remanng players wll prefer to form the mnmal coalton contaned on the wnnng coalton snce there wll be less people to share the spols wth. The second condton states that all mnmal wnnng coaltons are equally lkely, whch s very reasonable once the frst condton s accepted. The last condton s a soldarty or equal treatment property. The requstes above lead to the followng defnton. Defnton 3. Gven a smple game (N,v) SG,the Deegan Packel power ndex [5], DP, s a vector n R N where each coordnate ( N) s defned as follows: DP (N,v)= W m (v) S W m (v) S. The DP power ndex s ntroduced n [5] together wth a characterzaton by means of four propertes. The characterzaton of SS presented before shares three of them, namely, eff, sym and npp. Indeed, DP concdes wth SSn the class of unanmty games. However, the DP power ndex does not satsfy trp. Instead, t satsfes the so-called DP-mergeablty property that s ntroduced next. Two smple games (N,v)and (N,w)are mergeable f for every par of mnmal wnnng coaltons S W m (v) and T W m (w), t holds that S T and T S. If two games (N,v) and (N,w) are mergeable, the mnmal wnnng coaltons n the maxmum game (N,v w) are precsely the unon of the mnmal wnnng coaltons n the two orgnal games (N,v)and (N,w). Hence, the mergeablty condton guarantees that W m (v w) = W m (v) + W m (w). Recall the defnton of a merged or maxmum game, (N,v w), gven for every S N by, (v w)(s) = max{v(s), w(s)}.
8 680 M. Álvarez-Mozos et al. Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 dp-mera power ndex f satsfes DP-mergeablty f for every par of mergeable smple games (N,v),(N,w) SG, f(n,v w) = W m (v) f(n,v)+ W m (w) f(n,w) W m. (v w) The property above states that the power n a merged game s a weghted mean of the power n the two component games. The weghts come from the number of mnmal wnnng coaltons n each component game, dvded by the number of mnmal wnnng coaltons n the merged game. Hence, t concdes wth trp n the sense that t assesses the power n a merged game n terms of the power n the two component games. At ths pont, the propertes needed to present the frst characterzaton of the Deegan Packel ndex have been ntroduced. Theorem 3.2 [5] The Deegan Packel ndex, DP, s the unque power ndex satsfyng eff, sym, npp and dp-mer. More recently, [9] proposed a dfferent characterzaton of the Deegan Packel ndex. Ths characterzaton s based on the so-called DP-mnmal monotoncty property whch s nspred by the strong monotoncty property ntroduced n [2] to characterze the Shapley value. The property s formally ntroduced next. dp-mm A power ndex f satsfes DP-mnmal monotoncty f for every par of smple games (N,v),(N,w) SG and every player N such that W m (v) W m (w), f (N,v) W m (v) f (N,w) W m (w). The dp-mm property states that f the mnmal wnnng coaltons that contan a player N are mnmal wnnng coaltons n another game, then the power of player n the former game tmes ts number of mnmal wnnng coaltons s never bgger than the power of the player n the latter game tmes ts number of mnmal wnnng coaltons. Hence, dp-mm descrbes the way n whch the power of an agent changes when hs poston n the smple game s mproved. The characterzaton of DP power ndex proposed n [9] replaces the dp-mer property by the dp-mm property. Theorem 3.3 [9] The Deegan Packel ndex, DP, s the unque power ndex satsfyng eff, sym, npp and dp-mm. In the scentfc lterature concernng power ndces, one can fnd another power ndex that takes only mnmal wnnng coaltons nto account. The so-called Publc Good ndex proposed n [6] consders that each player s power s proportonal to the amount of mnmal wnnng coaltons n whch he partcpates. Defnton 3.4 Gven a smple game (N,v) SG,thePublc Good ndex [6], PG, sa vector n R N where each coordnate ( N) s defned as follows: W m (v) PG (N,v)= j N W m j (v). The frst characterzaton of ths power ndex by means of a set of propertes s proposed n [6]. The characterzaton follows the sprt of the characterzaton of the DP ndex
9 Optmzaton 68 Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 presented n Theorem 3.2. Indeed, the property of dp-mer s replaced by the pg-mer whch s formally ntroduced below. pg-mer A power ndex f satsfes PG-mergeablty f for every par of mergeable smple games (N,v),(N,w) SG and every N, f (N,v w) = f (N,v) j N W m j (v) +f (N,w) j N W m j (w) j N W m. j (v w) Hence, pg-mer descrbes the power n the merged game as a weghted mean of the powers n the two component games as the dp-mer does. However, the weghts used dffer from the ones used n dp-mer. Next, the counterpart of Theorem 3.2 for the PG ndex s presented. Theorem 3.5 [6] The Publc Good ndex, PG, s the unque power ndex satsfyng eff, sym, npp and pg-mer. More recently, [0] proposed a dfferent characterzaton of the Publc Good ndex. Ths characterzaton s parallel to the one for the DP ndex presented n Theorem 3.3. It s based on the so-called PG-mnmal monotoncty property whch s smlar to the DP-mnmal monotoncty property stated above. The property s formally ntroduced next. pg-mm A power ndex f satsfes PG-mnmal monotoncty f for every par of smple games (N,v),(N,w) SG and every player N such that W m (v) W m (w), f (N,v) W m j (v) f (N,w) W m j (w). j N The pg-mm property keeps a close relaton wth the pg-mm property. Both propertes descrbe the relaton between the power of an agent n two dfferent smple games when the mnmal wnnng coaltons that contan the player n one game are mnmal wnnng coaltons n the other game. The dfference les on the scalars that multply the power n each of the smple games. Hence, usng pg-mm property, a counterpart of Theorem 3.3 s obtaned for the PG ndex. Theorem 3.6 [0] The Publc Good ndex, PG, s the unque power ndex satsfyng eff, sym, npp and pg-mm. The four characterzaton results presented n ths secton are summarzed n Table. 4. Two new power ndces based on null player free wnnng coaltons In Secton 2, thess and PBC power ndces are ntroduced. These ndces are based on the swngs of each player, that s, on the wnnng coaltons contanng the player that become loosng when the player leaves them. In Secton 3, power ndces based on mnmal wnnng coaltons are ntroduced, namely DP and PG. In ths secton, two new power ndces are ntroduced followng []. A wnnng coalton S W (v) s sad to be a null player free wnnng coalton f no null player s contaned on t, that s, f for every S there s T W (v) such that T \ / W (v). The set of null player free wnnng coaltons s denoted by W np (v). As before, for every j N
10 682 M. Álvarez-Mozos et al. Table. Parallel characterzatons of DP and PG. DP PG dp-mer pg-mer eff eff [5] sym sym [6] npp npp Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 dp-mm pg-mm eff eff [9] sym sym [0] npp npp player N, W np (v) denotes the set of null player free wnnng coaltons contanng player,.e. W np (v) ={S W np (v) : S}. Note that for every (N,v) SG,the followng relaton holds, W m (v) W np (v) W (v). Thus, the set of null player free wnnng coaltons can be seen ether as a refnement of the set of wnnng coaltons or as an extenson of the set of mnmal wnnng coaltons. Note that a smple game s determned by ts set of null player free wnnng coaltons, W np (v). The clam before holds snce the set of wnnng coaltons can be easly obtaned from W np (v),.e. W (v) ={T 2 N : there s S W np (v) such that S T }. It s also easy to obtan the set of mnmal wnnng coaltons gven the set of null player free wnnng coaltons and vce versa, as follows, W m (v) ={T W np (v) : for every S T, S / W np (v)}. () W np (v) ={S U : there s T W m (v) such that T S} (2) U W m (v) In [] two new power ndces based on null player free wnnng coaltons are ntroduced. In the paper, the new power ndces are denoted by f and g. However, the notaton s slghtly modfed here for the sake of clarty. The new power ndces consder that only null player free wnnng coaltons should be taken nto account when t comes to measurng the power. In other words, these power ndces are based on the nformaton contaned on the set W np. In ths way, null players, whch by defnton do not partcpate n coaltons of W np,are assgned no power. The formal defntons are ntroduced next. Defnton 4. The f np power ndex s defned for every (N,v) SG and N by, f np (N,v)= W np (v) S W np (v) S.
11 Optmzaton 683 Defnton 4.2 The g np power ndex s defned for every (N,v) SG and N by, g np (N,v)= j N W np (v) W np j (v). Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 The dea behnd the power ndces defned above s n lne wth the defntons of the Deegan Packel and the Publc Good ndces (see Defntons 3. and 3.4). The only dfference s that f np and g np consder all wnnng coaltons that do not contan null players nstead of only consderng mnmal wnnng coaltons. A drect consequence of ths fact s that non-null players whch do not partcpate n many mnmal wnnng coaltons are allocated more power. Consequently, f np consders that all null player free wnnng coaltons are equally lkely and that the players n a null player free wnnng coalton dvde the spols equally. g np assumes that the power of each player s proportonal to the number of null player free wnnng coaltons n whch he partcpates. The Shft power ndex ntroduced n [8] s smlar to the Publc Good ndex and the g np power ndex; however, t s based on a set of coaltons whch s contaned on the set of mnmal wnnng coaltons. A set of few ndependent propertes s a convenent tool to descrbe a power ndex and eases the comparson among dfferent power ndces. In order to characterze f np and g np, the followng monotoncty propertes are ntroduced. f np -mm A power ndex f satsfes f np -mnmal monotoncty f for every par of smple games (N,v),(N,w) SG and every player N such that W m (v) W m (w), f (N,v) W np (v) f (N,w) W np (w). g np -mm A power ndex f, satsfes g np -mnmal monotoncty f for every par of smple games (N,v),(N,w) SG and every player N such that W m (v) W m (w), f (N,v) j N W np j (v) f (N,w) j N W np j (w). The f np -mm and g np -mm propertes are based on the strong monotoncty property used n [2] to characterze the Shapley value. Indeed, both descrbe the behavour of a value n two smple games, (N,v)and (N,w), n whch there s a player N such that W (v) W (w), n other words, v(s ) v(s) w(s ) w(s) for every S N \. The dfference les on the relaton between the power of player n both games. The strong monotoncty property states that player s power n (N,w) s at least as bg as hs power n (N,v). Instead, f np -mm and g np -mm propertes state that the relaton holds after multplyng the payoffs by the denomnator of the defntons of f np and g np respectvely. The followng results show that f np and g np are characterzed wth a close set of propertes of the ones used n Theorems 3.3 and 3.6 to characterze DP and PG, respectvely. Theorem 4.3 and f np -mm. The power ndex f np s the unque power ndex that satsfes eff, npp, sym Proof () Exstence. From Defnton 4., t straghtforward to check that f np satsfes eff, npp and sym. Forf np -mm property, note that by Equaton (2), W m (v) W m (w)
12 684 M. Álvarez-Mozos et al. mples W np and hence, (v) W np (w). Then, f np (N,w)= = W np (w) W np (w) S W np (w) S W np (v) S S + W np (w) S W np (w)\w np (v) S, Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 f np (N,w) W np (w) = S W np (v) S + S W np (w)\w np (v) S S W np (v) = f np S (N,v) W np (v). (2) Unqueness. The unqueness s proved by nducton on the number of mnmal wnnng coaltons. If W m (v) =, then v = u S where W m (v) ={S}. If a power ndex, f satsfes eff, npp and sym, we have, f (N,v)= { S f S 0 f / S. Hence, the unqueness holds when W m (v) =. Next, assume that a power ndex satsfyng the propertes s unque for every (N,v) SG wth less than m > mnmal wnnng coaltons,.e., f s unque for every (N,v) SG such that W m (v) < m.let(n,v) SG wth W m (v) = {S,...,S m }. Take T = m k= S k. Then, for each / T let us defne (N,w) SG by W m (w) = W m (v). Then, snce W m (v) = W m (w), applyng f np -mm twce, f (N,v) W m (v) =f (N,w) W m (w). Fnally, note that W m (w) < m and hence, by nducton, the rght hand sde of the equalty above s unque. It remans to prove the unqueness for T.Bysym, there s a constant c R such that for every T, f (N,v) = c. Moreover, by eff and the unqueness for any / T, c s unque whch concludes the proof. Theorem 4.4 and g np -mm. The power ndex g np s the unque power ndex that satsfes eff, npp, sym, Proof The proof follows mmedately from a reasonng smlar to the one used n the Proof of Theorem 4.3. Hence, the two Theorems above show that the dfferences between f np and g np are restrcted to a monotoncty property. Moreover, the only dfference among SS, DP, PG, f np and g np s the type of monotoncty satsfed by each power ndex. Fnally, the parallel characterzatons of f np and g np are depcted n Table Concluson In a smple game, a member s consdered crtcal for a wnnng coalton when hs elmnaton from the coalton turns t nto a losng one. In a mnmal wnnng coalton, every
13 Optmzaton 685 Table 2. Parallel characterzatons of f np and g np. f np f np -mm eff sym npp g np g np -mm eff sym npp Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 member of the coalton s crtcal. The Deegan Packel and Publc Good ndces are based on mnmal wnnng coaltons. A player s null when t s not crtcal for any wnnng coalton. However, n most of the cases, a null player partcpates n many wnnng coaltons. For ths reason, the new ndces, f np and g np, are based on wnnng coaltons that do not contan null players. The characterzatons provded n ths paper hghlght the fact that the new power ndces share most of ther defnng features wth other well-known ndces. The project ntated wth ths paper s not closed and we have related future work n mnd. The two man lnes of ths future work are to extend these ndces to more complex models and to propose tools to compute these ndces. One of the models developed for representng decson-makng bodes more adequately s the one of smple games wth a coalton structure. In [7,9] extensons of the Deegan Packel and Publc Good ndces are proposed and characterzed for smple games wth a coalton structure. The ndces characterzed n ths paper can be extended to the model of smple games wth a coalton structure. Moreover, we also want to consder more complex models lke games wth graph-restrcted communcaton or games wth levels structure of cooperaton. Although the mathematcal expresson of the ndces characterzed n ths paper s smple, one of the dffcultes s ther computaton for games wth a bg number of players. Two tools have been used to compute power ndces n large games: the multlnear extensons [20,2] and [0] and the generatng functons [22]. One of the deas that we want to develop n the near future s to fnd methods whch allow to compute the proposed ndces by means of these two tools. Acknowledgements A. A. Pnto acknowledges the fnancal support of LIAAD INESC TEC through program PEst, USP-UP project, Faculty of Scences, Unversty of Porto, Calouste Gulbenkan Foundaton, FEDER, POCI 200 and COMPETE Programmes, PTDC/MAT/207/200 and Fundação para a Cênca e a Tecnologa (FCT). J. M. Alonso-Mejde and M. Álvarez-Mozos acknowledge the fnancal support of the Spansh Mnstry of Economy and Compettveness through Projects ECO C02-02/ECO and MTM C03-03 and of Xunta de Galca through Project INCITE PR. The authors would also lke to thank the comments and suggestons of two anonymous referees. References [] Alonso-Mejde JM, Ferrera F, Álvarez-Mozos M, Pnto AA. Two new power ndces based on wnnng coaltons. J. Dffer. Equ. Appl. 20;7:
14 686 M. Álvarez-Mozos et al. Downloaded by [b-on: Bbloteca do conhecmento onlne UP] at 02:46 29 May 205 [2] Young HP. Monotonc solutons of cooperatve games. Internat. J. Game Theory. 985;4: [3] Shapley LS, Shubk M. A method for evaluatng the dstrbuton of power n a comtee system. Am. Polt. Sc. Rev. 954;48: [4] Banzhaf JF. Weghted votng does not work: a mathematcal analyss. Rutgers Law Rev. 965;9: [5] Deegan J, Packel EW. A new ndex of power for smple n-person games. Internat. J. Game Theory. 979;7:3 23. [6] Holler MJ. Formng coaltons and measurng votng power. Polt. Stud. 982;30: [7] Bertn C, Gambarell G, Stach I. A publc help ndex. In: Braham M, Steffen F, edtors. Power, freedom, and votng. Berln: Sprnger; [8] Alonso-Mejde JM, Frexas J. A new power ndex based on mnmal wnnng coaltons wthout any surplus. Decs Support Syst. 200;49: [9] Lorenzo-Frere S, Alonso-Mejde JM, Casas-Mendez B, Festras-Janero MG. Characterzatons of the Deegan-Packel and Johnston power ndces. Eur. J. Oper. Res. 2007;77: [0] Alonso-Mejde JM, Casas-Méndez B, Holler MJ, Lorenzo-Frere S. Computng power ndces: multlnear extensons and new characterzatons. Eur. J. Oper. Res. 2008;88: [] Penrose LS. The elementary statstcs of majorty votng. J. Roy. Statst. Soc. 946;09: [2] Coleman JS. Control of collectvtes and the power of a collectvty to act, socal choce. New York, NY: Gordon and Breach; 97. [3] Feltkamp V. Alternatve axomatc characterzatons of the Shapley and Banzhaf values. Internat. J. Game Theory. 995;24: [4] Dubey P. On the unqueness of the Shapley value. Internat. J. Game Theory. 975;4:3 39. [5] Dubey P, Shapley LS. Mathematcal propertes of the Banzhaf power ndex. Math. Oper. Res. 979;4:99 3. [6] Holler MJ, Packel EW. Power. Luck and the rgth ndex. J. Econ. 983;43:2 29. [7] Alonso-Mejde JM, Casas-Méndez B, Festras-Janero MG, Holler MJ. Axomatzatons of publc good ndces wth a pror unons. Soc. Choce Welfare. 200;35: [8] Johnston RJ. Envronment and plannng. C, Government & polcy. [9] Alonso-Mejde JM, Casas-Méndez B, Festras-Janero MG, Holler MJ. The Deegan-Packel ndex for smple games wth a pror unons. Qual Quant. 20;45: [20] Owen G. Multlnear extensons of games. Manage. Sc. 972;8: [2] Owen G. Multlnear extensons and the Banzhaf value. Nav. Res. Logst. Q. 975;22: [22] Algaba E, Blbao JM, Fernández-García JR, López JJ. Computng power ndces n weghted multple majorty games. Math. socal sc. 2003;46:63 80.
Reduced drift, high accuracy stable carbon isotope ratio measurements using a reference gas with the Picarro 13 CO 2 G2101-i gas analyzer
Reduced drft, hgh accuracy stable carbon sotope rato measurements usng a reference gas wth the Pcarro 13 CO 2 G2101- gas analyzer Chrs Rella, Ph.D. Drector of Research & Development Pcarro, Inc., Sunnyvale,
More informationFirst digit of chosen number Frequency (f i ) Total 100
1 4. ANALYSING FREQUENCY TABLES Categorcal (nomnal) data are usually summarzed n requency tables. Contnuous numercal data may also be grouped nto ntervals and the requency o observatons n each nterval
More informationRCBC Newsletter. September Richmond County Baseball Club. Inside this issue: Johnny Ray Memorial Classic. RCBC on You Tube
September 2016 Rchmond County Baseball Club 1400 Travs Ave. Staten Island, NY 10314 RCBC Newsletter If you have any nterestng nfo or news you would lke ncluded n a future newsletter, please emal to jm@rcbclub.com.
More informationEvaluation of a Center Pivot Variable Rate Irrigation System
Evaluaton of a Center Pvot Varable Rate Irrgaton System Ruxu Su Danel K. Fsher USDA-ARS Crop Producton Systems Research Unt, Stonevlle, Msssspp Abstrat: Unformty of water dstrbuton of a varable rate center
More informationEvolutionary Sets of Safe Ship Trajectories: Evaluation of Individuals
Internatonal Journal on Marne Navgaton and Safety of Sea Transportaton Volume 6 Number 3 September 2012 Evolutonary Sets of Safe Shp Trajectores: Evaluaton of Indvduals R. Szlapczynsk Gdansk Unversty of
More informationEquilibrium or Simple Rule at Wimbledon? An Empirical Study
Equlbrum or Smple Rule at Wmbledon? An Emprcal Study Shh-Hsun Hsu, Chen-Yng Huang and Cheng-Tao Tang Revson: March 2004 Abstract We follow Walker and Wooders (200) emprcal analyss to collect and study
More informationNew Roads to International Environmental Agreements: The Case of Global Warming *
New Roads to Internatonal Envronmental Agreements: The Case of Global Warmng * Second draft: February, 24 Johan Eyckmans K.U.Leuven, Centrum voor Economsche Studën, Naamsestraat 69, B-3 Leuven, Belgum
More informationBlockholder Voting. Heski Bar-Isaac and Joel Shapiro University of Toronto and University of Oxford. March 2017
Blockholder Votng Hesk Bar-Isaac and Joel Shapro Unversty of Toronto and Unversty of Oxford March 2017 Abstract By ntroducng a shareholder wth many votes (a blockholder to a standard model of votng, we
More informationA PROBABILITY BASED APPROACH FOR THE ALLOCATION OF PLAYER DRAFT SELECTIONS IN AUSTRALIAN RULES
Journal of Sports Scence and Medcne (2006) 5, 509-516 http://www.jssm.org Research artcle The 8th Australasan Conference on Mathematcs and Computers n Sport, 3-5 July 2006, Queensland, Australa A PROBABILITY
More informationOPTIMAL LINE-UPS FOR A YOUTH SOCCER LEAGUE TEAM. Robert M. Saltzman, San Francisco State University
OPTIMAL LINE-UPS FOR A YOUTH SOCCER LEAGUE TEAM Robert M. Saltzman, San Francsco State Unversty ABSTRACT Coaches n some dvsons of the Amercan Youth Soccer Organzaton (AYSO) are asked to fll out ther team
More informationM.H.Ahn, K.J.Lee Korea Advance Institute of Science and Technology 335 Gwahak-ro, Yuseong-gu, Daejeon , Republic of Korea
The Methodology on Exposure Dose Evaluaton Modelng Related to Arbtrary Accdent n the Temporary Storage Faclty for Low and Intermedate Level Waste - 9133 M.H.Ahn, K.J.Lee Korea Advance Insttute of Scence
More informationEngineering Analysis of Implementing Pedestrian Scramble Crossing at Traffic Junctions in Singapore
Engneerng Analyss of Implementng Pedestran Scramble Crossng at Traffc Junctons n Sngapore Dr. Lm Wee Chuan Eldn Department of Chemcal & Bomolecular Engneerng, Natonal Unversty of Sngapore, 4 Engneerng
More informationHigh Speed 128-bit BCD Adder Architecture Using CLA
Hgh Speed 128-bt BCD Archtecture Usng CLA J.S.V.Sa Prasanth 1, Y.Yamn Dev 2 PG Student [VLSI&ES], Dept. of ECE, Swamy Vvekananda Engneerng College, Kalavara, Andhrapradesh, Inda 1 Assstant Professor, Dept.
More informationMuscle drain versus brain gain in association football: technology transfer through
Muscle dran versus bran gan n assocaton football: technology transfer through player emgraton and manager mmgraton G. J. Allan a * and J. Moffat b a Correspondng Author: Department of Economcs, Sr Wllam
More informationEndogenous Coalition Formation in Global Pollution Control
Fondazone En Enrco Matte Endogenous Coalton Formaton n Global Polluton Control Mchael Fnus and Banca Rundshagen NOTA DI LAVORO 43.001 JUNE 001 Coalton Theory Network Unversty of Hagen, Germany Ths paper
More informationEnglish Premier League (EPL) Soccer Matches Prediction using An Adaptive Neuro-Fuzzy Inference System (ANFIS) for
Englsh Premer League (EPL) Soccer Matches Predcton usng An Adaptve Neuro-Fuzzy Inference System (ANFIS) for Amadn, F. I 1 and Ob, J.C. 2 Department of Computer Scence, Unversty of Benn, Benn Cty. Ngera.
More informationCoalition Formation in a Global Warming Game: How the Design of Protocols Affects the Success of Environmental Treaty-Making
Coalton Formaton n a Global Warmng Game: How the Desgn of Protocols Affects the uccess of Envronmental Treaty-Mang Frst draft: March, 23 Ths verson: November, 23 Johan Eycmans K.U.Leuven, Centrum voor
More informationADDITIONAL INSTRUCTIONS FOR ISU SYNCHRONIZED SKATING TECHNICAL CONTROLLERS AND TECHNICAL SPECIALISTS
A ADDITIONAL INSTRUCTIONS FOR ISU SYNCHRONIZED SKATING TECHNICAL CONTROLLERS AND TECHNICAL SPECIALISTS DIFFICULTY GROUPS OF FEATURES 1 DEFINITIONS: Change of Rotaton: Refers to TURNS or LINKING STEPS rotatng
More informationDevelopment of Accident Modification Factors for Rural Frontage Road Segments in Texas
Development of Accdent Modfcaton Factors for Rural Frontage Road Segments n Texas Domnque Lord* Zachry Department of Cvl Engneerng & Center for Transportaton Safety Texas Transportaton Insttute Texas A&M
More informationPlanning of production and utility systems under unit performance degradation and alternative resource-constrained cleaning policies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Plannng of producton and utlty systems under unt performance degradaton
More informationNumerical Study of Occupants Evacuation from a Room for Requirements in Codes
Numercal Study of Occupants Evacuaton from a Room for Requrements n Codes HL MU JH SUN Unversty of Scence and Technology of Chna State Key Laboratory of Fre Scence Hefe 2300326, CHINA muhl@mal.ustc.edu.cn
More informationA comparison study on the deck house shape of high speed planing crafts for air resistance reduction
csnak, 2014 Int. J. Nav. Archt. Ocean Eng. (2014) 6:867~875 http://dx.do.org/10.2478/ijnaoe-2013-0218 pissn: 2092-6782, eissn: 2092-6790 A comparson study on the deck house shape of hgh speed planng crafts
More informationOWNERSHIP STRUCTURE IN U.S. CORPORATIONS. Mohammad Rahnamaei. A Thesis. in the. John Molson School of Business
OWNERSHIP STRUCTURE IN U.S. CORPORATIONS Mohammad Rahnamae A Thess n the John Molson School of Busness Presented n Partal Fulfllment of the Requrements For the Degree of Master of Scence (Busness Admnstraton)
More informationPERFORMANCE AND COMPENSATION ON THE EUROPEAN PGA TOUR: A STATISTICAL ANALYSIS
PERFORMANCE AND COMPENSATION ON THE EUROPEAN PGA TOUR: A STATISTICAL ANALYSIS C. Barry Pftzner and Chrs Spence, Department of Economcs/Busness, Randolph-Macon College, Ashland, VA, bpftzne@rmc.edu, cspence@rmc.edu
More informationOPTIMIZATION OF PRESSURE HULLS OF COMPOSITE MATERIALS
OPTIMIZATION OF PRESSURE HULLS OF COMPOSITE MATERIALS J.Franco a, A.Corz a*.a.peña b a Materal Composte Group. Unversdad de Cadz. Avda/Ramon Puyol s/n. 11205 Algecras (Span) *alcorz@caltech.es b Calpe
More informationThe impact of foreign players on international football performance
MPRA Munch Personal RePEc Archve The mpact of foregn players on nternatonal football performance Orhan Karaca Ekonomst Magazne, Research Department October 008 Onlne at http://mpra.ub.un-muenchen.de/11064/
More informationITRS 2013 Silicon Platforms + Virtual Platforms = An explosion in SoC design by Gary Smith
ITRS 2013 Slcon Platforms + Vrtual Platforms = An exploson n SoC desgn by Gary Smth 2013 2013 Gary Gary Smth Smth EDA, EDA, Inc. Inc. All All Rghts Rghts Reserved. Reserved. 1 The Fve Desgn Constrants
More informationAn Enforcement-Coalition Model: Fishermen and Authorities forming Coalitions. Lone Grønbæk Kronbak Marko Lindroos
An Enforcement-Coalton Model: Fshermen and Authortes formng Coaltons Lone Grønbæ Kronba Maro Lndroos December 003 All rghts reserved. No part of ths WORKING PAPER may be used or reproduced n any manner
More informationEVALUATION MISSION ON OMT PROGRAMMES IN THE URBAN AND SEMI-URBAN WATER SUPPLY SECTOR SUPPORTED BY THE NETHERLANDS GOVERNMENT. March - April 1986
1 R 822 D 86 FC'K.. EVALUATON MSSON ON OMT PROGRAMMES N THE URBAN AND SEM-URBAN WATER SUPPLY SECTOR SUPPORTED BY THE NETHERLANDS GOVERNMENT 1 1 March - Aprl 1986 Fnal report The Hague, TABLE OF CONTENTS
More informationSchool of Civil Engineering, Shandong University, Jinan , China
2017 Internatonal Conference on Energy, Power and Envronmental Engneerng (ICEPEE 2017) ISBN: 978-1-60595-456-1 Evaluaton on Sustanable Utlzaton of Water Resources n Shandong Provnce Based on Water Footprnt
More informationWORKING PAPER SERIES Long-term Competitive Balance under UEFA Financial Fair Play Regulations Markus Sass Working Paper No. 5/2012
WORKING PAPER SERIES Impressum ( 5 TMG) Herausgeber: Otto-von-Guercke-Unverstät Magdeburg Fakultät für Wrtschaftswssenschaft Der Dekan Verantwortlch für dese Ausgabe: Otto-von-Guercke-Unverstät Magdeburg
More informationComprehensive evaluation research of volleyball players athletic ability based on Fuzzy mathematical model
ISSN : 0974-7435 Volume 10 Issue 3 Comprehensve evaluaton research of volleyball players athletc ablty based on Fuzzy mathematcal model Shangbn L, Peyu Zhao, Yngshuang Lu, Lxn Wu* Physcal Educaton Department,
More informationComparisons of Means for Estimating Sea States from an Advancing Large Container Ship
Downloaded from orbt.dtu.dk on: Jan 31, 18 Comparsons of Means for Estmatng Sea States from an Advancng Large Contaner Shp Nelsen, Ulrk Dam; Andersen, Ingrd Mare Vncent; Konng, Jos Publshed n: Proceedngs
More informationOn coalition formation: durable coalition structures
Matematcal Socal Scences 45 (003) 85 03 www.elsever.com/locate/econbase a On coalton formaton: durable coalton structures a b, Salvador Barbera `, Anke Gerber * Departament d Economa d Hstora ` Economca
More informationPeace Economics, Peace Science and Public Policy
Peace Economcs, Peace Scence and Publc Polcy Volume 17, Issue 1 2011 Artcle 1 Lone Wolf Terrorsm Peter J. Phllps Unversty of Southern Queensland, phllpsp@usq.edu.au Copyrght c 2011 Berkeley Electronc Press.
More informationEvaluating Rent Dissipation in the Spanish Football Industry *
Evaluatng Rent Dsspaton n the Spansh Football Industry * Gudo Ascar Dp. d Economa Poltca e Metod Quanttatv Va S. Felce 5 27100 Pava, Italy Tel: (+39) 0382 506211 Fax: (+39) 0382 304226 gascar@eco.unpv.t
More informationD S E Dipartimento Scienze Economiche
D S E Dpartmento Scenze Economche Workng Paper Department of Economcs Ca Foscar Unversty of Vence Carlo Carraro Johan Eyckmans Mchael Fnus ISSN: 1827/336X No. 44/WP/2006 Revsed Verson July 2006 Optmal
More informationCOMPENSATING FOR WAVE NONRESPONSE IN THE 1979 ISDP RESEARCH PANEL
COMPENSATING FOR WAVE NONRESPONSE IN THE 1979 ISDP RESEARCH PANEL 1. Introducton Graham Kalton, Unversty of Mchgan ames Lepkowsk, Unversty of Mchgan Tng-Kwong Ln. Natonal Unversty of Sngapore The choce
More informationStructural Gate Decomposition for Depth-Optimal Technology Mapping in LUT-based FPGA
Structural Gate Decomposton for Depth-Optmal Technology Mappng n LUT-based FPGA Abstract Jason Cong and Yean-Yow Hwang Department of Computer Scence Unversty of Calforna, Los Angeles Los Angeles, CA 9004
More informationMethodology for ACT WorkKeys as a Predictor of Worker Productivity
Methodology for ACT WorkKeys as a Predctor of Worker Productvty The analyss examned the predctve potental of ACT WorkKeys wth regard to two elements. The frst s tme to employment. People takng WorkKeys
More informationHow Geo-distributed Data Centers Do Demand Response: A Game-Theoretic Approach
IEEE TRANSACTIONS ON SMART GRIDS 1 How Geo-dstrbuted Data Centers Do Demand Response: A Game-Theoretc Approach Nguyen H. Tran, Member, IEEE, Da H. Tran, Shaole Ren, Member, IEEE, Zhu Han, Fellow, IEEE,
More informationRCBC Newsletter. August Richmond County Baseball Club. Inside this issue: 2016 College Showcase Camp. Tournament Update.
August 2016 Rchmond County Baseball Club 1400 Travs Ave. Staten Island, NY 10314 RCBC Newsletter If you have any nterestng nfo or news you would lke ncluded n a future newsletter, please emal to jm@rcbclub.com.
More informationRADIAL STIFFNESS OF A BICYCLE WHEEL AN ANALYTICAL STUDY
ADIAL TIFFE OF A BICYCLE WHEEL - A AALYTICAL TUDY José aría ínguez Dpto. de Físca Aplcada II Facultad de Cenca y Tecnología Unversdad del País Vasco Aptdo. 644 488 Blbao PAI Emal: osemara.mnguez@ehu.es
More informationPedestrian Facilities Planning on Tianjin New Area program
Avalable onlne at www.scencedrect.com ScenceDrect Proceda - Socal and Behavoral Scenc es 96 ( 2013 ) 683 692 13th COTA Internatonal Conference of Transportaton Professonals (CICTP 2013) Pedestran Facltes
More informationA Study on Parametric Wave Estimation Based on Measured Ship Motions
1 A Study on Parametrc Wave Estmaton Based on Measured Shp Motons Ulrk Dam NIELSEN * and Tosho ISEKI ** Abstract The paper studes parametrc wave estmaton based on the wave buoy analogy, and data and results
More informationA Prediction of Reliability of Suction Valve in Reciprocating Compressor
Purdue Unversty Purdue e-pubs nternatonal Compressor Engneerng Conference School of Mechancal Engneerng 1996 A Predcton of Relablty of Sucton Valve n Recprocatng Compressor W. H. You Samsung Electroncs
More informationMulti-Criteria Decision Tree Approach to Classify All-Rounder in Indian Premier League
Internatonal Journal of Adanced Scence and Technology Mult-Crtera Decson Tree Approach to Classfy All-Rounder n Indan Premer League Pabtra Kumar Dey 1, Dpendra Nath Ghosh 2, Abhoy Chand Mondal 3 1 Assstant
More informationDRAFT FOR PUBLIC CONSULTATION INTERCONNECTION AGREEMENT v.2.0 FOR IP KULATA/SIDIROKASTRO DEFINITIONS, BUSINESS RULES, EXCEPTIONAL EVENT
RAFT FOR PUBLIC CONSULTATION INTERCONNECTION AGREEMENT v.2.0 FOR IP KULATA/SIIROKASTRO EFINITIONS, BUSINESS RULES, EXCEPTIONAL EVENT ARTICLE 1: EFINITIONS All terms of the INTERCONNECTION AGREEMENT shall
More informationDecomposition guide Technical report on decomposition
June 2013 Decomposton gude Techncal report on decomposton Erasmus MC Start date of project: 20 Aprl 2012 Duraton: 36 months 1 Table of contents Abstract... 4 Acknowledgements... 5 Introducton... 6 Part
More informationAn intro to PCA: Edge Orientation Estimation. Lecture #09 February 15 th, 2013
An ntro to PCA: Edge Orentaton Estmaton Lecture #09 February 15 th, 2013 Revew: Edges Convoluton wth an edge mask estmates the partal dervatves of the mage surface. The Sobel edge masks are: " #!1 0 1!2
More informationPeak Field Approximation of Shock Wave Overpressure Based on Sparse Data
Peak Feld Approxmaton of Shock Wave Overpressure Based on Sparse Data Yongl Zhang, Taln Han, Yuqun Chen, Enku Zhang, and Xuan Lu Abstract To obtan the shock wave feld dstrbuton, two knds of calber weapons
More informationIEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 2, MARCH
IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 2, MARCH 2016 937 How Geo-Dstrbuted Data Centers Do Demand Response: A Game-Theoretc Approach Nguyen H. Tran, Member, IEEE, Da H. Tran, Shaole Ren, Member,
More informationPERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 19. MICHAEL FINUS * University of Hagen and National University of Singapore
Journal of Appled Economcs. Vol IX, No. 1 (May 2006), 19-47 PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS 19 PERMIT TRADING AND STABILITY OF INTERNATIONAL CLIMATE AGREEMENTS JUAN-CARLOS
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(3): Research Article
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(3):326-332 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Research on comprehensve evaluaton model-based NBA schedule
More informationInternal Wave Maker for Navier-Stokes Equations in a Three-Dimensional Numerical Model
Journal of Coastal Research SI 64 511-515 ICS2011 (Proceedngs) Poland ISSN 0749-0208 Internal Wave Maker for Naver-Stokes Equatons n a Three-Dmensonal Numercal Model T. Ha, J.W. Lee and Y.-S. Cho Dept.
More informationBETHANY TAX INCREMENT FINANCING DISTRICT NO. 1 NOTICE OF TWO PUBLIC HEARINGS
BETHANY TAX NCREMENT FNANCNG DSTRCT NO. 1 NOTCE OF TWO PUBLC HEARNGS On December 12, 2017 at 7:00 P.M., at Bethany Cty Hall, 6700 N.W. 36th Street, Bethany, Oklahoma, the Cty Councl of the Cty of Bethany
More informationReferee Bias and Stoppage Time in Major League Soccer: A Partially Adaptive Approach
Econometrcs 2014, 2, 1-19; do:10.3390/econometrcs2010001 OPEN ACCESS econometrcs ISSN 2225-1146 www.mdp.com/journal/econometrcs Artcle Referee Bas and Stoppage Tme n Major League Soccer: A Partally Adaptve
More informationWhat does it take to be a star?
Unversty of Freburg Department of Internatonal Economc Polcy Dscusson Paper Seres Nr. 1 What does t take to be a star? The role of performance and the meda for German soccer players Erk E. Lehmann and
More informationModeling the Performance of a Baseball Player's Offensive Production
Brgham Young Unversty BYU ScholarsArchve All Theses and Dssertatons 006-03-09 Modelng the Performance of a Baseball Player's Offensve Producton Mchael Ross Smth Brgham Young Unversty - Provo Follow ths
More informationMass Spectrometry. Fundamental GC-MS. GC-MS Interfaces
Mass Spectrometry Fundamental GC-MS GC-MS Interfaces Wherever you see ths symbol, t s mportant to access the on-lne course as there s nteractve materal that cannot be fully shown n ths reference manual.
More informationRelative Salary Efficiency of PGA Tour Golfers: A Dynamic Review
Relatve Salary Effcency of PGA Tour Golfers: A Dynamc Revew Julo Cesar Alonso Unversdad Ices Julan Benavdes Unversdad Ices Based on one-year sample, Nero (2001) estmated golfers' usng four performance
More informationImpact of Intelligence on Target-Hardening Decisions
CREATE Research Archve Publshed Artcles & Papers 5--29 Impact of Intellgence on Target-Hardenng Decsons Vck M. Ber Unversty of Wsconsn Madson, ber@engr.wsc.edu Chen Wang Unversty of Wsconsn - Madson, cwang37@wsc.edu
More informationNo TRINIDAD AND TOBAGO.
r)( /6 / 2 TRNDAD AND TOBAGO. General Loan and nscrbed Stock. No. 25.-1912. 6th May. AN ORDNANCE to declare the terms and condtons applcable to Loans authorsed to be rased by the Government of Trndad and
More informationAalborg Universitet. Published in: 9th ewtec Publication date: Document Version Publisher's PDF, also known as Version of record
Aalborg Unverstet Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea Chozas, Jula Fernandez; Jensen,. E. Helstrup; Sørensen, H. C.; Kofoed, Jens Peter; Kabuth, Alna Krstn
More informationExperimental And Numerical Investigation Of The Flow Analysis Of The Water-Saving Safety Valve
Expermental And Numercal Investgaton Of The Flow Analyss Of The Water-Savng Safety Valve Muhammed Safa KAMER s PhD Student n Department of Mechancal Engneerng n Kahramanmaras Sutcu Imam Unversty, Turkey.
More informationLSSVM Model for Penetration Depth Detection in Underwater Arc Welding Process
ISS 1746-7659, England, UK Journal of Informaton and Computng Scence Vol. 5, o. 4, 2010, pp. 271-278 LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process WeMn Zhang 1, 2, GuoRong Wang
More informationDETECTION AND REFACTORING OF BAD SMELL
Internatonal Journal of Software Engneerng & Applcatons (IJSEA), Vol.4, No.5, September 2013 DETECTION AND REFACTORING OF BAD SMELL CAUSED BY LARGE SCALE Jang Dexun 1, Ma Pejun 2, Su Xaohong 3, Wang Tantan
More informationInvestigation on Hull Hydrodynamics with Different Draughts for 470 Class Yacht
Proceedngs Investgaton on Hull Hydrodynamcs wth Dfferent Draughts for 470 Class Yacht Yong Ma 1, *, Shje Ln 1,2, Yangyng He 1, Xaoshan Le 1,2 and Song Zhang 1,2 1 School of Sports Engneerng and Informaton
More informationRecreational trip timing and duration prediction: A research note
Recreatonal trp tmng and duraton predcton: A research note Ataelty Halu a and Le Gao a* a School of Agrcultural and Resource Economcs, The Unversty of Western Australa, Crawley, WA 6009, Australa *E-mal
More informationInvestigating Reinforcement Learning in Multiagent Coalition Formation
Investgatng Renforcement Learnng n Multagent Coalton Formaton Xn L and Leen-Kat Soh Department of Computer Scence and Engneerng Unversty of Nebrasa-Lncoln 115 Ferguson Hall, Lncoln, NE 66588-0115 {xnl,
More informationInternational Journal of Engineering and Technology, Vol. 8, No. 5, October Model Systems. Yang Jianjun and Li Wenjin
Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 1 Relablty Optmzaton Desgn of Submarne Free-Runnng Model Systems Yang Janjun and L Wenjn Abstract Wth regard to the relablty
More informationAvailability assessment of a raw gas re-injection plant for the production of oil and gas. Carlo Michelassi, Giacomo Monaci
16 th IMEKO TC4 Symposum Explorng New Fronters of Instrumentaton and Methods for Electrcal and Electronc Measurements Avalablty assessment of a raw gas re-njecton plant for the producton of ol and gas
More informationPLAYERS AGENT REGISTRATION REGULATIONS
PLAYERS AGENT REGISTRATION REGULATIONS 1 DEFINITIONS 1.1 In these Players Agent Regstraton Regulatons, the followng terms shall have the followng meanngs: Agency Actvty means actng n any way and at any
More informationReport No. FHWA/LA.13/508. University of Louisiana at Lafayette. Department of Civil and Environmental Engineering
TECHNICAL REPORT STANDARD PAGE Report No. FHWA/LA.13/508 4. Ttle and Subttle A Comprehensve Study on Pavement Edge Lne Implementaton 7. Author(s) Xaoduan Sun, Ph.D., P.E. Subassh Das 9. Performng Organzaton
More informationCrash Frequency and Severity Modeling Using Clustered Data from Washington State
Proceedngs of the IEEE ITSC 2006 2006 IEEE Intellgent Transportaton Systems Conference Toronto, Canada, September 17-20, 2006 WB7.1 Crash Frequency and Severty Modelng Usng Clustered Data from Washngton
More informationLake Clarity Model: Development of Updated Algorithms to Define Particle Aggregation and Settling in Lake Tahoe
Lake Clarty Model: Development of Updated Algorthms to Defne Partcle Aggregaton and Settlng n Lake Tahoe Goloka B. Sahoo S. Geoffrey Schladow John E. Reuter Danel Nover Davd Jassby Lake Clarty Model Weather
More informationSports Injuries in School Gaelic Football: A Study Over One Season
Sports njures n School Gaelc Football: A Study Over One Season A. W. S. Watson Sports njures Research Centre, Unversty of Lmerck, Lmerck, reland. Abstract School football njures were studed over the seven
More informationResponse based sea state estimation for onboard DSS Safe and Efficient Marine Operations
Response based sea state estmaton for onboard DSS Safe and Effcent Marne Operatons Ulrk Dam Nelsen AMOS Workshop, NTNU, Trondhem, 13 th and 14 th November, 2014 Contents Introducton: Context Montorng and
More informationInternational Journal of Industrial Engineering Computations
Internatonal Journal of Industral Engneerng Computatons 2 (20) 93 202 Contents lsts avalable at GrowngScence Internatonal Journal of Industral Engneerng Computatons homepage: wwwgrowngscencecom/ec A mult-obectve
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
Ths document s downloaded from DR-NTU, Nanyang Technologcal Unversty Lbrary, Sngapore. Ttle capacty analyss usng smulaton Author(s) Ctaton Huang, Shell Yng; Hsu, Wen Jng; He, Yuxong; Song, Tancheng; De
More informationRisk analysis of natural gas pipeline
Rsk analyss of natural gas ppelne Y.-D. Jo 1, K.-S. Park 1, J. W. Ko, & B. J. Ahn 3 1 Insttute of Gas Safety Technology, Korea Gas Safety Corporaton, South Korea Department of Chemcal Engneerng, Kwangwoon
More informationAalborg Universitet. Published in: 9th ewtec Publication date: Document Version Accepted author manuscript, peer reviewed version
Aalborg Unverstet Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea Chozas, Jula Fernandez; Jensen,. E. Helstrup; Sørensen, H. C.; Kofoed, Jens Peter; Kabuth, Alna Krstn
More informationSustainability Profiling of Long-living Software Systems
Sustanablty Proflng of Long-lvng Software Systems Ahmed D Alharth, Mara Spchkova and Margaret Hamlton RMIT Unversty, Melbourne, Australa Emal: {ahmedalharth, maraspchkova,margarethamlton}@rmteduau Abstract
More informationPREDICTION OF POLYDISPERSE STEAM BUBBLE CONDENSATION IN SUB-COOLED WATER USING THE INHOMOGENEOUS MUSIG MODEL
PREDICTION OF POLYDISPERSE STEAM BUBBLE CONDENSATION IN SUB-COOLED WATER USING THE INHOMOGENEOUS MUSIG MODEL C. Lfante *, T. Frank *, A.D. Burns, D. Lucas and E. Krepper * ANSYS Germany GmbH, Staudenfeldweg
More informationEvaluating the Effectiveness of Price and Yield Risk Management Products in Reducing. Revenue Risk for Southeastern Crop Producers * Todd D.
Evaluatng the Effectveness of Prce and Yeld Rsk Management Products n Reducng Revenue Rsk for Southeastern Crop Producers * Todd D. Davs ** Abstract A non-parametrc smulaton model ncorporatng prce and
More informationTransportation Research Forum
Transportaton Research Forum On the Impact of HOT Lane Tollng Strateges on Total Traffc Level Author(s): Sohel Sbdar and Mansoureh Jehan Source: Journal of the Transportaton Research Forum, Vol. 48, No.
More informationJIMAR ANNUAL REPORT FOR FY 2001 (Project ) Project Title: Analyzing the Technical and Economic Structure of Hawaii s Pelagic Fishery
1 JIMAR ANNUAL REPORT FOR FY 2001 (Project 653540) P.I. Name: PngSun Leung, Khem Sharma and Sam Pooley Project Research Assstant: Naresh Pradhan Project Ttle: Analyzng the Techncal and Economc Structure
More informationCS 2750 Machine Learning. Lecture 4. Density estimation. CS 2750 Machine Learning. Announcements
CS 75 Machne Learnng Lecture 4 ensty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 539 Sennott Square CS 75 Machne Learnng Announcements Homework ue on Wednesday before the class Reports: hand n before the
More informationDynamic Analysis of the Discharge Valve of the Rotary Compressor
Purdue Unversty Purdue e-pubs Internatonal Compressor Engneerng Conference School of Mechancal Engneerng 8 Dynamc Analyss of the Dscharge Valve of the Rotary Compressor Bo Huang Shangha Htach Electrcal
More informationJournal of Environmental Management
Journal of Envronmental Management 90 (2009) 3057 3069 Contents lsts avalable at ScenceDrect Journal of Envronmental Management journal homepage: www.elsever.com/locate/jenvman Sustanable value assessment
More informationFast Adaptive Coding Unit Depth Range Selection Algorithm for High Efficiency Video Coding
Sensors & Transducers 2014 by IFSA Publshng, S. L. http://www.sensorsportal.com Fast Adaptve Codng Unt Depth Range Selecton Algorthm for Hgh Effcency Vdeo Codng Fang Shuqng, Yu Me, Chen Fen, Xu Shengyang,
More informationDriver s Decision Model at an Onset of Amber Period at Signalised Intersections
Probablty to stop 1.00 0.90 0.80 0.70 0.60 0.40 0.30 0-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 1st veh n platoon 2nd veh n platoon
More informationInvestigation on Rudder Hydrodynamics for 470 Class Yacht
Proceedngs Investgaton on Rudder Hydrodynamcs for 470 Class Yacht She Ln 1,, Yong Ma, *, Wetao Zheng, Song Zhang 1,, Xaoshan Le 1, and Yangyng He 1, 1 Graduate School of Wuhan Sports Unversty, Wuhan 430079,
More informationMajor League Duopolists: When Baseball Clubs Play in Two-Team Cities. Phillip Miller. Department of Economics. Minnesota State University, Mankato
Major League Duopolsts: When Baseball Clubs Play n Two-Team Ctes Phllp Mller Department of Economcs Mnnesota State Unversty, Mankato September 2006 Abstract: Ths paper focuses on examnng the attendance
More informationGAS-LIQUID INTERFACIAL AREA IN OXYGEN ABSORPTION INTO OIL-IN-WATER EMULSIONS
AS-LIQUID INTERFACIAL AREA IN OXYEN ABSORPTION INTO OIL-IN-WATER EMULSIONS ómez-díaz, D. a, omes, N. b, Texera, J.A. b, Belo, I. b a Department of Chemcal Engneerng, Unversty of Santago de Compostela,
More informationSectoral Business Cycle Synchronization in the European Union *
Sectoral Busness Cycle Synchronzaton n the European Unon * Antóno Afonso, # $ Davde Furcer + January 2007 Abstract Ths paper analyses sectoral busness cycle synchronzaton n an enlarged European Unon usng
More informationPRESSURE DROP ANALYSIS OF STEAM GENERATION PARABOLIC TROUGH PLANTS
PRESSURE DROP ANALYSIS OF STEAM GENERATION PARABOLIC TROUGH PLANTS Heko Schenk 1 and Tobas Hrsch 2 1 M.Sc., Researcher, Insttute of Techncal Thermodynamcs, German Aerospace Center (DLR), Stuttgart (Germany),
More informationPeculiarities of the Major League Baseball Posting System
Peculartes of the Major League Baseball Postng System Duane W. Rockerbe Unversty of Lethbrdge Revsed July 2007 Abstract The postng system used n major league baseball to obtan free agent players from Japan
More informationJohnnie Johnson, Owen Jones and Leilei Tang. Exploring decision-makers use of price information in a speculative market
Johnne Johnson, Owen Jones and Lele Tang Explorng decson-makers use of prce nformaton n a speculatve market Abstract We explore the extent to whch the decsons of partcpants n a speculatve market effectvely
More informationAerator Performance in Reducing Phenomenon of Cavitation in Supercritical Flow in Steep Channel Bed
Engneerng Internatonal Conference UNNES Conservaton 13 Proceedng Aerator Performance n Reducng Phenomenon of Cavtaton n Supercrtcal Flow n Steep Channel Bed Yer Sutopo 1, Bud Wgnyosukarto, Istarto, dan
More information