MPRA Munch Personal RePEc Archve Barganng agenda, tmng, and entry Lucano Fant and Domenco Buccella Unversty of Psa, Kozmnsk Unversty, Warsa January 015 Onlne at http://mpra.ub.un-muenchen.de/64089/ MPRA Paper No. 64089, posted. May 015 3:47 UTC
Barganng Agenda, Tmng, and Entry Lucano Fant * and Domenco Buccella Abstract In a unonsed Cournot duopoly, the present paper extensvely re-examnes the subect of the barganng scope beteen frms and unons. It nvestgates the endogenous equlbrum agenda (Rght-to-Manage vs Effcent Barganng) that can arse under three tmng specfcaton of the barganng game both for a gven duopoly and monopoly th threat of entry. A novel result s that, n sequental negotatons, Effcent Barganng emerges n equlbrum for a range of the unons poer larger than n smultaneous negotatons. Moreover, gven the potental market deterrence effect of the Effcent Barganng, the conventonal sdom that ths agenda s socally effcent can be reversed. Keyords: Effcent Barganng; Rght-to-manage; Cournot duopoly; Frm-unon barganng agenda JEL Classfcaton: J51, L13 * Lucano Fant, Department of Economcs and Management, Unversty of Psa, Va Cosmo Rdolf, 10, I 5614 Psa (PI), Italy. E-mal address: lfant@ec.unp.t; tel.: +39 050 16 369; fax: +39 050 16 384. Domenco Buccella, Department of Economcs, Kozmnsk Unversty, Jagełłonska Street, 57/59 03301 Warsa, Poland. E-mal: buccella@kozmnsk.edu.pl; tel.: + 48 51 9 153 1
1 Introducton The subects of the scope of barganng and the choce of the negotaton agenda are pvotal n labour-management relatons and negotatons and, therefore, for the functonng of labour market nsttutons n the most advanced economes, notably n Europe. In the present ork, e focus the analyss on the to most frequently dscussed models n the economc lterature, and emprcally observed n real ord barganng agendas: the Rght-to-Manage () and the Effcent Barganng () models. In the model (Nckell and Andres 1983; Dobson 1997; Naylor 00; Correa-López and Naylor, 004), unonsed labour and frms bargan over ages; nevertheless, once ages are fxed, the frms have the rght to decde the employment level. On the other hand, n the model, the frms and unonsed labour negotate over ages and employment ether smultaneously (e.g. McDonald and Solo 1981; Ashenfelter and Bron, 1986; Espnosa and Rhee 1989; Bughn 1995, 1996), or n a sequental ay (Mannng, 1987a,b). Precsely, the present paper analyses hch nsttuton about the scope of barganng, and therefore the barganng agenda, may preval at market equlbrum and hether frms and unons may (endogenously) agree th ths nsttuton. The reference frameork of the artcle s a unonzed Cournot duopoly th frms producng homogeneous goods. Three dfferent cases related to the tmng of the barganng game are taken nto consderaton. In ths respect, the paper provdes an exhaustve treatment of the dfferent strategc effects of the barganng agenda n relaton th the dfferent cases of the tmng of the barganng game, so also ntegratng the prevous lterature hch treated only partally as ell as separately such cases. In the frst case, n the presence of the mxed duopoly, the frm hch ntroduces the agenda negotate ages and employment hen the frm decdes output; n other ord, the frm s Stackelberg age folloer. In the second case, the frm th the agenda negotate ages and employment hen the frm bargans the age th ts unon, that s, the frm s Stackelberg output leader. Fnally, n the thrd case, despte the dverse agendas, both frms negotate th unons frst ages concurrently, and subsequently the frm negotates th ts unon over employment, hle the frm chooses employment unlaterally; n other ords, there s no leadershp. The negotaton processes beteen unons and frms ental nterestng problems not only for the barganng partes, but also for consumers and socety. The comprehenson of these ssues are sgnfcant for the desgn of polces to regulate labour markets for ther approprate functonng, the organsaton of productve actvtes n dfferent sectors of the economy and product markets as ell as the assessment of the effects on socal elfare. Consequently, governments and polcy-makers as ell as guarantees authortes such as anttrust bodes are concerned. The artcle contrbutes to the grong lterature on unonsed olgopoly (e.g., Horn and Wolnsky, 1988; Dorck 1989; Bughn, 1995; Correa-López and Naylor, 004; Fant and Meccher, 011, 013). Hoever, despte the relevance of the topc for the labour economcs as ell as the ndustral organzaton, the analyss of the barganng agenda selecton and the mpact of dfferent labour market nsttutons on labor and product markets s scanty n the exstng lterature. The present paper s one of the fe that focuses exactly on these ssues. Noteorthy exceptons are the orks of Petraks and Vlasss (000), Kraft (006), Vannn and Bughn (000), and Fant (014, 015). Petraks and Vlasss (000) buld a model here the benchmark equlbrum nsttuton s. Then, the authors test hether the agenda lasts all the possble devatons hch need both barganng partes to agree th. They sho that an agreement on the agenda can never occur. On the other hand, dependng on hether the unons barganng poer s
larger or loer than that of frms, an agreement arses on ether or a mxed result here, n equlbrum one frm-unon par selects hle the other par chooses. Kraft (006) mrrors the assumpton of Petraks and Vlasss (000) that, hen one frm commts to, then the rval frm alays becomes a Stackelberg folloer n the output market. Nevertheless, Kraft (006) argues, n sharp contrast th Petraks and Vlasss (000), that s the frms domnant strategy for a large range of the barganng poer parameter. In an olgopoly context, Vannn and Bughn (000) concentrates on the frms decson hether to adopt cost-rasng strateges through the recognton of labour unons. The authors sho that n precse crcumstances (lo unon poer, lo product dfferentaton and centralsed barganng), frms can prefer an arrangement rather than a arrangement, despte hgher unt age costs. Hoever, Kraft (006) and Vannn and Bughn (000) do not take nto account the unon s utltes to determne the equlbrum agenda and, therefore, abstract from the ssue of the endogenous agreement on the barganng scope. Thus, the approach of those papers th regard the ssues of the barganng scope and agenda s totally dfferent from the one of the present paper. As a consequence, ther results are not drectly comparable th those of the present ork, hch follos and complements Fant (014, 015) ho revsted such an ssue n a standard game-theoretc approach. Fant (014) frst compares the exogenously gven equlbra, and then nvestgates hch agenda endogenously arses n equlbrum hen the barganng nsttutons are the monopoly unon and, and n the mxed duopoly, the frm negotates ages and employment hen the other frm decdes the output level ( frm Stackelberg age folloer). The author fnds that, hen the equlbrum s exogenous, frms prefer hen the unon barganng poer s loer, equals or slghtly hgher than that of frms hle, for a suffcently hgh value of the unon barganng poer, unons prefer. On the other hand, for a medum-hgh value of the unons barganng poer, the partes agree on the monopoly unon nsttuton. As for the endogenous equlbra, Fant (014) shos that the barganng partes agree on the selecton of the agenda for arrangement for a de medum-hgh value range of the unon s poer. Fant (015) analyse the endogenous selecton of the barganng agenda n a duopoly here, n the mxed case, the frm th the agenda negotate ages and employment hen the frm bargans the age th ts unon ( frm Stackelberg output leader). Fant (015) shos that only can arse as sub-game perfect Nash equlbrum (SPNE) n pure strateges and under the rsk-domnance crteron, provded that the unon barganng poer s not too hgh. Nonetheless, the prevous contrbutons have carred out ther analyss consderng the duopoly market structure as gven, therefore abstractng from the topc of the potental entry and the use of the barganng agenda as a market entry deterrent mechansm. The focus on the relatonshp beteen entry and barganng agenda s the subect of the papers of Bughn (1999) and Buccella (011). Bughn (1999) consders dfferent market structures, that s, duopoly vs. monopoly th threat of potental entry, and dfferent entry modes and constrants on the choce of barganng scope. Bughn (1999) proposes the tmng of the game hen the frm n the mxed duopoly s a Stackelberg folloer. The author argues that, under a unonzed duopoly, the agenda arses as the ndustry equlbrum for each frm. Adoptng the same tmng of Bughn (1999) and makng use of a conectural varaton model, Buccella (011) shos that a conflct of nterest among the partes arses th regard to the barganng agenda, n sharp contrast th the prevous fndng (due to some lmtatons n Bughn s result). In partcular, hen the duopoly s the gven market structure, s the frms domnant strategy hle s the unons domnant strategy. Hoever, n the case of threat of entry, the ncumbent barganng partes can agree on the agenda to deter a potental entrant to enter the market. 3
The prmary results of the paper are as follos. In the absence of entry, the specfcaton of the tmng n the negotaton process s fundamental to determne the endogenous equlbrum agenda beteen frms and unons. In lne th Buccella (011), e sho that, hen n the mxed duopoly the frm s Stackelberg age folloer, no endogenous equlbrum barganng agenda arses n unon-frm negotatons. On the other hand, hen n the mxed duopoly the frm s Stackelberg output leader, e confrm the results of Fant (015). Fnally, n the absence of leadershp, that s, hen the frm negotates sequentally over ages and employment, e fnd that, smlarly to Fant (015), only the Effcent Barganng can emerge as the endogenous equlbrum agenda, n pure strateges and under the rskdomnance crteron for a range of the unon s poer values larger than that of the case of smultaneous (.e., provded that the unon s barganng poer s not extremely hgh). In the presence of potental entry, the tmng of the negotaton, the entry mode as ell as the restrctons on barganng are fundamental to determne the equlbrum agenda n each barganng unt. The central results are manly confrmed: the s the predomnant endogenous equlbrum agenda that arses n pure strateges, even for a larger range of the unon barganng poer parameter than for the gven duopoly market structure. Nonetheless, n crcumscrbed stuaton, also the agenda can emerge as the equlbrum barganng agenda. Noteorthy, the ncumbent unon-frm unt can strategcally use only the agenda as an entry deterrence tool. The remander of the artcle s organzed as follos. Secton descrbes the basc duopoly model. Secton 3 develops the case of the unonsaton of the labour market under the to nsttutons, and, and the three tmng characterzatons. Secton 4 derves the subgame perfect Nash equlbrum outcomes as ell as the key propostons th regard to the choce of the preferred agreement by frms and unons hen duopoly s the establshed market structure. Secton 5 extends the analyss to an olgopoly ncumbent-entrant game th threat of potental entry, and provdes the key fndngs and propostons concernng the agreed agenda. Fnally, the last secton summarses the man results and mplcatons, and propose plausble drectons for further research on the topc. The basc model As Bughn (1999), Petraks and Vlasss (000), Naylor (003), and Kraft (006), ust to menton a fe, e consder a duopolstc Cournot model. The to frms, labelled 1 and, produce homogeneous goods. The lnear (nverse) product demand s p a q q,, 1,; (1) here p s the market prce (the slope s normalsed to the unty), q and q are the output levels of the to frms. Wthout loss of generalty, t s possble to normalze the parameters a 1. Labour, l, represents the unque nput factor. A constant returns-to-scale technology characterses the producton functon - dentcal for both frms - th constant (margnal) returns to labour, such that q l, 1, () 4
here l represents the labour force employed by frm. The th frm faces an average and margnal cost 0 for every unt of output produced, here s the age per unt of labour. Therefore, the frm s cost functon s lnear and descrbed by: ( ) C q l q. (3) Thus, the expresson for each frm s profts s Π (1 q q ) q,, 1,;. (4) 3 The unonsed labour market. Both frms are unonzed, and negotatons are conducted at decentralzed level. We assume that the members of the unons are large enough to meet the frm s labour demand. We consder the to typcal negotaton models of the trade-unon economcs (Booth, 1995): 1) the Rght-to-Manage model () (e.g. Nckell and Andres, 1983), n hch ages are the outcome of negotatons beteen frms and unonzed labour; hoever, once ages are set, the frms have the rght to set the employment levels; and ) the effcent barganng model () hch prescrbes that the unon and the frm are barganng over both ages and employment (or, more realstcally, hours of ork). Wages and employment negotatons may occur ether smultaneously (e.g. McDonald and Solo, 1981; Ashenfelter and Bron, 1986), or sequentally (Mannng, 1987a,b). Each frm-specfc unon has the follong utlty functon: 1 V l. (5) We assume that unons are dentcal. Therefore, by recallng that q l, (5) becomes: V q, (6) that s, the unons obectve functon s to maxmse the total age bll. Let us begn by llustratng the cases of and, both n the smultaneous and sequental confguratons. 3.1. Rght-to-manage nsttuton Frst, e construct a frm-unon to-stage game accordng to the Rght-to-Manage () model. In the frst stage, each frm-unon barganng unt smultaneously negotates over 1 Ths a specfc case of the more general Stone-Geary utlty functon,.e., Pencavel (1984, 1985), Dorck and Spencer (1994): ( ) V l, here s the reservaton or compettve age. A value of θ 1 gves the rent-maxmsng case (.e., the unon seeks to maxmse the total rent); values of θ < ( > )1 mply that the unon s less (more) concerned about ages and more (less) concerned about obs). Moreover, the unons ams to maxmse the age bll hen 0. 5 θ
ages (gven the output chosen by frms); n the second stage, frms smultaneously choose ther output level (gven the ages barganed th the unons). We solve for the equlbrum n the usual backard fashon. In the second stage of the game, frms compete on quanttes (the market game). The FOCs of (4) lead to the frms reacton functons 1 q( q) (1 q),, 1,; (7) From (7), e obtan frm s output, for gven, 1 q(, ) (1 + ),, 1,;. (8) 3 In the frst stage of the game, under, the frm-unon barganng unt selects maxmze the follong generalzed Nash product to rt... 1 ( ) ( ) ( ) b b b max N V Π q (1 q q ) q,, 1,; (9) here b represents the barganng poer of the unon. Usng (8), the maxmsaton of (9) th respect to leads to the sub-game perfect best-reply functon n ages of the unon frm par under the assumpton of a non-cooperatve Cournot Nash equlbrum n the product market: b ( ) (1 + ), 1,; (10) 4 Solvng the system of equatons n (10), e obtan the sub-game perfect equlbrum ages: b 4 b /. (11) Further substtuton of (11) nto (8), (4) and (6) determnes, after the usual algebra, the equlbrum values output, profts and unon s utlty 1 b / ( b) q q q 3(4 b) / Π Π Π V V V / 4( b) [ 3(4 b) ] b( b) 3(4 b) (1) (13) (14) The apex e.g. / denotes the choce of the type of barganng arrangement by frms and, respectvely. 6
3.. Effcent Barganng nsttuton. Case A: Smultaneous age and employment negotatons Under the smultaneous effcent barganng, the unon and the management of the frm negotate the ages and employment at the same tme. Gven the assumpton of dentcal unons havng symmetrc poer across unts barganng unts, e have to maxmze the follong generalsed Nash product, rt..., q 1 ( ) ( ) ( ) b b b 1 b max N V Π q (1 q q ) q (15) From the system of frst-order condtons of the effcent barganng game beteen frms and unons, the frms reacton functons n output as ell as the unons ages functons are 1 q( q, ) (1 q ) b,, 1,; (contract curve) (16) ( q, q) b(1 q q),, 1,; (rent-sharng curve) (17) From (16), the frm s output level, for gven [ b(1 ) (1 + ) + )] q(, ) (3 b)(1 b) Substtutng (18) nto (17), e get b[(1 b) + )] ( ) 3 b,, s,, 1,;. (18),, 1,; (19) hch defnes the sub-game perfect best-reply functon n ages of the barganng unt. Solvng the system n (19), e obtan the sub-game perfect equlbrum ages b 3 /. (0) Further substtuton of (0) nto (18), (4) and (6) allos for the dervaton of the equlbrum values of output, profts and unon s utlty q q q 3 (1) / (1 b) Π Π Π 9 () / b V V V 9 (3) / 1 7
Case B: Sequental age and employment negotatons Under the sequental effcent-barganng the unon and the management of the frm negotate the ages and employment at dfferent stages. In the frst stage, each frm-unon par negotates over ages; n the second stage, each unon-frm par bargans the employment level (gven the prevously barganed ages). In other ords, the frm-unon barganng unt selects n the frst stage and n the second stage q. We solve for the equlbrum n the usual backard fashon. In ths case, e have to maxmse the follong generalsed Nash product, b 1 b b 1 b max N ( V) ( Π ) ( q ) (1 q q ) q (4) rt... q here b s the unon s barganng poer. In the frst stage, from the system of FOCs of the effcent barganng game beteen frms and unons, the frms output reacton functons are: 1 q( q, ) (1 q) b,, 1,; (5) From (5), e obtan the frm s output level, for gven [(1 b) + ( b) ] q(, ),, 1,; (6) (1 b)(3 b), : Makng use of (6), n the frst stage the frm-unon barganng unt negotates therefore, maxmses the follong generalsed Nash product: and, rt... b 1 b ( ) ( ) ( ) b max N V Π q (, ) (1 q(, ) q(, ) ) q(, ) The FOCs of the effcent barganng game beteen frms and unons lead to b[(1 b) + ] ( ) ( b) 1 b. (7),, 1,;, (8) hch defne the sub-game perfect best-reply functon n ages of unon frm par. Solvng the system n (8), e obtan the sub-game perfect equlbrum ages, / b(1 b) 4 3b (9) Further substtuton of (9) nto (6) allos for the dervaton of the output level: 8
/ ( b) q q q (4 3 b)(3 b) (30) Fnally, by substtutng both (9) and (30) nto (4) and (6), e obtan the equlbrum profts and unon utltes: / Π Π Π V V V / 4 ( b) (1 b) [(4 3 b)(3 b) ] (31) b( b) (1 b). (3) (4 3 b) (3 b) 3.3 The mxed case: one barganng unt chooses and the other one chooses. Let us consder the case that the barganng unt chooses hle the rval selects. As regards the mxed case, there are three alternatves for ho the rules of the game can be specfed, to of them relates to the smultaneous negotatons and one to the sequental negotatons over age and employment levels. Smultaneous, mxed case 1 (Bughn, 1999; Buccella, 011; Fant, 015): n the second stage, frm and unon bargan over age and employment takng as gven the negotated age at and frm s output. Frm chooses employment for gven age and output of the barganng unt and ts on age at. In the frst stage, the frm and the unon bargan over the age takng as gven the solutons of the producton stage for age and output n and output n. In ths case, frm acts as Stackelberg age folloer,, 1,,. Smultaneous, mxed case (Fant, 015): n the second stage, frm selects ts optmal quantty, takng the age and employment level n as gven. In the frst stage, frm and unon bargan over age and employment takng as gven the negotated age n and frm s reacton functon to frm output decson n the producton stage; frm and unon bargan over the age takng nto consderaton ts on reacton functon to frm output choce n the subsequent producton stage, and takng as gven the age and employment level n. In ths case, frm s Stackelberg output leader,, 1,,. Mxed sequental : n the second stage, frm selects ts optmal quantty, takng ts on age level and the age level n as gven, hle frm and unon bargan effcently over employment. In the frst stage, the frm and the unon n bargan the age level takng as gven ts on reacton functon and the negotated employment n the frm ; the frm and the unon n negotate effcently the age level, takng as gven the reacton functon of frm to the negotated employment n the frm, and ts on effcently negotated employment,, 1,,. In the follong, e examne all the three cases. Smultaneous, mxed case 1 9
The equlbrum outcomes under the mxed olgopoly th the game specfcaton rules n Case 1 are here derved. Assume that the unon-frm par bargans under, hle the unon-frm par negotates under. In the second stage, the unon-frm par negotates over age and employment and, therefore, maxmses (15). Solvng for q the system of the FOCs n (16) and (17), e derve q (1 q ) (33) hch represents frm output as functon of the rval frm s output. On the other hand, from (4), the FOCs for frm determne the reacton functon n (7). Solvng the system composed by (33) and (7) for the frms quanttes, e obtan q (1 + ), (34) 3 the frm s output as functon of the rval frm s age rate and q (1 ) (35) 3 the frm s optmal response as functon of. In the frst stage of the game, the barganng unt under sets takng as gven (34) and (35). The FOCs leads to to maxmze (9), / b (36) 4 the optmal age of the barganng unt under. Further substtuton of (36) nto (34) allos for the dervaton of q / 4 + b, (37) 1 the frm s equlbrum output. Insertng back (36) nto (35), e obtan q / b (38) 6 the frm s output level n equlbrum. Fnally, nsertng (37) and (38) nto (17), the barganed age n frm 1 s / b(4 + b) (39) 1 10
the optmal barganng unt age under. Drect substtutons of the equlbrum quanttes and ages nto (4)-(6) allo to compute the equlbrum profts and unon utltes / (1 b)( b+ 4) / ( b) Π, Π 144 36 (40) / b(4 + b) / b( b) V, V. 144 4 (41) Smultaneous, mxed case The equlbrum outcomes of the mxed duopoly th the smultaneous bargan as n case are here derved. Assume agan that frm negotates th ts unon under, hle frm negotates under. From equaton (4), the frst order condton for frm determnes the best response functon, dentcal to (7). Therefore, makng use of (1), (4) and (7), the maxmzaton problem n (9) for the barganng unt s b 1 b 1 b q max N ( V) ( Π ) ( q ) 1 q q, 1,,. (4) rt..., q The FOCs lead to the follong expressons 1 b q 1+ b (contract curve) (43) b (1 q + ) (rent sharng curve) (44) Solvng the system of equatons (43)-(44) for, e obtan b(1 + ), (45) 4 and consequently q 1+ (46) the frm-unon par output and age as functon of the rval age level. Takng nto account of the on optmal response n the subsequent stage, the barganng problem of the frm-unon par under s to set to maxmse 11
rt... 1 b b b 1 b 1 q 1 q max N ( V) ( Π ) (47) The FOC leads to b(1 q ) (48) the barganed age n unt under as functon of the output n unt. Substtuton of (46) nto (48) allos us for the dervaton of the equlbrum barganed age n unt under / b. (49) 4 + b Further substtuton of (49) nto (45) and (46) leads us to / b( + b) (4 + b) (50) q + b 4 + b / (51) the frm s output level n equlbrum. Further substtutons of (49) and (51) nto the counterpart for of (7), leads us to q / b, (5) (4 + b) the frm s equlbrum output. Smple substtutons of (49)-(5) nto (4) and (6) allo dervng the equlbrum profts and unon utltes / (1 b)( + b) Π (4 + b) V / b( + b) (4 + b), V, / / ( b) Π [(4 + b)] (53) b( b). (4 + b) (54) Mxed sequental Let the frm-unon par ( ) choose (). In the second stage, frm and unon bargan effcently over employment, taken as gven and, and frm s reacton functon, hle frm selects ts optmal quantty, takng as gven and, and the frmunon s barganed output. Therefore, n the second stage, the frm s reacton functon s 1
(7). Gven (7), the frm-unon par maxmses (4) th respect to q, and the barganed employment s equal to q(, ) n (43). Substtuton of (43) nto (7) leads us to q [1 b+ ( + b)]. (55) 3 b Further substtutons of (7) and (55) nto (4) and (47), and subsequent maxmsaton of the Nash Products th respect to and, leads us to (45) for the barganng unt and b(1 + b) ( b) (56) for the barganng unt. Solvng the system of equatons (45) and (56) for obtan and, e / bb [ + ( b)( + b)] 8 b+ [(4 b)(4 + b)] (57) / b(3b 4), (58) 8 b+ [(4 b)(4 + b)] the equlbrum ages n the mxed case th sequental effcent barganng. Further substtutons of (57) and (58) nto (43) and (55) allo us for the dervaton of the equlbrum quanttes q / ( b)[ b+ ( b)( + b)] (3 b)[8 b+ (4 b)(4 + b)] (59) q / ( b) (4 3 b) (3 b)[8 b+ (4 b)(4 + b)] (60) Subsequent substtutons of (57)-(59) nto (4) and (6) allo for the dervaton of the equlbrum values of the profts and unon utltes / 4(1 b)( b) [ b+ ( b)( + b)] Π (3 b) [8 b+ (4 b)(4 + b)] V / b( b)[ b+ ( b)( + b)] (3 b)[8 b+ (4 b)(4 + b)], V, / 4 / (4 3 b) ( b) Π (3 b) [8 b+ (4 b)(4 + b)] b(4 3 b) ( b) (3 b)[8 b+ (4 b)(4 + b)] (61). (6) 4 The equlbrum agendas 13
No e are n poston to conduct the follong analyss. We compare frm s profts and unons elfare under the three labour market nsttutons, and e nvestgate hch barganng agenda ll endogenously emerge n the subgame perfect Nash equlbrum (SPNE) for both frms and unons. 4.1 The game th smultaneous and mxed case 1 Let us frst consder the game th smultaneous and the characterzaton of the mxed case 1. Gven the payoffs n (13), (14), (), (3), (40) and (41), e obtan the subsequent Tables 1 and hch summarse profts and unon s utltes, respectvely, n the four strategc stuatons. An analytcal nspecton allos us to derve the follong results. Proposton 1 (Buccella, 011; Fant, 014) In a unonzed Cournot duopoly th smultaneous and the characterzaton of the mxed case 1, s the domnant strategy for frms; ths s n explct conflct th the unons nterests because s ther domnant strategy as regards the barganng agenda. Therefore, under the endogenous determnaton of the SPNE, no agreement on the barganng agenda may occur beteen unons and frms. The ratonale for ths result s as follos. In the mxed case, the frm th the agenda has hgher negotated ages and produces larger output hen the compettor s a frm th a agenda, and profts for the frm are hgher than those of the frm. The reason s that, because of the common prce for the products and loer ages, the margns for the frm are hgher than the frm. Moreover, loer output and ages for the frm ensure loer total costs. On the other hand, from the unons pont of ve, s the domnant strategy because of hgher negotated ages and employment levels. Table 1: Proft matrx, smultaneous, mxed case 1 Proft Matrx Case 1 Frm 1 4( b) 4( b) 3(4 b) 3(4 b) [ ] (1 b)( b+ 4) 144 ; [ ] Frm ( b) 36 ( b) (1 b) ; 36 9 (1 b)( b+ 4) ; 144 ; (1 b ) 9 14
Table : Unons matrx, smultaneous, mxed case 1 Unon rent Matrx Case 1 Unon Unon 1 b( b) 3(4 b) b( b) 3(4 b) ; b( b) b(4 + b) ; 4 144 b(4 + b) b( b) ; 144 4 b b ; 9 9 4. The game th smultaneous and mxed case Let us consder the game th smultaneous and the characterzaton of the mxed case. Gven the payoffs n (13), (14), (), (3), (53) and (54), e obtan the follong Tables 3 and 4 hch sum up profts and unon s utltes, respectvely, n the four strategc stuatons. A closer analytcal nspecton reveals the follong results. Proposton (Fant, 015) In a unonzed Cournot duopoly th smultaneous and the characterzaton of the mxed case : a) as regards frms, t holds that: hen 1 > b.833, the unque SPNE s /; hen.833 > b.4, there exst to SPN equlbra, / and /; hen.4 > b 0 the unque SPNE s /; b) as regards unons, there exsts a unque SPNE, gven by /, rrespectve of the values of b, that s, s the domnant strategy for unons. Proof: From drect payoff comparson n Tables 3 and 4; see also Fant (015). Table 3: Proft matrx, smultaneous, mxed case Proft Matrx Case Frm 1 4( b) 4( b) [ 3(4 b) ] ; [ 3(4 b) ] (1 b)( + b) ( b) ; (4 + b) [(4 + b)] Frm ( b) [(4 + b)] (1 b) 9 (1 b)( + b) ; (4 + b) ; (1 b ) 9 15
Table 4: Unons matrx, smultaneous, mxed case Unon rent Matrx Case Unon Unon 1 b( b) 3(4 b) b( b) 3(4 b) b( b) b( + b) ; (4 + b) (4 + b) ; b( + b) (4 + b) b( b) b b ; (4 + b) 9 9 ; The results n Proposton are n contrast th those n Proposton 1. The ntuton behnd ths fndng s as follos. It can be easly verfed that the frm hch selects th the mxed case produces more output than n the dentcal stuaton n case 1 by payng loer ages. Therefore, the frm mproves ts margns and, ts proftablty. On the other hand, for b [.4,.833), the frm hch adopts n the mxed case experences an ncrease n ts / / age to a level such that / / Π Π, hle Π >Π. As a consequence, the game shos multple symmetrc equlbra. Fnally, for b [.833,1), the frms payoff / / structure s such that / / Π Π and Π Π : the s the frms domnant strategy. Wth regards to unons, drect payoff comparson shos that, once agan, s ther domnant strategy. Thus, from Proposton and the above analyss, e can derve the follong result. Proposton 3 (Fant, 015) The unambguous agreement beteen unons and frms th regard to the scope of barganng s on the agenda, provded that.4 > b 0. When.833 > b.4, there are multple equlbra: n ths case, the game shos the structure of a coordnaton game for frms. Therefore, n prncple, t could also be possble a coordnaton beteen frms toards the selecton of the agenda. Focusng on the case of multple equlbra for frms (.e. the stuaton.833 > b.4 ), e note that there s also one mxed-strategy equlbrum (see Fant, 015). Moreover, consderng only, for smplcty, the pure-strategy equlbrum selecton problem, t s shon the follong: Proposton 4 (Fant, 015) The equlbrum Pareto-domnates the equlbrum (that s the frms ould coordnate on the equlbrum). The strategc par (, ) rskdomnates the strategc par (, ) f.66 > b 0.(The proof easly follos from Table 3). 3 3 A Nash equlbrum s Payoff-domnant f t s Pareto superor to all other Nash equlbra n the game. On the other hand, a Nash equlbrum s consdered Rsk-domnant f t s less rsky (e.g., Harsany and Selten, 1988). To analogous defntons of the Rsk-domnance n a x symmetrc coordnaton game are the follong: 1) a strategy s Rsk-domnant f t s a best response to a 50-50 randomzaton by the other player; and ) a strategy s Rsk-domnant f t has the smallest probablty n the mxed strategy Nash equlbrum. 16
Therefore, f e assume that the frms are nterested n mnmsng the rsk of coordnaton falure n the selecton of the labour market nsttuton, the unque outcome s the agenda for b 3. To sum up, e have shon that the agenda s the arrangement on hch each frm/unon par may agree th, provded that the unon s barganng poer s ether suffcently lo ( b.4 under pure strateges) or not too hgh ( b 3under rsk-domnance crteron). 4.3 The game th sequental Let us fnally consder the game characterzed by the sequental. Gven the payoffs n (13), (14), (31), (3), (61) and (6), e obtan the follong Tables 5 and 6 hch summarze profts and unon s utltes, respectvely, n the four strategc stuatons. An analytcal nspecton leads to the follong results. Proft Matrx Case Frm 1 Table 5: Proft matrx, sequental Frm 4 (4 3 b) ( b) 4( b) [ 3(4 b) ] ; 4( b) ; (3 b) [8 b+ (4 b)(4 + b)] [ 3(4 b) ] 4(1 b)( b) [ b+ ( b)( + b)] (3 b) [8 b+ (4 b)(4 + b)] 4(1 b)( b) [ b+ ( b)( + b)] (3 b) [8 b+ (4 b)(4 + b)] ; 4 (4 3 b) ( b) (3 b) [8 b+ (4 b)(4 + b)] 4 ( b) (1 b) [(4 3 b)(3 b) ] 4 ( b) (1 b) ; [(4 3 b)(3 b) ] Table 6: Unons matrx, sequental Unon rent Matrx Case Unon 1 b( b) 3(4 b) b( b) 3(4 b) ; b( b)[ b+ ( b)( + b)] (3 b)[8 b+ (4 b)(4 + b)] ; b(4 3 b) ( b) (3 b)[8 b+ (4 b)(4 + b)] Unon b(4 3 b) ( b) (3 b)[8 b+ (4 b)(4 + b)] b( b)[ b+ ( b)( + b)] (3 b)[8 b+ (4 b)(4 + b)] b( b) (1 b) (4 3 b) (3 b) b( b) (1 b) ; (4 3 b) (3 b) ; 17
Proposton 5 In a unonzed Cournot duopoly th sequental : a) as regards frms, t holds that: hen 1 > b.79, the unque SPNE s /; hen.79 > b.61, there exst to SPN equlbra, / and /; hen.61 > b 0 the unque SPNE s /; b) as regards unons, there exsts a unque SPNE, gven by /, for.93 > b 0, hle for 1 > b.93, there exst to SPN equlbra, namely / and /. The results n Proposton 5 as regards frms are smlar to those n Proposton, though vald for dfferent ranges of the barganng poer parameter. In fact, the frm hch selects n the mxed duopoly th sequental barganng produces more output than the rval th, by payng a hgher age, as Fgure 1 shos. Nonetheless, for a suffcently lo value of the unon barganng poer, the total output s not so large to drve don the product prce, and / / the negotated ages are lo enough to ensure that Π >Π, as Fgure depcts. On the other hand, for b [.61,.79), the frm hch adopts n the mxed case experences / / an ncrease n ts barganed age to a level such that Π Π, hle / / Π > Π, leadng to multple equlbra. Fnally, for a suffcently hgh value of the unon barganng poer ( b.79 ), the total output n the mxed duopoly s large enough to reduce the prce at a level that s more proftable. In fact, n the mxed case, the common prce for the goods loers hle the age level pad by the frm s extremely hgh th respect to that of the rval. Fgure 1 Up: Frm Output (left box) and age (rght box) n sequental negotatons; Don: ndustry output 18
Fgure Frm Profts (left box) and unon utlty (rght box) n sequental negotatons When both frms negotate th, the total output s even larger than the mxed case and, the effect s a prce level loer than the mxed case. Consequently e have that / / / / Π > Π and Π Π : s the most preferred agenda for frms. The stuaton for the unons s not only quanttatvely (as for frms, as seen above) but also qualtatvely slghtly dfferent under sequental (rather than smultaneous). In fact, for b (0,.93), s the alays most preferred agenda. Hoever, for b.93, every unon has an ncentve to devate toards the agenda, provded that the rval barganng unt negotates th, and vce versa. Therefore, to asymmetrc equlbra arse. The result that each unon fnds convenent to stch to hen ts poer s very hgh s due to the fact that under sequental ages and unon s utltes tends to strongly reduce for too hgh unon s poer, as clearly dsplayed n Fgs. 1 and. Ths s a feature of the sequental game, because a rse n unon s poer n the stage of employment determnaton mght make the unon even orse off, 4 n that such a rse alters the level of employment for any gven level of the age, and n prncple e can not say hether the barganng set n the frst stage alters n a ay favourable to the unon or the employer. Consequently, e cannot say ho the age ll change. (Mannng, 1987a, 130). 5 Therefore, e may argue that n the present Cournot model an extremely hgh unon s poer alters the level of employment to the extent that n the frst stage ages become relatvely loer. Let us focus on the case of multple equlbra. As regards frms, for.79 > b.61, the game s a standard coordnaton game. In addton to the to pure-strategy equlbra, there s also one mxed-strategy equlbrum. We consder agan only the pure-strategy equlbrum selecton problem, accordng to the Pareto-domnance and Rsk-domnance crtera. Concernng the Pareto-domnance crteron, the frms ould coordnate on the equlbrum: from Table 5, t can be easly checked that domnates. On the other hand, accordng to the rsk-domnance crteron, f e assume agan that each frm assgns a 4 Ths may never occur n a one stage barganng game such as the smultaneous, here an ncrease n the unon s barganng poer alays makes unons better off. 5 As noted by Mannng (1987a, 130, here q s the unon s poer n the stage of the employment barganng) one mplcaton of ths result s that t s concevable that both unon and employer could agree to rase or loer q or, rather more strangely, that the unon mght ant to reduce ts nfluence over employment hle the employer mght ant to ncrease t. 19
probablty of 1 to the and each, then the par (,) rsk-domnates the par (,) f the expected payoff of exceeds the expected payoff of, that s, f / / / / Π +Π Π +Π. Smple algebrac computaton shos that the par (, ) rsk-domnates the par (, ) f.68 > b 0. On the other hand, concernng unons, for 1 > b.93, the game presents the characterstcs of an ant-coordnaton game here nether the Pareto-domnance nor the rsk-domnance crteron allo for the selecton of an equlbrum. These fndngs can be summed up n the next Proposton. Proposton 6 The unambguous agreement beteen unons and frms th regard to the scope of barganng s on the agenda, provded that.61 > b 0. Moreover, the strategc par (, ) rsk-domnates the strategc par (, ) f.68 > b 0. Thus, f e assume agan that the frms are nterested n mnmsng the rsk of coordnaton falure n the selecton of the labour market nsttuton, the unque outcome s the agenda for b.68, a value slghtly hgher than the mxed case. To summarse, also n the presence of sequental negotatons, the agenda s the arrangement on hch each barganng par may agree th, provded that the unon s barganng poer s not too hgh ( b.61 under pure strateges and b.68 under the rsk-domnance crteron). The fndngs of ths secton have shon that, n the negotatons process beteen frms and unons, the specfcaton of the tmng s crucal to determne the endogenous equlbrum agenda. We have shon that only can arses as the endogenous equlbrum arrangement on hch each barganng unt can agree, provded that: 1) the barganng unts concurrently negotate ages n the mxed duopoly as n the smultaneous, case, and sequental. In fact, n those cases, as Fgure 3 shos, the barganed age of the frm s lo enough to make ths agenda suffcently proftable; and ) the unon s poer s ntermedate under pure strateges ( b.4 n the case of smultaneous, mxed case ; b.61 n the case of sequental ) or not too hgh under the rsk-domnance crteron ( b.66 smultaneous, mxed case ; b.68, sequental ). Fgure 3 frm, negotated ages n the mxed duopoly 0
4.4 Dscusson of the outcomes of the three tmng cases of the barganng agenda game The results of ths secton have shon that the endogenous choce of the unon-frm barganng agenda crucally depends on the specfcaton of the tmng. In fact, hen the tmng s specfed as n the mxed case 1, here the frm s Stackelberg age folloer, no endogenous agreement beteen the barganng partes arses (Buccella, 011; Fant, 014). Hoever, n the mxed case, th the frm Stackelberg output leader (Fant, 015) and n the case of mxed sequental barganng, th no leadershp, s the sole nsttuton that can emerge as the endogenous agenda. These fndngs reveal that emerges as equlbrum n the to cases hen ages are concurrently negotated n the rval unts, suggestng that n the mxed case 1, havng knoledge of the age level at the rval frm, the unt does not reduce enough the negotated age to a level to mprove ts proftablty. Moreover, a ne result s that, n sequental barganng, appears as the equlbrum agenda for a range of the unons poer larger than n the mxed case both under pure strateges and the rskdomnance crteron. Ne results also are that unons may prefer and that the mxed agenda s the equlbrum for unons hen ther poer s remarkably hgh. 5 The entry game In the prevous subsectons, e have nvestgated the endogenous selecton of the barganng agenda by consderng a smultaneous game beteen frms and unons. In other ords, e have examned the case here duopoly s the market structure. In the follong, e deal th the ssue of the barganng agenda selecton n the context of market entry. As benchmark, e scrutnse the equlbra that arse hen the frms have the rght to choose the barganng agenda, and then the endogenous selecton. As Bughn (1999) and Buccella (011), e analyse the strategc selecton of barganng scope n negotatons for dfferent market structures, that s, duopoly vs. monopoly th threat of potental entry. We also consder dfferent entry modes and constrants on the choce of barganng scope: 1) commtted barganng, here the ncumbent frst selects ts barganng agenda, and then the entrant s oblged to on the pack and adopt the agenda of the ncumbent; and ) flexble barganng, here the entrant can freely choose ts agenda. Follong Bughn (1999) and Buccella (011), entry n the ndustry s modelled as a change from a monopoly to a duopoly market structure. We denote frm 1 as the ncumbent and frm the potental entrant. The proft functon n (4) for the potental entrant frm no ncorporates the term E, hch represents an exogenous fxed cost. The game, as usual, s solved by backard nducton to derve sub-game perfect Nash equlbra. Dependng on the market structure, the game s a four/fve-stage game. The tmng of the game s the follong. In the frst stage, the ncumbent frm/unon par chooses hch barganng agenda to ntroduce nto negotatons, that s, ether or. In the case of blockaded duopoly (duopoly s the gven market structure), n the second stage the entrant frm/unon par, gven the range of ts possbltes, decdes the barganng agenda to adopt hen there s flexble barganng; or adopt the agenda of the ncumbent par n the presence of the commtted barganng. In the case of monopoly th threat of entry, n the second stage, the potental entrant unt, on the bass of ts possbltes, decdes hether to enter n the ndustry, hereas n the thrd stage t selects the agenda hen there s flexble barganng, or ntroduce the agenda of the ncumbent par hen there s commtted barganng. The last stages of the game are equal to those of secton 3. Fgure 4 depcts the smplfed general frameork. 1
Fgure 4 Tmng of the game, general frameork The analyss of the entry game leads to a rather rch taxonomy. In fact for each of the three tmng characterzatons of the barganng, e have to dstngush for the to cases of blockaded duopoly and monopoly th threat of entry. In turn, for each of the to entry modes, the dstncton s relatve to the dfferent constrants on the choce of the agenda by the entrant frm (.e. commtted vs. flexble barganng). Fnally the analyss s separated accordng to hether the endogenous barganng agenda s chosen only by frms (FC) or n agreement beteen frms and unons (EC). Ths leads to tenty-four dfferent outcomes to dscuss and compare beteen them. 5.1 The game th smultaneous and mxed case 1 Let us frst consder the game th smultaneous and the characterzaton of the mxed case 1. Gven the payoffs n Tables 1 and, and follong Buccella (011), a close analytcal nspecton allos us to derve the follong results. a) Blockaded entry Proposton 7 (Buccella, 011) In a unonzed Cournot duopoly th smultaneous and the characterzaton of the mxed case 1, s the domnant strategy for frms, both under flexble and commtted barganng; ths s n explct conflct th the unons nterests because s ther domnant strategy th regard to the barganng agenda. As a consequence, under the endogenous determnaton of the SPNE, no agreement on the barganng agenda may occur beteen unons and frms. b) Threat of entry On the other hand, n the case of threat of entry, under flexble barganng the ncumbent frm ( M ) selects, agan n conflct of nterest th ts unon. In fact, f the ncumbent selects, the entrant ll devate toard hch guarantees larger profts than the rval frm n the mxed case. Hoever, as Bughn (1999) and Buccella (011) pont up, n the case of commtted barganng, f the fxed costs the entrant has to face are such that (1 b) 4( b) Π < < Π 4 9(4 b) / M / 1 E 1
/ M here Π 1 are the monopoly profts th, a duopoly exsts under, but the ncumbent remans a monopolst f t selects. In ths case, the ncumbent frm may commt to to deter market entry. Bughn (1999) does not derve analytcally the threshold value of the unon barganng poer; hoever, smple algebra shos that the monopoly profts of frm 1 th are larger than duopoly profts f b.73. Because s the unon s most preferred agenda, the barganng partes at each unt have a common nterest n selectng. Proposton 8 summarzes these fndngs. Proposton 8 (Buccella 011) In the case of flexble barganng, the threat of market entry strengthens the argument for the ncumbent frm thout elmnatng the conflct of nterest th ts unon as regards the barganng agenda. By contrast, n the case of commtted barganng, the agenda can be used as a market entry deterrence mechansm, provded that the unon s relatve barganng poer s not too hgh (.e. b <.73). 5. The game th smultaneous and mxed case Let us consder the game th smultaneous and the characterzaton of the mxed case. As benchmark, e analyze the entry game th blockaded entry and frms choosng the barganng agenda. a) Blockaded entry and FC a.1) flexble barganng In the case of flexble barganng, f the ncumbent chooses, the entrant evaluates / / Π e Π. Gven the payoffs n Table 3, e get that the entrant selects because / / Π Π f b.4 hle, f b >.4, the entrant opts for the agenda / / because Π < Π. On the other hand, f the ncumbent chooses, the entrant / / compares Π e Π. In ths case, e get that the entrant selects because / / / / Π Π f b.88, hle t selects for b >.88 because Π < Π. Gven the choces of the entrant, n the frst stage the ncumbent has to evaluate: / / - for b.4, Π 1 and Π 1 : the ncumbent chooses because / / / / Π > Π. Thus, the equlbrum s Π, Π ; 1 1 / / - for.4 < b.88, Π 1 and Π 1 chooses. Therefore, equlbrum s / / - for.88 < b.1, Π 1 and Π 1 : because selects. As a consequence, the equlbrum s These fndngs can be summarsed n the follong Proposton. 1 / / : because Π1 > Π1, the ncumbent / / Π 1, Π ; Π > Π, the ncumbent / / 1 1 / / 1 Π, Π. Proposton 9 In a blockaded unonzed Cournot duopoly th smultaneous and the characterzaton of the mxed case, n the entry game th frms choosng the agenda and 3
flexble barganng, t holds that: hen 1 > b.4, the unque SPNE s /; hen.4 > b 0 the unque SPNE s /. Prop. 9 shos that n the mxed case the results of Prop. 7 does not longer hold, as regards the flexble barganng under FC. Ths s due to the fact that n the mxed case the frm adoptng becomes leader n the output (employment) game (nstead of folloer n the age determnaton game) and thus one frm may fnd convenent to stch from to (hle the rval frm contnues to adopt ). a.) commtted barganng As regards the commtted barganng, the results do not change th respect to Prop. 7. No e turn next to the case of the endogenous choce of the barganng agenda th threat of market entry. b) Threat of entry and FC Proposton 8 s also vald n the case of monopoly th potental entry under both constrants hen frms choose the agenda. Let us no turn the attenton to the case of the endogenous choce of the barganng. a) blockaded entry and EC a.1) flexble barganng Gven the payoffs n Tables 3 and 4 and the above analyss, f the ncumbent chooses : / / - the entrant endogenously selects because Π Π f b.4 ; hoever, / / at the same tme, V V b (0,1) ; - the entrant ould lke to negotate adoptng the agenda f b >.4 because / / / / Π > Π ; hoever, V V b (0,1). Thus, the barganng partes n the entrant unt are n conflct of nterest. On the other hand, f the ncumbent chooses : - the entrant endogenously negotates th the f b.88 because / / and V V b (0,1) ; Π > Π, / / / / - the entrant ould lke to negotate th f b >.88 because Π > Π ; / / hoever, V V b (0,1). Thus, there s conflct of nterest beteen the entrant frm and ts unon. As a consequence, for b.88, the entrant unt endogenously selects. Concernng the / / ncumbent, for 0 b.88, Π > Π : thus, the ncumbent chooses. Moreover, as 1 1 4
/ / regards the unon, t s V1 V1 b (0,1). Therefore, the endogenous choce s. Proposton 10 sums up these fndngs. Proposton 10 In a blockaded unonzed Cournot duopoly th smultaneous and the characterzaton of the mxed case, n the entry game th endogenous choce of the agenda and flexble barganng, t holds that, hen.88 b 0, the unque SPNE s /. Prop. 10 shos that n the mxed case th blockaded entry and flexble barganng the conflct of nterests beteen partes, hch s not resolvable n the mxed case 1 (see Prop. 7), may be elmnated hen unon s poer s suffcently (very) hgh. a.) commtted barganng Concernng the commtted barganng, the results of Proposton 7 hold also n ths case. No e focus on the endogenous choce of the barganng agenda th threat of market entry. b) Threat of entry and EC b.1) flexble barganng In the presence of flexble barganng, e have a novel result and thus the frst part of Prop. 8 does no longer hold, as belo detaled. / M / On the one hand, f s the selected agenda, e have that Π > Π and 1 1 / M / / M Π1 > Π1 here Π 1 denotes the monopoly profts th : the agenda cannot be utlsed as an entry deterrence mechansm. On the other hand, hen s the selected agenda, e have that, for b >.956, f the fxed / M / costs are such that Π1 < E < Π1, the agenda can be used as a tool to prevent market entry n case the entrant barganng unt ould lke to ntroduce negotatons. b.) commtted barganng, M / As regards the commtted barganng, f the fxed costs are such that Π 1 < E < Π 1 the ncumbent and the unon can, also n ths case, ntroduce as market deterrent provded that the unon s relatve barganng poer s b <.73: that s Proposton 8 contnues to hold true. Proposton 11 summarzes these fndngs. Proposton 11 In the case of flexble barganng, can be used as entry deterrence mechansm f b >.956 hen the entrant ould lke to adopt ; cannot be used to deter entry. In the case of commtted barganng, Proposton 8 holds. The man noveltes as regards the mxed case of smultaneous th respect to the establshed results regardng the mxed case 1 concern the flexble barganng case and are that n the blockaded duopoly: 1) s no longer the domnant strategy for frms and also may become the SPNE provded b suffcently lo (.e. b.4 as regards pure strateges); ) there s an agreement on the agenda beteen partes provded a hgh unon s 5
poer (.e. b 0.88); 3) under threat of entry may used to deter entry provded that the unon s poer s very hgh (.e. b 0.956). 5.3 The game th sequental Let us fnally consder the game th sequental. We start the analyss th the case of the frms selectng the agenda and blockaded entry. a) Blockaded entry and FC a.1) flexble barganng In the presence of flexble barganng, gven the frm payoffs n Table 5, f the ncumbent / / has selected, the entrant chooses for b.61 because Π > Π hle, for / / b >.61, the entrant ntroduces the agenda because Π < Π. On the other hand, f the ncumbent has selected, the entrant opts for the for b.79, because / / Π Π, hereas s the preferred agenda for b >.79. Consequently, n the frst stage, the ncumbent compares: / / - for b.61, Π 1 and Π 1 : due to the fact that Π / / chooses. Therefore, the equlbrum s Π, Π ; / / - for.61 < b.79, Π 1 and Π 1 : gven that Π chooses and, thus, the equlbrum of the game s 1 > Π, the ncumbent / / 1 1 / / - for.79 < b.1, Π 1 and Π 1 : gven that Π / ncumbent chooses. Hence, the equlbrum s Π, The results can be summed up n the follong Proposton. > Π, the ncumbent / / 1 1 / / Π 1, 1 Π ; > Π, the / / 1 1 Π. / Proposton 1 In a blockaded unonzed Cournot duopoly th sequental, n the entry game th frms choosng the agenda and flexble barganng t holds that: hen 1 > b.61, the unque SPNE s /; hen.61 > b 0 the unque SPNE s /. Prop. 1 modfes Prop. 9 n the sense that s less lkely the occurrence of the equlbrum. Thus e may state (from the comparson of Props. 7, 9 and 1) that hen frms choose the agenda, the arrangement s 1) alays chosen, rrespectve of the unon s poer, n the mxed case one (here the frm adoptng s a folloer n the age determnaton game); ) chosen f the unon s poer s not too lo (.e. for b.4 ) n the mxed case (here the frm adoptng s a leader n the product market game); 3) chosen only the unon s poer s hgh (.e. for b.61) n the sequental case (here there s a smultaneous choce n each stage of the game by both frms adoptng mxed agendas). a.) commtted barganng 6