DEPARTMENT OF ECONOMICS UNIVERSITY OF CRETE. Endogenous managerial incentive contracts in a differentiated duopoly, with and without commitment

Transcription

1 DEPARTMENT OF ECONOMICS UNIVERSITY OF CRETE BE.NE.TeC. Workng Paper Seres Workng Paper: Endogenous manageral ncentve contracts n a dfferentated duopoly, wth and wthout commtment Constantne Manasaks, Evangelos Mtrokostas, Emmanuel Petraks Busness Economcs & NEw TeChnologes Laboratory

2 Endogenous manageral ncentve contracts n a dfferentated duopoly, wth and wthout commtment Constantne Manasaks Evangelos Mtrokostas Emmanuel Petraks June 2009 Abstract In a dfferentated Cournot duopoly, we examne the contracts that frms owners use to compensate ther managers and the resultng output levels, profts and socal welfare. If products are ether suffcently dfferentated or suffcently close substtutes, owners use Relatve Performance contracts. For ntermedate levels of product substtutablty, they use Market Share contracts. When owners do not commt over the types of contracts, each type s an owner s best response to hs rval s choce. Product substtutablty has dfferental effects on output levels and profts, dependng on the confguraton of contracts n the ndustry. Fnally, manageral ncentve contracts are welfare enhancng f they ncrease consumers surplus. Keywords: Olgopoly; Manageral delegaton; Endogenous contracts. JEL classfcaton: D43; L21 Ths s a substantally revsed verson of Endogenous strategc manageral ncentve contracts crculated as Department of Economcs, Unversty of Crete, B.E.NE.Te.C. Workng Paper Seres, No The authors wsh to thank Cham Fershtman, Nkolaos Georgantzs, Mchael Kopel and partcpants at the XXII Jornadas de Economa Industral - JEI2006 meetng - at Barcelona and the ASSET Meetngs 2006 at Lsbon for ther helpful comments and suggestons. Full responsblty for all shortcomngs s ours. Correspondng author. Department of Appled Mathematcs and Department of Economcs, Unversty of Crete, 71409, Heraklon, Crete, Greece. Tel: , Fax: , e-mal: manasaks@stud.soc.uoc.gr. Department of Economcs, Unversty of Crete; e-mal: mtrokostase@erms.soc.uoc.gr. Department of Economcs, Unversty of Crete; e-mal: petraks@erms.soc.uoc.gr. 1

3 1 Introducton It s well establshed that n modern frms, where ownershp and management are separated (Fama and Jensen, 1983), one of the key aspects of corporate governance codes relates to manageral compensaton decson-makng (van Wtteloostujn et al., 2007). Wthn ths framework, exstng evdence suggests that owners desgn ther managers compensaton contracts so as to motvate them to gan a compettve advantage n the market (Murphy, 1999; Jensen et al., 2004). The strategc use of manageral ncentve contracts has been ntroduced n the lterature by the path-breakng papers of Vckers (1985), Fershtman (1985), Fershtman and Judd (1987) and Sklvas (1987). In ths lne of research, each owner has the opportunty to compensate hs manager wth an ncentve contract, combnng own profts and sales or revenues, n order to drect hm to a more aggressve behavor n the market, so as to force the rval frm to reduce output. 1 Emprcal studes by Jensen and Murphy (1990) and Lambert et al. (1991) report that manageral compensaton s often assocated wth frms profts and sze, as measured by sales or revenues. In a smlar ven, Gbbons and Murphy (1990), along wth Joh (1999) and Aggarwal and Samwck (1999) report that a wdely used practce among frms owners, when desgnng ther managers compensaton contracts, s to take nto account the relatve performance of own profts aganst ther rvals profts. Mller and Pazgal (2001; 2002; 2005) formalze these arguments wth the relatve performance contracts, where a manager s compensaton s a lnear combnaton of own profts and the relatve performance aganst the rvals profts. In ths case too, frms end up n a prsoners dlemma stuaton. However, frms profts are hgher than the respectve under contracts combnng own profts and sales or revenues. From another perspectve, Peck (1988) and Borkowsk (1999) menton that market share s hghly ranked n managers objectves and Jansen et al. (2007) and Rtz (2008) offer formal analyses of contracts combnng own profts and own market share. 1 In partcular, n the above seres of papers, n two-staged olgopoly models, n the frst stage of the game, proft-maxmzng owners choose compensaton schemes for ther managers that are lnear combnatons of own profts and ether own sales or own revenues. In the second stage, managers, knowng compensaton schemes, compete n quanttes. Each owner, when determnng hs manager s ncentves, has an opportunty to become a Stackelberg leader, provded that the rval owners do not delegate output decsons to managers. In equlbrum, all owners act n the same way at the game s contract stage and frms end up n a prsoners dlemma stuaton wth relatvely hgher output and lower profts. 2

4 The lterature, so far, seems to seek for an explanaton regardng the emergence of the dfferent types of manageral ncentve contracts. In ths context, Jansen et al. (2009) fnd that n a Cournot model wth product homogenety, frms owners have domnant strategy to compensate ther managers wth relatve performance contracts. Our paper contrbutes to the relevant lterature by nvestgatng the mpact of product substtutablty on the types of contracts that frms owners choose to compensate ther managers, as well as on the resultng output levels, profts and socal welfare. In partcular, the present paper attempts to address the followng four questons. Frst, what s the effect of product substtutablty, and the respectve compettveness n the fnal good market, on the output levels set by managers and the resultng frms profts? Second, how does the degree of product substtutablty affect the frms owners decsons, regardng the types of contracts that they wll choose to compensate ther managers? Our thrd queston has been motvated by a careful revew of the exstng lterature n the feld of strategc manageral ncentve contracts. Ths lterature has been grounded on the assumpton that frms owners commt over the types of contracts that they choose to compensate ther managers. Then, the queston that easly arses s whether the results obtaned wth ex-ante commtment stll hold wthout commtment. The fnal queston that the present paper addresses s relevant to the socetal effects of the dfferent manageral ncentve contracts. To address the above questons, we buld upon Jansen et al. (2009) framework, wth one mportant departure. We assume that the two competng frms produce dfferentated nstead of homogeneous products. In ths envronment, we consder a three-staged game wth observable actons: In stage one, each frm s owner commts to one type of contract to compensate hs manager. More specfcally, each owner commts to a contract that s a lnear combnaton of own profts and ether own revenues (Profts-Revenues contract), or compettor s profts (Relatve Performance contract) or, fnally, own market share (Market Share contract). In the second stage of the game, gven that the types of contracts have become common knowledge and can not be reset, each owner sets the weght (manageral ncentve parameter) between own profts and ether own revenues, or compettor s profts, or own market share. At the fnal stage, managers compete n quanttes. We argue that the effect of product substtutablty on the output levels set by managers and 3

5 the resultng frms profts depends crucally on the confguraton of contracts. In the symmetrc confguratons where both owners compensate ther managers ether wth Profts-Revenues or wth Relatve Performance contracts, output and profts decrease n the degree of product substtutablty. The reason s that as products become closer substtutes, the market segment that each frm explots decreases. A drect consequence s that the output level that each manager sets and the resultng profts decrease as products become closer substtutes. On the contrary, when both managers are compensated wth Market Share contracts, the aforementoned negatve product dfferentaton effect s domnated by the postve competton effect accordng to whch, as products become closer substtutes and competton for market share among managers becomes fercer, each manager tends to ncrease output. Ths tends to ncrease profts too. Regardng the asymmetrc confguratons, where managers are compensated wth contracts of dfferent types, we dentfy that product substtutablty has dfferental effects on output levels and profts. In partcular, the output level set by the manager who s compensated wth the advantageous contract, n terms of output expanson and profts, hasau-shapedrelatonnthe degree of product substtutablty. Intutvely, as products become closer substtutes, ths manager ncreases the output level n order to explot the compettve advantage that hs contract gves hm. On the contrary, the output level set by the rval manager decreases as products become closer substtutes. Frm s profts follow the same pattern as the output level n each case. As far as the second queston s concerned, we show that the types of contracts that owners choose to compensate ther managers depend crucally on the degree of product substtutablty. In partcular, when products are suffcently dfferentated, owners compensate ther managers wth Relatve Performance contracts. Intutvely, Relatve Performance contracts result n a relatvely more severe overproducton stuaton, as compared wth the respectve of Market Share contracts. Ths overproducton stuaton has two effects on profts. On the one hand t tends to ncrease profts but on the other hand, t tends to decrease them through prce decrease. Our analyss suggests that the overproducton s postve effect on profts s stronger under Relatve Performance contracts, rather than the respectve under Market Share contracts. Hence, owners compensate ther managers wth Relatve Performance contracts. For ntermedate levels of product substtutablty, owners choose to compensate ther managers wth Market Share con- 4

6 tracts. Ths s so because the prsoners dlemma stuaton, characterzed by relatvely hgher output and lower profts, under Market Share contracts s less severe than the respectve under Relatve Performance contracts. Ths reasonng s reversed f products are suffcently close substtutes, n whch case owners compensate ther managers wth Relatve Performance contracts. Our fndngs further suggest that gven an owner s choce, over the type of contract to compensate hs manager, hs rval s best response s a contract of the same type. Then, we examne the case where there s no ex-ante commtment over the types of contracts that owners choose to compensate ther managers. In ths envronment, the followng twostaged game s studed: n the frst stage, each frm sownerchoosesthetypeofcontractand sets the correspondng manageral ncentve parameter. Hence, we assume that the precse contract (the type of contract and the manageral ncentve parameter) that each owner sets s not observable by the rval owner, before contract-settng s everywhere completed. In the second stage, managers compete n quanttes. Interestngly enough, we fnd that each type of contract can be an owner s best response to the rval owner s choce. The ntutve explanaton behnd ths fndng s based on the condtons that must be fulflled n equlbrum: frstly, snce producton decsons are taken by managers, n equlbrum, ther reacton curves must be ntersected. Secondly, the fact that a frm s owner offers an ncentve contract to hs manager, as a strategc tool n order to become Stackelberg leader aganst the rval frm, standard textbook analyss of the Stackelberg model mples that, n equlbrum, there must be tangency between ths frm s soproft curve and the rval frm manager s reacton curve. Regardng the fourth queston, we fnd that the symmetrc use of manageral ncentve contracts by frms owners s welfare enhancng, compared to the benchmark case of No-delegaton, except f owners compensate ther managers wth Market Share contracts and products are suffcently close substtutes. We also fnd that socal welfare n the asymmetrc confguratons of contracts les between the respectve levels n the symmetrc confguratons. Our analyss also suggests that socal welfare decreases n the degree of product substtutablty, because of the domnant negatve product dfferentaton effect. Comparng our results wth those obtaned n Jansen et al. (2009), who restrct ther attenton to the case of homogeneous products, the followng observatons are n order. Frst, we dentfy the dfferental effects of product dfferentaton on the output levels set by managers 5

7 under the dfferent confguratons of contracts. Second, we reconfrm Jansen et al. (2009) result that frms owners compensate ther managers wth Relatve Performance contracts, when products are perfect substtutes. Moreover, we fnd that ths s an equlbrum whenever products are ether suffcently dfferentated or suffcently close substtutes. On the contrary, for ntermedate degrees of product substtutablty, we fnd that owners use Market Share contracts. Thrd, Jansen et al. (2009) state that whenever an owner compensates hs manager wth a Relatve Performance contract whle the rval owner uses ether a Profts-Revenues or a Market Share contract, the former owner drects hs manager towards the maxmum level of aggressveness and the latter owner s best response s to drect hs manager towards a strct proft-maxmzng behavor. 2 Our analyss suggests that ths s an equlbrum stuaton but only n the polar case of homogeneous products. For the remanng spectrum of product substtutablty, we fnd that the latter owner sets the manageral ncentve parameter at a level that drects hs manager away from strct proft-maxmzaton. Note also that our paper s a frst attempt to evaluate the socetal effects of the dfferent manageral ncentve contracts. The only excepton s van Wtteloostujn et al. (2007) who compare the welfare effects of symmetrc profts-sales contracts and symmetrc relatve performance contracts wth the respectve n the benchmark case of Nodelegaton. However, they don not compare socal welfare across the dfferent confguratons of contracts. The rest of the paper s organzed as follows. Secton 2 presents the model. In Secton 3, we study the equlbrum manageral ncentve contracts wth owners commtment and n Secton 4, we carry out the respectve analyss under no-commtment. Secton 5 ncludes the welfare analyss. Fnally, Secton 6 concludes. 2 The Model Our model bulds upon Jansen et al. (2009) framework, wth one mportant departure. We assume that the two competng frms produce dfferentated nstead of homogeneous products. In partcular, we assume that each frm faces the followng (nverse) demand functon: 2 See Proposton 1 n Jansen et al. (2009, p. 146). 6

8 P =1 q γq j,,j =1, 2, 6= j, 0 <γ 1 (1) where p and q are, respectvely, the prce and quantty of frm s product, q s the quantty of ts rval s product, and γ s the degree of product substtutablty. Namely, the hgher s γ, the closer substtutes the two products are. 3 We further assume that frms have equally effcent producton technologes, reflected n constant margnal producton costs,.e. c = c j = c<1. Thus,frm s profts are gven by: Π =(1 q γq j c) q (2) In ths ndustry, each frm has an owner and a manager. Followng Fershtman and Judd (1987), owner, s a decson maker whose objectve s to maxmze the profts of the frm. Ths could be the actual owner, a board of drectors, or a chef executve offcer. Manager refers to an agent that the owner hres to make real tme operatng decsons. Each frm s owner has the opportunty to compensate hs manager by offerngtohma taket-or-leave-t ncentve contract. 4 In partcular, each owner chooses one among three dfferent types of contracts. The frst type s the Profts-Revenues (PR) one. Followng Fershtman and Judd (1987) and Sklvas (1987), under ths type of contract, the ncentve structure takes a partcular form: the rsk-neutral manager s pad at the margn, n proporton to a lnear combnaton of own profts and own revenues. More formally, frm s manager wll be gven ncentve to maxmze: U PR = a PR Π +(1 a PR )R (3) where Π and R are frm s profts and revenues respectvely. 5 a PR s the manageral ncen- 3 Note that under ths demand functon, hgher product dfferentaton (lower γ) leads to hgher market sze. 4 In the strategc delegaton lterature, t s a regular assumpton that frms owners have all the barganng power durng negotatons wth ther managers,.e., they offer to ther managers take-t-or-leave-t ncentve contracts (see Vckers, 1985; Fershtman and Judd, 1987; Sklvas, 1987; and Mller and Pazgal, 2001; 2002; 2005, Jansen et al, 2007; 2009, Rtz, 2008). The only excepton s van Wtteloostujn et al. (2007), where the owner and (canddate) manager bargan over the manageral ncentve parameter, soastheownertomaxmzeprofts and the manager to optmze bonus. 5 Followng Fershtman and Judd (1987), U PR reward s lnear n profts and sales, he s pad A + B U PR wll not be the manager s reward n general. Snce the manager s for some constants A, B,wthB > 0. Snce he s 7

9 tve parameter that s chosen optmally by frm s owner so as to maxmze hs profts. We assume that a PR [0, 1]. Observe that f a PR =1, manager s behavor concdes wth owner s objectve for strct proft-maxmzaton. If a PR < 1, frm s manager moves away from strct proft-maxmzaton towards ncludng consderaton of sales and thus, he becomes a more aggressve seller n the market. The second type of contract s the Relatve Performance (RP) one. Followng Mller and Pazgal (2001; 2002; 2005), under ths type of contract, frm s owner compensates hs manager puttng unt weght on own profts and a weght a RP utlty functon takes the form: 6 on rval s profts. Thus, manager s U RP = Π a RP Π j (4) As n Jansen et al. (2007; 2009) we further assume that a RP [0, 1]. Hence, we do not allow owners to drect ther managers towards colluson. If a RP =0, manager s behavor concdes wth owner s objectve for strct proft-maxmzaton. As a RP 1, manager becomes a more aggressve seller n the market. The thrd type of contract s the Market Share (M )one. AsnJansenet al. (2007; 2009) and Rtz (2008), under ths type of contract, frm s owner compensates hs manager wth a contract consttuted by a lnear combnaton of own profts and own market share. In ths case, manager s utlty functon takes the form: U M = Π + a M q q + q j (5) wth a M beng the respectve manageral ncentve parameter optmally chosen by owner n order to maxmze hs profts. In order to examne whch types of manageral ncentve contracts wll frms owners choose to compensate ther managers, we consder a three-staged game wth observable actons: n the frst stage, each frm s owner commts to one among the three dfferent types of contracts. Then, n rsk-neutral,heactssoastomaxmzeu PR and the values of A and B are rrelevant. 6 In Mller and Pazgal (2002), owner compensates hs manager puttng weght of (1 a RP ) on own profts and a weght a RP on the dfference between own profts and the rval frm s profts, mplyng that U RP (1 a RP )Π + a RP (Π Π j ).Thssequvalenttoeq.(4). = 8

10 the second stage of the game, gven that the types of contracts have become common knowledge and can not be reset, each owner sets the correspondng manageral ncentve parameter a D, D : PR, RP, M. In the thrd stage of the game, managers compete alàcournot. 7 The equlbrum concept employed s the subgame perfect equlbrum. 3 Equlbrum manageral ncentve contracts under commtment In ths part of the paper we consder that frms owners commt over the types of contracts that they choose to compensate ther managers. The payoffs of the dfferent subgames are presented n the followng Payoff Matrx. The representaton of the game n the strategc form OWNER 2 PR RP M PR Π pr 1, Πpr 2 Π pr rp 1, Π pr rp 2 Π pr m 1, Π pr m 2 OWNER 1 RP Π rp pr 1, Π rp pr 2 Π rp 1, Πrp 2 Π rp m 1, Π rp m 2 M Π m pr 1, Π m pr 2 Π m rp 1, Π m rp 2 Π m 1, Πm 2 Due to symmetry, the number of canddate equlbra s reduced to sx, namely: Symmetrc Profts-Revenues Contracts (pr), Symmetrc Relatve Performance Contracts (rp), Symmetrc Market Share Contracts (m), Coexstence of Relatve Performance and Profts-Revenues Contracts (rp-pr), Coexstence of Relatve Performance and Market Share Contracts (rp-m), 7 At ths pont, t s useful to bear n mnd two alternatve nterpretatons of the game. Accordng to the frst one, followng Fershtman and Judd (1987) and Sklvas (1987), an owner hres a manager and drects hm through an approprate ncentve contract. The alternatve nterpretaton s the one presented by Mller and Pazgal (2002), where, the problem faced by the owner of each frm s to choose the best type of manager among those that are avalable, whle each manager s commtted to behavng n a certan manner by vrtue of hs personalty type. More specfcally, n Mller and Pazgal (2002), potental managers take on a contnuum of atttudes toward relatve performance whch s captured by ther type, ϕ. However, the dfference between Fershtman and Judd (1987) and Mller and Pazgal (2002) s only semantc, snce owners have all the barganng power (by assumpton) when settng the contracts. 9

11 Coexstence of Market Share and Profts-Revenues Contracts (m-pr). 8,9 Let us begn our analyss by nvestgatng the effects of the dfferent contract types on managers behavor n the output competton stage of the game. The reacton curve of a PRcompensated manager s gven by q PR (q j )= 1 2 (A γq j a PR c). Ths mples that manager consders a PR c as the margnal cost of producton. For a PR (0, 1], ths margnal cost s lower than that consdered by the owner hmself n the benchmark case of No-delegaton. Thus, the lower the manageral ncentve parameter set by owner, the hgher the aggressveness of hs manager and the hgher the output level that the latter sets. Note also that the slope of manager s reacton curve s dqpr dq j = γ 2. Hence, as γ 1 and products become closer substtutes, manager s best response to manager j decreases. Moreover, dqpr dq j = dqc dq j suggests that the PRcompensated manager s reacton curve s an outward and parallel shft of the respectve curve n the benchmark case of No-delegaton. Regardng an RP-compensated manager, hs reacton curve n the last stage of the game s gven by q RP (q j )= 1 2 A c γ 1 a RP qj, mplyng that manager consders γ 1 a RP as the rval manager s best response. Snce a RP qj [0, 1], γ 1 a RP qj γqj C suggests that the rval s best response that an RP-compensated manager antcpates s lower than that antcpated by an owner n case of No-delegaton. An mmedate consequence s that an RPcompensated manager sets output at a level hgher than that set by an owner. Regardng the slope of manager s reacton curve, t s gven by dqrp dq j = 1 2 γ 1 a RP, suggestng that as γ 1 and products become closer substtutes, manager s best response to manager j decreases. Dagrammatcally, the manager s reacton curve s the benchmark s one rotated through the ntercept. Fnally, the reacton curve for an M-compensated manager s gven by ϑu M = A c dq M 2q M γq j + am q j =0. Ths reacton curve s a thrd-degree, dfferentable and concave (q M +q j) 2 8 The frst four canddate equlbra (pr, rp, m, rp-pr) were solved analytcally for obtanng manageral ncentve parameters, quanttes and profts. See Appendx A1-A4. The respectve results for the last two canddate equlbra (rp-m, m-pr) were obtaned through numercal smulatons. See Appendx A5-A6. Further detals are avalable from the authors upon request. 9 As a benchmark, we consder the No-delegaton case where producton decsons are taken by frms owners. In ths case, the reacton functon n the output competton stage s q c (qj)=(a c c γqj)/2 c whle equlbrum output, profts and total welfare are q c =(A c)/(2 + γ), Π c =(q c ) 2 and TW c =(3+γ)(A c) 2 /(2 + γ) 2 respectvely. 10

12 functon. Dagrammatcally, ths reacton curve s (slghtly) hll-shaped and after a relatvely short nterval, t turns negatvely sloped (Jansen et al., 2007). Let us now nvestgate the mpact of product dfferentaton on output levels and profts under the dfferent canddate equlbrum confguratons of contracts. The followng Proposton summarzes: Proposton 1 () When both owners compensate ther managers ether wth Profts-Revenues or wth Relatve Performance contracts, frm s output level and profts decrease n γ. () When both owners compensate ther managers wth Market Share contracts, frm s output level (profts) ncreases (decrease) n γ. () In the asymmetrc confguratons of contracts (rp-pr, rp-m, m-pr), frm s output level and profts have a U-shaped relaton n γ, wth the mnmum attaned around γ =0.8, andfrm j s output and profts decrease n γ. Accordngtothefrst part of Proposton 1, the ntuton goes as follows. Recall that the hgher the degree of product dfferentaton (lower γ), the hgher the sze of the market and the respectve market segment that corresponds to each frm. As γ ncreases, the brands sold become closer substtutes and as a result, the sze of the market and the segment that each frm explots decrease. Hence, as γ 1, thsnegatve product dfferentaton effect becomes more severe and the output level set by manager decreases too. An mmedate consequence s that frm s profts also decrease n γ. In the symmetrc confguraton of M contracts, the degree of product substtutablty has a twofold mpact on output levels. On the one hand, as γ 1 the aforementoned negatve product dfferentaton effect tends to decrease the output level set by each manager. On the other hand, as γ ncreases and products become closer substtutes, competton among managers for ganng hgher market share becomes fercer. Hence, each manager tends to ncrease output. The latter postve competton effect domnates the negatve product dfferentaton effect and thus, as γ 1 the output level set by manager ncreases. In turn, ths overproducton tends to ncrease revenues and profts but t decreases prces that subsequently tend to decrease profts. Ths latter negatve prce effect domnates the postve output effect and frm s profts decrease n γ. 11

13 Regardng the asymmetrc confguratons of contracts, the ntuton behnd our result goes as follows. Note frst that q rp pr > q rp pr j, q rp m >q rp m j and q m pr >q m pr j always hold. The respectve nequaltes for profts hold too. These nequaltes underlne the relatve compettve advantage (n terms output expanson and profts) between managers compensated wth dfferent types of contracts. Hence, Proposton 1() suggests that the output level set by manager, who explots the relatve compettve advantage aganst hs rval, has a U-shaped relaton n γ wth the mnmum attaned around γ =0.8. Intutvely, for suffcently dfferentated products (low γ), the output level set by both managers decreases n γ because of the negatve product dfferentaton effect. But, as γ ncreases and products become closer substtutes, manager ncreases the output level n order to explot the compettve advantage that hs contract gves hm. Clearly, frms profts follow the same pattern as the output levels n each confguraton of contracts. Let us now compare the equlbrum output levels under the dfferent confguratons of contracts, n order to capture ther relatve compettveness. The followng Corollary summarzes our fndngs: Corollary 1 () q pr >q rp >q c. () q m >q c,fandonlyf γ> () q pr >q m. (v) q m >q rp,fandonlyf γ> (v) In each asymmetrc confguraton of contracts (rp-pr, rp-m, m-pr), each frm s output level les between the respectve levels n the symmetrc confguratons. The followng observatons are n order. Frst, the symmetrc use of ether PR or RP manageral ncentve contracts ncreases output, as compared to the benchmark of No-delegaton. The ntuton goes as follows. Owner, by compensatng hs manager wth an ncentve contract drects hm to a more aggressve behavor n order to force the rval manager to reduce output. Because each owner acts n the same way at the game s contract stage, frms end up n an overproducton stuaton. 10 Note also that ths overproducton ncreases as products become 10 These fndngs are n the sprt of the well-known result n the ndustral organzaton lterature, accordng to whch, frms competng n quanttes have no ncentve to engage n Stackelberg warfare. 12

14 and d(qpr q rp ) dγ d(q pr q c ) dγ closer substtutes (hgher γ) and competton becomes fercer,.e. > 0, d(qrp q c) dγ > 0 > 0. Second, the symmetrc use of M contracts results n overproducton, as compared to the benchmark of No-delegaton, but only f products are suffcently homogeneous,.e. γ>0.666, and competton among managers for ganng market share s too ferce. Thrd, regardng the relatve severty of the overproducton stuaton, we fnd that t s the most ferce n case of PR contracts, whle t s more ntense under M contracts rather than under RP contracts whenever products are hghly substtutable,.e. γ>0.881, and competton s too ferce. We now turn to the frst stage of the game and nvestgate the types of contracts that owners wll choose to compensate ther managers. The followng Proposton summarzes: Proposton 2 When frms owners commt over the types of contracts that they choose to compensate ther managers: () When products are ether suffcently dfferentated (γ 0.242) or suffcently close substtutes (γ 0.881), owners compensate ther managers wth Relatve Performance contracts. () For ntermedate degrees of product substtutablty (0.243 <γ<0.881), owners compensate ther managers wth Market Share contracts. The ntuton behnd these results goes as follows: When γ<0.881, t holds that q rp (Corollary 1(v)), whch n turn mples that p rp <p m.thsquantty (prce) effect suggests that profts under RP-compensated managers tend to be hgher (lower) than the respectve under M-compensated managers. It proves that for suffcently dfferentated products,.e. γ 0.242, the quantty effect on profts s stronger under RP contracts, rather than under M contracts. Hence, owners compensate ther managers wth RP contracts. >q m For ntermedate degrees of product substtutablty,.e <γ<0.881, t s the prce effect that s stronger under RP contracts, rather than under M contracts, and owners choose to compensate ther managers wth M contracts. When products are suffcently close substtutes,.e. γ 0.881, t holds that q m >q rp. In ths case, frms owners realze that compensatng ther managers wth M contracts would result n a relatvely more severe prsoners dlemma stuaton, characterzed by relatvely hgher output and lower profts, than the respectve under RP contracts. In order to avod ths too ferce prsoners dlemma stuaton, owners choose to compensate ther managers wth RP contracts. 13

15 Note also that owners wll never choose to compensate ther managers wth PR contracts. Ths happens because these contracts result n the most severe prsoners dlemma stuaton (Corollary 1(), ()). Last, but not least, we fnd that for each γ-area stated above, no owner has ncentves to devate from the respectve symmetrc equlbrum confguraton of contracts. 11 Ths suggests that gven owner s choce, over the type of contract to compensate hs manager, owner j s best response s a contract of the same type. 4 Equlbrum manageral ncentve contracts under no-commtment So far analyss, as well as the bulk of the receved lterature n the feld of strategc manageral ncentve contracts, consders that frms owners commt over the types of contracts that they choose to compensate ther managers. In ths part of the paper we nvestgate the case where there s no such ex-ante commtment. We do so by consderng a two-staged game wth the followng tmng: n the frst stage, each frm s owner chooses one type of contract to compensate hs manager and sets the correspondng manageral ncentve parameter. The crucal, yet (due to the symmetrc ndustry) reasonable assumpton here s that the precse contract (the type of contract and the manageral ncentve parameter) that owner sets s not observable by the rval owner, before contract-settng s everywhere completed. 12 Ths mples that each owner can ndependently shft from one type of contract to another. In the second stage of the game, managers compete alàcournot. Thus, we propose a confguraton of contracts, as a canddate equlbrum, and subsequently check whether or not t survves all possble devatons, at the frst stage. If yes, the proposed equlbrum s a sub-game perfect Nash equlbrum. Let us consder the Symmetrc Profts-Revenues Contracts, as a canddate equlbrum. Fgure 1 offers the vsualzaton of ths canddate equlbrum (pont E PR ). Note that n equlbrum, 11 The detaled proof s avalable from the authors upon request. 12 A crucal assumpton of the relevant lterature s that delegaton s observable. Katz (1991) argues that unobservable contracts have no commtment value at all. Fershtman and Judd (1987) support that even f contracts are not observable, they wll become common knowledge when the game s beng repeated for several perods. More recently, Kockesen and Ok (2004) argue that to the extent that renegotaton s costly and/or lmted, n a general class of economc settngs, strategc aspects of delegaton may play an mportant role n contract desgn, even f the contracts are completely unobservable. 14

16 two condtons must be fulflled: frstly, snce producton decsons are taken by managers, ther reacton curves RC1 PR and RC2 PR must be ntersected. Secondly, the fact that frm s owner offers an ncentve contract to hs manager, as a strategc tool n order to become the Stackelberg leader aganst frm j, mples that n equlbrum there must be tangency between frm s soproft curveπ and manager j s reacton curve RCj PR. Symmetrc Profts-Revenues Contractssanequlbrumconfguraton only f no owner has an ncentve to unlaterally devate, n the frst stage of the game, by offerng to hs manager ether an RP or an M contract. Of course, such a devaton has to be proftable for the owner. Suppose, for nstance, that owner 2 stcks to the PR contract, belevng that owner 1 wll compensate hs manager wth the same type of contract. Thus, n the frst stage of the game owner 2 sets a pr 2 = γ2 2c(2+γ) c(γ 2 2γ 4). Consder now that owner 1 devates towards compensatng hs manager wth an RP contract. In ths case, owner 1 uses hs stage 1 reacton functon a rp pr 1 (a pr 2 ) to optmally adjust a 1 for hs manager s contract. 13 Thus, n the frst stage of the game owner 1 sets a pr 1d = γ2 2c(2+γ) c(γ 2 2γ 4). Observe that apr 2 = arp pr 1d. Interestngly enough, the devant owner 1 s profts wll be Π pr, mplyng that the magntude of owner 1 s ncentve to devate from 1d = Πpr 1 the Symmetrc Profts-Revenues confguraton towards compensatng hs manager wth an RP contract, s zero. Dagrammatcally, when owner 1 devates from the Symmetrc Profts-Revenues confguraton towards compensatng hs manager wth an RP contract, owner 1 drects hs manager to the reacton curve RC1 RP and, by readjustng the manageral ncentve parameter, optmally readjusts ts slope untl RC RP 1. However, the manager of the devant owner sets output at a level equal to the one he would set s the Symmetrc Profts-Revenues Contracts canddate equlbrum. Intutvely, ths s the unque output level that fulflls the equlbrum condtons stated above. The followng Proposton summarzes: Proposton 3 When frms owners do not commt over the types of contracts that they choose to compensate ther managers, each type of contract s owner s best response to owner j s choce. 13 a rp pr γ[γ 2+c(2 γa 1 (a 2 )= 2 )] γ(γ+2) 4 c[2γ+a 2(γ 2 4)] 15

17 q 2 RP RC 1 RC RP * 1 PR RC 1 FIRM 2 S ISOPROFIT CURVE Π 2 Ẹ RP. E PR FIRM 1 S ISOPROFIT CURVE Π 1 PR RC 2 RP RC 2 q 1 Fgure 1: Equlbrum manageral ncentve contracts under no-commtment Observe that the two-staged game s characterzed by multplcty of equlbra. Subsequently, the followng queston arses: whch types of the manageral ncentve contracts wll fnally emerge n equlbrum? Usng the equlbrum results of Secton 3 and employng focal pont analyss, we renforce our arguments stated n Proposton 2. Note also that the aforementoned equlbrum condtons must hold for all the dfferent types of contracts that owners can offer to ther managers, regardless the functonal forms of cost and demand and the mode of competton,.e. Cournot or Bertrand. Thus, assumng no ex-ante commtment over the types of contracts that owners wll offer to ther managers, even a contract of dfferent type could be an owner s best response to the rval owner s choce. 5 Welfare analyss In ths Secton we perform a welfare analyss. Socal welfare s defned as the sum of consumers surplus and frms profts: 16

18 SW w = CS w + Π w,w= pr, rp, m, rp pr, rp m, m pr (6) CS w = 1+γ (Q w ) 2 4 where Q w and Π w s the total ndustry output and profts respectvely. 14 Regardng the symmetrc confguratons of contracts, one can easly check that SW w >SW c, w = pr, rp, m, except f managers are compensated wth M contracts and γ < The ntuton s straghtforward. When both managers are compensated ether wth PR or wth RP contracts, consumers surplus s hgher and frms profts are lower than the respectve n the benchmark case of No-delegaton. Nevertheless, the negatve frms profts effect s always domnated by the postve consumers surplus effect. As a consequence, the symmetrc use of ether PR or RP contracts s always preferable from the socal welfare pont of vew. When both managers are compensated wth M contracts, consumers surplus s hgher than the respectve n the benchmark, f and only f γ> On the contrary, frms profts are hgher but only for ntermedate degrees of product substtutablty,.e <γ< Wereconfrm n ths case too that the welfare effects of the symmetrc use of M contracts are drven by the consumers surplus effect. Clearly, socal welfare n each confguraton of contracts follows the pattern that output levels follow. The followng Proposton summarzes: Proposton 4 () SW pr >SW rp >SW c. () SW m >SW c,fandonlyfγ> () SW pr >SW m. (v) SW m >SW rp,fandonlyfγ> (v) In each asymmetrc confguraton of contracts (rp-pr, rp-m, m-pr), socal welfare les between the respectve levels n the symmetrc confguratons. 14 Substtutng the relevant expressons nto eq. (6), we obtan socal welfare n the sx contract confguratons under consderaton. More specfcally, socal welfare for the frst four confguratons of contracts s gven n Appendx B. Regardng the last two confguratons, socal welfare was obtaned numercally, through the smulatons results, concernng output, presented n Tables 1 and 2 respectvely. Further detals are avalable from the authors upon request. 17

19 The above Proposton replcates our fndngs, regardng the comparson of the equlbrum output levels under the dfferent confguratons of contracts (see Corollary 1). An mmedate consequence s that socal welfare n the asymmetrc confguratons les between the respectve levels n the symmetrc confguratons (Proposton 4 (v)). We also fnd that socal welfare decreases n the degree of product substtutablty. Ths happens because of the negatve product dfferentaton effect that decreases frms profts always; and consumers surplus, except f managers are compensated wth M contracts and γ< Concluson Ths paper extends the analyss of Jansen et al. (2009) by assumng that the two competng frms produce dfferentated nstead of homogeneous products. In ths context, we have nvestgated the mpact of product substtutablty on the types of contracts that frms owners choose to compensate ther managers, as well as on the resultng output levels, profts and socal welfare. We have dentfed the dfferental effects of product substtutablty on the output levels set by managers and the resultng frms profts, dependng on the confguraton of contracts n the ndustry. We have also shown that the types of contracts that owners choose to compensate ther managers depend crucally on the degree of product substtutablty. In partcular, f products are ether suffcently dfferentated or suffcently close substtutes, owners compensate ther managers wth Relatve Performance contracts. For ntermedate degrees of product substtutablty, owners choose Market Share contracts. When owners do not commt over the types of contracts, each type of contract can be an owner s best response to the rval owner s choce. Fnally, manageral ncentve contracts are welfare enhancng but only when they ncrease consumers surplus. Our results have been derved n the context of a duopolstc market where competng frms, wth equally effcent producton technologes, produce dfferentated products under a lnear demand system. We are of the opnon that a duopolstc market reveals all the essental dfferences between the dfferent types of contracts. Ths argument could also be supported by the smlarty of fndngs between a two- and a three-frm ndustry, n Jansen et al. (2009). We are also aware of the lmtatons of our analyss, assumng specfc functonal forms. However, the 18

20 equlbrum condtons that drve our results allow us to argue that these results wll also hold under general demand and cost functons. The use of more general forms would jeopardze the clarty of our fndngs, wthout sgnfcantly changng ther qualtatve character. Appendx Appendx A: Equlbrum outcomes for the dfferent confguratons of contracts A1: Symmetrc Profts-Revenues Contracts a pr = γ2 2c (2 + γ) c (γ 2 2γ 4) ; qpr = A2: Symmetrc Relatve Performance Contracts 2(1 c) 4+2γ γ 2 ; Πpr = 2 2 γ 2 (1 c) 2 (γ 2 2γ 4) 2 a rp = γ 2+γ ; qrp = A3: Symmetrc Market Share Contracts (2 + γ)(1 c) 4 γ ; Π rp 2 (1 c) 2 = 4(1+γ) 16 (1 + γ) a m = h ³ B ³ γ 7 ³ B B γ + γ +10 (1 c) 2 B = 1+γ(γ +6) 2(6+γ) 2 q m = ³ B + γ +7 (1 c) 4(6+γ) Π m = ³ B + γ +7 h 17 ³ B B γ + γ +4 (1 c) 2 16 (6 + γ) 2 A4: Coexstence of Relatve Performance and Profts-Revenues Contracts a rp pr 1 = γ [γ (2 + γ) 4] γ [γ (2 + γ)+4] 8 ; arp pr 2 = γ2 (γ 1) c γ 2 (2 + γ) 4 c (3γ 2 4) 19

21 q rp pr 1 = [γ (2 + γ) 4] (1 c) 6γ 2 ; q rp pr [γ [γ (2 + γ) 4] 8] (1 c) 2 = 8 4(3γ 2 4) 2 γ Π rp pr 2 [γ (2 + γ) 4] 2 (1 c) 2 1 = 8(4 3γ 2 ) 2 ; Π rp pr [γ [γ (2 + γ) 4] 8] (2 γ)(1 c)2 2 = 48γ

22 A5: Coexstence of Relatve Performance and Market Share Contracts Table 1 summarzes the smulaton results concernng output for ths contract confguraton. q rp m 1 q rp m 2 q rp m 1 q rp m 2 c γ =0.1 γ = c γ =0.2 γ = c γ =0.3 γ = c γ =0.4 γ = c γ =0.5 γ =

23 A6: Coexstence of Market Share and Profts-Revenues Contracts Table 2 summarzes the smulaton results concernng output for ths contract confguraton. q m pr 1 q m pr 2 q m pr 1 q m pr 2 c γ =0.1 γ = c γ =0.2 γ = c γ =0.3 γ = c γ =0.4 γ = c γ =0.5 γ =

24 Appendx B: Total Welfare TW PR = 4[3 γ (γ 1)] (A c)2 [γ (γ 2) 4] 2 TW RP = (2 + γ)(6 γ)(1 c)2 16 (γ +1) TW M = ³ 7+γ + h B 41 ³ B γ γ + B (1 c) 2 16(γ +6) 2,B=1+γ(γ +6) TW (rp pr) = [768 + γ [ γ [ γ [352 + γ (γ 8) [γ (γ 3) 16]]]]] (1 c)2 64 (4 3γ 2 ) 2 References Aggarwal RK, Samwck AA Executve compensaton, strategc competton, and relatve performance evaluaton: theory and evdence. Journal of Fnance 54: Borkowsk SC Internatonal manageral performance evaluaton: a fve-country study. Journal of Internatonal Busness Studes 30: Fama EF, Jencen MC Separaton of ownershp and control. Journal of Law and Economcs 26: Fershtman C Manageral ncentves as a strategc varable n duopolstc envronment. Internatonal Journal of Industral Organzaton 3: Fershtman C, Judd K Equlbrum ncentves n olgopoly. Amercan Economc Revew 77: Gbbons R, Murphy KJ Relatve performance evaluaton for chef executve offcers. Industral and Labor Relatons Revew 43: 30S-51S. Jansen T, van Ler A, van Wtteloostujn A A note on strategc delegaton: the market share case. Internatonal Journal of Industral Organzaton 25: Jansen T, van Ler A, van Wtteloostujn A On the mpact of manageral bonus systems on frm proft and market competton: The cases of pure proft, sales, market share and relatve profts compared. Manageral and Decson Economcs 30:

25 Jensen MC, Murphy KJ Performance pay and top management ncentves. Journal of Poltcal Economy 98: Joh SW Strategc manageral ncentve compensaton n Japan: relatve performance evaluaton and product market colluson. Revew of Economcs and Statstcs 81: Katz M Game playng agents: Unobservable contracts as precommtments. RAND Journal of Economcs 22: Kockesen L, Ok EA Strategc delegaton by unobservable ncentve contracts. Revew of Economc Studes 71: Lambert RA, Larcker DF, Wegelt K How senstve s executve compensaton to organzatonal sze. Strategc Management Journal 12: Mller N, Pazgal A The equvalence of prce and quantty competton wth delegaton. RAND Journal of Economcs 32: Mller N, Pazgal A Relatve performance as a strategc commtment mechansm. Manageral and Decson Economcs 23: Mller N, Pazgal A Strategc trade and delegated competton. Journal of Internatonal Economcs 66: Peck MJ The Large Japanese Corporaton. In The U.S. Busness Corporaton: An Insttuton n Transton, Meyer JR, Gustafson JM. (ed). Cambrdge MA: Ballnger; Rtz R Strategc ncentves for market share. Internatonal Journal of Industral Organzaton 26: Sklvas S The strategc choce of manageral ncentves. RAND Journal of Economcs 18: Vckers J Delegaton and the theory of the frm. The Economc Journal (supplement) 95: van Wtteloostujn A, Jansen T, van Ler A Barganng over manageral contracts n delegaton games: manageral power, contract dsclosure and cartel behavor. Manageral and Decson Economcs 28: