Coopetition in a Mixed Oligopoly Market

Transcription

1 Coopetton n a Med Olgopoly Market Duc-De Ngo, Mahto Okura To cte ths verson: Duc-De Ngo, Mahto Okura. Coopetton n a Med Olgopoly Market <halshs > HL Id: halshs Submtted on Feb 008 HL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Coopetton n a Med Olgopoly Market * Duc De NGO LEO, Unversté d Orléans Postal ddress: Rue De los, P 6739, Orléans Cede, France E-mal: duc-de.ngo@laposte.net Mahto OKUR Nagasak Unversty Postal ddress: 4--1, Katafuch, Nagasak, , Japan E-mal: okura@nagasak-u.ac.jp January 5, 008 STRCT In ths study, we am to nvestgate the mpact of prvatzaton on the degree of cooperaton and competton n a med olgopoly market. We consder a duopoly market that comprses one sempublc frm and one prvate frm. Each frm s assumed to determne the level of two types of effort: the cooperatve effort made to enlarge the total market sze and the compettve effort made to ncrease market share. In a contest framework, our results show that the compettve effort level of the sempublc frm s smaller than that of the prvate frm. The more the sempublc frm s concerned for socal welfare, the less t competes. On the bass of average costs, we then analyze the case n whch only the sempublc frm undertakes cooperatve effort. In ths case, the prvate frm behaves as a free rder. Furthermore, we fnd that the sempublc frm epends more cooperatve effort than does the prvate frm. Key words: Coopetton, Med olgopoly, Contests, Free rder. JEL Classfcaton: C7, L13, L33 * The authors apprecate helpful comments from Govann attsta Dagnno, Xaver Galegue, and semnar partcpants at LEO (Unversty of Orleans) and Koshro Ota, kra Maeda, Jun Nakabayash, and partcpants at the 6th Internatonal Conference of the Japan Economc Polcy ssocaton. Mahto OKUR was supported n part by a Grant-n-d for Scentfc Research from Nagasak Unversty, JPN. 1

3 1. Introducton In realty, many frms choose to undertake not only compettve actvtes but also cooperatve actvtes. For eample, lfe nsurance frms may dvulge ther prvate nformaton to ther rvals n order to reduce the ncdence of nsurance fraud, whlst competng vgorously over nsurance premums, qualty and so on. Studes such as those of randenburger and Nalebuff (1996) and Dagnno and Padula (00) descrbe stuatons that contan both cooperatve and compettve actvtes smultaneously n terms of coopetton. Studes on coopetton have developed rapdly, partcularly n recent years, and the concept has been used to eplan many economc and socal phenomena n varous ndustres and n dfferent countres. However, to the best of our knowledge, prevous studes on coopetton have focused on the actvtes of prvate frms or publc frms. In other words, they have not addressed the behavor of the sempublc frm that ams to m proft mamzaton and welfare mamzaton. Eamples are dscussed n the net secton. The purpose of ths study s to nvestgate a stuaton n whch there are both sempublc and (purely) prvate frms n the market. Studes such as those of Merrll and Schneder (1966), Harrs and Wens (1980), ös (1986, 1991), Vckers and Yarrow (1988), and De Fraja and Delbono (1990) descrbe such a market as a med olgopoly market. For a gven set of market condtons, determned, for eample, by the number of frms and the tmng of decsons, the actvtes chosen by sempublc and prvate frms may dffer because of dfferences n ther respectve objectve functons. Specfcally, f one frm s sempublc rather than prvate, how does ths affect market equlbrum? To answer ths queston, we consder the smplest duopoly market that contans one sempublc frm and one prvate frm. Each frm chooses two types of effort level: cooperatve effort made to enlarge the market sze and compettve effort made to ncrease market share. In other words, we develop a coopetton model of effort levels n a med duopoly (olgopoly) market. One specfc am of ths research s to analyze coopetton by usng game theory. lthough researchers such as randenburger and Nalebuff (1996) and Lado et al. (1997) have nssted on the usefulness of game theory for analyzng coopetton, few studes use game theory to analyze ths ssue (see, for eample, Ngo (006) and Okura (007)). However, game theory represents a smple way of formalzng complcated stuatons that ncorporate both cooperatve and compettve behavor (Okura (007)). Thus, t s ratonal to develop an economc model to analyze coopetton.

4 The remander of ths study s organzed as follows. The net secton brefly descrbes actual eamples of med olgopoly. In Secton 3, we revew the related lterature n order to shed lght on the contrbuton made by our research. In Secton 4, we develop a model of cooperatve and compettve effort n a med olgopoly market that contans both prvate and sempublc frms. The model s used to derve several mportant and nterestng results. Concludng remarks are gven n Secton 5.. Eamples of coopetton Nowadays, wth prvatzaton and deregulaton waves n both developed and developng countres, we can fnd many eamples of coopetton n med olgopoly markets. For nstance, the three moble phone operators n the French market, Orange, SFR and ouygues Telecom, ntated a cooperaton project. Orange s a sempublc frm n the sense that 18.17% of ts holdng company, France Telecom, s controlled by the French government. Motvated to enhance the telecommuncatons servces offered to ther clents and thus ncrease ther profts n the saturated French market, these rvals decded to cooperate to offer the best homogenous publc wf servce coverng the whole country. To do so, n October 003, they created the Wreless Lnk ssocaton and have snce attracted nne members of varyng sze and some start-ups. ecause establshng a hgh qualty natonwde wf network s a comple task and requres enormous nvestment n nfrastructure and technology research, no operator can meet ths challenge alone. Hence, cooperaton between these rval operators unfes the complementary nnovatve technques and the dfferent eperences that each member has n dfferent processes, toward provdng a publc wf servce for the common good. Chung (1996) argues that n R&D tournaments, the knowledge generated by all agents may have postve spllover effects on the patentee. In other words, the wnner s proft ncreases wth the total nvestments of all players. Consequently, R&D tournaments among publc and prvate frms can lead to coopetton n a med olgopoly market. nother eample s the case of the Japanese lfe nsurance market 1. In ths market, there are two types of lfe nsurance provders, prvate and sempublc; the latter s Japan Post. In 005, the aggregate nsurance premums of Japan Post amounted to 16,67 bllon (about US$14 bllon). Its premum revenue eceeded that of Japan s largest prvate lfe nsurer Nppon, whch amounted to 4,84 bllon (about US$41 bllon). 1 more detaled eplanaton of ths s gven by Okura and Kasuga (007). 3

5 Thus, one must consder both prvate and sempublc frms n order to understand the Japanese lfe nsurance market. Japan Post was orgnally a completely publc entty, but n 003 t reformed as a sempublc organzaton to mprove ts effcency. Japan Post sells low-amount (less than 10 mllon (about US$87 thousand)) lfe nsurance products termed Kampo. Some types of Kampo are smlar to the nsurance products sold by prvate lfe nsurers. For eample, n 004, Japan Post started sellng blended lfe nsurance products (ncorporatng full-lfe and term nsurance), whch s one of the man lfe nsurance products sold by prvate Japanese lfe nsurers. oth nsurers cooperate to develop a healther and more dscplned lfe nsurance market. For eample, Japan Post was admtted to the Lfe Insurance ssocaton of Japan snce October, 007. Ths assocaton coordnates servces for polcyholders, evaluates moral hazard and so on 3. Japan Post and prvate lfe nsurers are epected to adopt cooperatve strateges to develop ther common nterests. However, both nsurers also compete on premums and quanttes to epand ther market shares. Thus, the Japanese lfe nsurance market can be consdered as a coopettve market. 3. Related lterature In general, economsts model the objectves of publc frms n two ways. One way s to specfy that a publc frm s objectve s pure socal welfare mamzaton (see, for eample, De Fraja and Delbono (1990), and more recently, Whte (1996), Fjell and Pal (1996), Mujumdar and Pal (1998), and Pal (1998)). s an etenson of the frst, the second approach s to specfy that the publc frm s only a partal socal welfare mamzer; see, for eample, ös (1991), and more recently, Matsumura (1998), árcena-ruz and Garzón (003), and Matsumura and Kanda (005). In ths paper, we adopt the second approach. Ths framework s more general than the frst because the latter can be treated as a specal case of the former. In many cases n the past, the state has held, and sometmes stll holds, a nonneglgble proporton of shares n prvatzed frms, and there are a number of frms that have a mture of prvate and publc ownershp. ecause prvatzed Japan Post wll be prvatzed n October 007 and wll change ts name to the Japan Post Co., Ltd. Japan Post wll be dvded nto four stock companes (mal, deposts, lfe nsurance, and networks). However, ths wll not mean complete prvatzaton because the Japanese government holds all the stocks of the holdng company that, n turn, holds all the stocks of the four new stock companes. In other words, after October 007, these companes wll consder not only prvate but also publc benefts. 3 For more detals, see the webpage, [ccessed: December 19, 007] 4

6 frms wth med ownershp must also respect the nterests of prvate shareholders, they cannot behave as pure welfare mamzers. Moreover, our paper s closely related to the nterestng work of Chung (1996) on the endogenzaton of przes n contests. Chung (1996) analyzes the effort levels epended by players and focuses on socal waste n rent-seekng contests, an mportant ssue n the rent-seekng contest lterature, n whch the prze ncreases wth the efforts of all players. Our research s also nspred by Krshnamurthy (1999) and Dearden and Llen (001), who model coopetton n a contest framework. oth study frm behavor under the assumpton that frms collaborate on advertsng to ncrease the total market, so representng the cooperaton aspect, at the same tme as attemptng to ncrease ther shares of that demand, representng the competton aspect. Our work contrbutes to ths lterature n two ways. Frst, whle prevous work assumes that payoff functons of players are smlar, we consder the general case n whch players pursue dfferent objectves and thus have dstnct payoff functons. Second, followng Ngo (006), we employ a two-stage model. s ponted out by Dumez and Jeunematre (006), there are two types of coopetton. In the one-stage game, cooperaton and competton occur smultaneously n a mult-dmenson framework, and n a two-stage or mult-stage game, cooperaton and competton take place sequentally. The mert of modelng coopetton n a contest framework s that t enables one to take nto account agents compettve efforts, whch are neglected n the tradtonal Cournot and ertrand models. Ngo (006) argues that many economc and socal phenomena can be vewed as coopetton contests n whch agents spend resources n order to wn one or more przes. Many eamples of coopetton contests can be found n real lfe: employees compete wth each other for promoton n organzatonal herarches but also work collectvely to develop ther frms; domestc frms compete for market share but also jon together aganst foregn frms; athletes compete for przes but are mutually responsble for attractng a crowd. 4. The model For smplcty, we consder a model of two frms. Suppose that these frms play a two-stage game. Frm s sempublc, whle frm s prvate. 5

7 In the frst stage, both frms choose ther cooperatve effort levels smultaneously. The cooperatve effort level s denoted by y for {, }, whch ncreases the total market. The overall market demand functon s ( a+ y + y ), where a represents ntal demand wthout any cooperatve effort. In the second stage, both frms smultaneously choose ther compettve effort levels, whch are denoted by. Compettve effort levels can enhance ndvdual frms compettve power and market shares. That s, the market share of frm denoted by s s s 1/ where = 0, = 0 =. /( + ) otherwse If there s no compettve effort, the market s dvded equally to two frms. Otherwse, the pe share of frm s determned by the rato / ( + ). Let the nverse demand functon be p ( ). ssume that p '( ) < 0 assumed to be constant and the same for both frms. Then, the objectve functon of frm s 4. verage cost denoted by c s U =Π = p c a+ y + y k k y ( )( ) y + (1) y y, k and where p p( + ) efforts respectvely. ecause frm s a sempublc frm, ts objectve functon s k y y represent the costs of ependng compettve and cooperatve U ( ) Π = αw + 1 α () where W, whch represents the socal surplus, s the sum of the producer's proft and the consumer's surplus; the parameter [ 0,1] α can be nterpreted at two levels. t one level, t represents the weght of the government's partcpaton n the frm. t the other level, t can be regarded as the mportance level 4 Here we consder a determnstc outcome competton n whch each party receves a share of what s under dspute. The equvalent results under a probablstc competton,.e. a wnner-take-all competton, can be derved under the assumpton of rsk neutralty.. 6

8 attrbuted to the government's objectve,.e. the socal welfare, n contrast wth the proft objectve. α = 0 sgnfes that the frm s solely concerned about ts proft. α = 1means that the frm ams to mamze the socal welfare rregardless of ts proft. It follows that Π = + + ( p c)( a y y ) k k y y + Thus, the socal surplus can be wrtten as a+ y+ y 0. (3) ( ) ( ) ( ) y( ) W = p q dq c a+ y + y k + k y + y. (4) To derve the etensve form game, we solve the game by backward nducton. That s, the equlbrum n the second stage s derved on the bass of the frst stage before the frst stage has been played. Once the equlbrum n the second stage s determned, the equlbrum n the frst stage s derved by usng the results from the second stage. The second stage s descrbed below. The frst-order condtons wth respect to are ( 1 α )( p c) ( a+ y + y) k( + ) ( ) U = = 0, (5) + ( p c) ( a+ y + y) k( + ) ( ) U = = + 0. (6) Gven α [ 0,1) =, the equlbrum compettve effort levels are ( 1 α ) ( p c)( a+ y + y ) ( α ) k, (7) = ( 1 α )( p c)( a+ y + y ) ( α ) k. (8) 7

9 and the market shares of publc and prvate frm are 1 α s =, α 1 s =. α When α 1, t s reasonable to assume that 0, = ε (where ε represents a very small postve number) and the market shares are s 0, s 1. These results are used to state the followng lemma. Lemma 1 (compettve effort levels): oth compettve effort levels satsfy ( 1 α ) = (9) Furthermore, the relatonshp between market shares of frm and : s ( 1 α ) = s Proof: From equatons (7) and (8), ( ) = 1 α = 1 α. (10) Q. E. D. Ths mples that the compettve effort level of the sempublc frm s below that of the prvate frm. The more concerned s the sempublc frm for socal welfare (the closer s α to 1), the less t competes. s a result of t, the market share of the publc frm s never bgger than the prvate frm s one. Several comments on the equlbrum cooperatve effort levels shown n equatons (7) and (8) are warranted. In ths contet, consder the case n whch only one varable changes. 8

10 Frst, k < 0 and k < 0 have the smple and ntutve mplcaton that the hgher s the j cost level, the lower s compettve effort. Second, consder the relatonshp between compettve and cooperatve effort levels. From equatons (7) and (8), the followng dervatves are obtaned. 1 ( 1 α ) p 1 c p a y y p c e = = =, (11) y y k k ( 1 α ) { '( + + ) + } ( α) ( α) 1 ( 1 α ) p 1 c p a y y p c e = = = y y k k ( 1 α ){ '( + + ) + } ( α) ( α) (1) ( ). a+ y + y p where e p a+ y + y s the prce elastcty of demand. Thus, f the demand functon s suffcently prce elastc,.e. e> p/( p c) then we have the followng results: () y > 0 mplyng that both types of effort spent by a frm are complements; () y > 0 mplyng that both types of effort spent by two dfferent frms are also complements. y contrast, f the demand s suffcently prce nelastc,.e. e< p/ ( p c) then we have the followng results: () y < 0 mplyng that both types of effort spent by a frm are substtutes; () y < 0 mplyng that both types of effort spent by two dfferent frms are also substtutes. In general, competton and cooperaton are consdered as two polar oppostes, that s, a hgher level of cooperaton naturally leads to a lower level of competton and vce versa. On the contrary, n the coopettve game, the relaton between competton and cooperaton can be postve or negatve dependng on the prce elastcty level of the demand. The followng lemma summarzes these results. j j Lemma (relatonshp between compettve and cooperatve efforts): If e s suffcently large ( e> p/ ( p c) ), then both types of effort are complements. In contrast, f e s suffcently small ( e< p/ ( p c) ), then both types of effort are substtutes. 9

11 Thrd, we nvestgate the effect of α. Dfferentatng equatons (7) and (8) wth respect to α yelds 1 = α ( α )( p c)( a + y + y ) ( α ) k < 3 ( p c)( a+ y + y) 0 ( α ) 3 k α = < α 0, (13). (14) Ths result s plausble. When α ncreases, frm has less ncentve to epand ts market share because t downweghts ts own payoff. Ths stuaton s smlar to the competton à la ertrand snce the competton efforts of frms and are complements, that s / = (1 α) > 0. s a result, both frms reduce ther compettve effort level. t present, we analyze the frst stage of the game. Substtutng equatons (7) and (8) nto equatons (1) and () yelds 1 U = ( p c )( a+ y + y) αp( a+ y+ y) ky( y + αy ) + α p() t dt ( α ) 1 U = p c a+ y + y k y ( ) ( )( ) α y a+ y + y 0 (15). (16) The frst-order condtons wth respect to y are U 1 ' ( ) 1 = p a+ y + y + p c p' a+ y 0 + y kyy =, (17) y ( α) ( ) ( ) ( ) α ( ) α U 1 ' ( ) 1 = p a+ y + y + p c k 0 yy =. (18) y α α ( ) ( ) To obtan nteror solutons from equatons (17) and (18), the followng condton must be satsfed: 1 p' ( a+ y + y) + p c = p 1 c 0. (19) e 10

12 From equatons (17) and (18), the followng proposton can be derved. Proposton 1 (the degree of cooperaton): ( ) 1 Defne that Ω p 1 1 α( α) e and 1 Ω p 1. Then, there are three outcomes for e cooperatve effort levels correspondng to three dfferent average cost levels. Case 1: If average cost s hgh,.e. c >Ω, both frms epend no cooperatve effort. Moreover, equlbrum compettve effort levels are = ( 1 α ) ( p ) ( α ) k c a and ( 1 α )( p c) ( α ) k a =. Case : If average cost s moderate,.e. Ω < c <Ω, only the sempublc frm epends cooperatve effort. The prvate frm free rdes. Case 3: If average cost s low,.e. c < Ω then, both frms epend cooperatve effort. Proof: From equaton (17), the followng condton s necessary for > 0. Ω c > 0. (0) From equaton (18), the followng condton s necessary for > 0 : Ω c > 0. (1) It s easy to verfy the followng nequalty because ( ) 0 α α : Ω < Ω. () From equatons (0) to (), all three cases n relaton to average costs can be derved. If equaton (0) s not satsfed, then the best strategy for both frms s to produce no output ( y = 0 and y = 0). The equlbrum compettve effort levels can be derved by substtutng y = 0 and y = 0 nto equatons (7) and (8). Q. E. D. 11

13 Proposton 1 has nterestng mplcatons. When α rses, case s more lkely to arse because Ω α > 0. Ths property mples that the sempublc frm behaves more lke a publc frm and the prvate frm s more lkely to free rde. In the contet of a quantty-settng olgopoly, n ther poneerng work, De Fraja and Delbono (1990) show that welfare may be hgher when a publc frm mamzes profts rather than welfare. Ther result suggests that, n some cases, a publc frm should be prvatzed so that t mamzes profts rather than welfare. In our coopettve framework, prvatzng publc frms would mtgate the freerder problem. Our fndng s consstent wth that of Matsumura (1998) who shows that, under normal condtons, governments should not hold all the shares. ecause welfare-mamzng behavor by the publc frm n a med duopoly s detrmental, publc frms that are not natural monopoles should be (at least partally) prvatzed. ( 1 α( α ) ) Ω p p Ω The smaller s e, the more lkely s case to arse because = < =. e e e e Ths mples that the lower s the prce elastcty of demand, the more lkely s the prvate frm to free rde. Net, we consder the case n whch equaton (4) s satsfed (that s, both equlbrum cooperatve effort levels are strctly postve). In ths case, followng lemma s satsfed. Lemma 3 (the cooperatve effort levels n case 3): If α = 0, then y = y. If α > 0, then y > y. Proof: We derve the followng equaton by combnng equatons (17) and (18): ( 1 α ){ 1 α( 3 α )} ( α ) Equaton (3) reduces to 1 p ( a + y + y ) ( α ) ( a + y + y ) k y y ' k y y = p' ( 1 α ){ 1 α( 3 α )} 1 ( α ) ( α ) p' ( a + y + y ) = k ( y y ) y. (3) 1

14 ( a + y + y ) = k ( y y ) α p' y ( ) α p' a+ y + y y y = 0. (4) k Ths equaton s satsfed wth strct equalty only f α = 0. y Q. E. D. Usng the lemma 3 to make a general comparson of cooperatve effort levels yelds the followng proposton. Proposton (cooperatve effort levels): The prvate frm has no strategc ncentve to spend more cooperatve effort than the sempublc frm. That s, y y. Proof: In case 1, both cooperatve effort levels are the same (zero). In case, the cooperatve effort level of the sempublc frm eceeds that of the prvate frm because y > 0 and y = 0. In case 3, from the lemma 3, y y whatever the value of α. Q. E. D. 5. Concludng remarks In ths study, we developed a coopetton model of a med olgopoly market. In partcular, we appled game theory to analyze a duopoly market shared by one sempublc frm and one prvate frm. We bult the model to descrbe a coopettve med olgopoly market n whch both publc and prvate frms determne ther levels of compettve effort to epand ther market shares havng chosen ther cooperatve effort levels to mamze the total market sze. 13

15 Our results show that the compettve effort level of the sempublc frm s below that of the prvate frm. The more concerned s the sempublc frm about socal welfare, the less t competes. On the bass of average costs, we then analyzed the case n whch only the sempublc frm epends cooperatve effort. In ths case, the prvate frm behaves as a free rder. Furthermore, we found that the sempublc frm epends more cooperatve effort than does the prvate frm. Our analyss generates many nsghts of nterest to the government, publc and prvate frms. Regardng the government, t can use the prvatzaton level as a mean to regulate the compettveness of publc frms and to mtgate free-rder problem. Our model offers an eplanaton of why publc frms almost always contrbute the most n cooperatve assocatons wth prvate frms but the former often have dffcultes n competng wth the latter. However, our research s ncomplete n several respects. Followng two out of such several aspects are the most nterestng and mportant. Frst, we assumed that both frms choose ther effort levels smultaneously. However, n realty, sempublc frms may choose ther cooperatve effort levels before prvate frms do. For eample, to ncrease socal benefts, Japan Post developed and enlarged the potental demand for ordnary cvlans who had lttle money. To represent ths, a Stackelberg model may be more approprate than a model à la Nash. Second, the etent to whch the sempublc frm cares about socal welfare s mplctly assumed to be common knowledge. Thus, the prvate frm knows the etent to whch the sempublc frm consders the socal surplus. If there s some uncertanty about ths and the prvate frm s rsk averse, the prvate frm may change ts cooperatve and compettve effort levels. These ssues reman open to dscusson. Much addtonal work s requred by future researchers to mprove our model. However, our results have mportant mplcatons for coopetton n med olgopoly markets. 14

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