Title. Agents. Citation 577; Issue Date Right.

Transcription

1 NOSIT: Nagasa Unversty's c Ttle uthor(s) Ctaton n conomc nalyss of Coopettve gents Oura, Mahto Communcatons n Computer and Info 577; 0 Issue Date 0 URL Rght 0 Sprnger-Verlag.; The fnal Ths document s downloaded

2 n conomc nalyss of Coopettve Tranng Investments for Insurance gents Mahto Oura Faculty of conomcs, Nagasa Unversty, Japan bstract. The man purpose of ths research s to nvestgate the effects of maret demand uncertanty n the coopettve nsurance maret. To that end, we buld a game-theory model ncludng tranng nvestments of nsurance agents n an nsurance maret wth demand uncertanty. e derve the followng results from our analyss. Frst, nsurance frms undertae less tranng nvestment f t s determned compettvely by nsurance frms. From ths result, we show how some assocatons n the nsurance maret coordnate the amount of tranng nvestment and produce a hgher amount of tranng nvestment. Second, we show how the effectveness of coopetton becomes larger when demand uncertanty s larger. e confrm from that fndng that realzng the coopettve stuaton s more mportant f the demand uncertanty n the nsurance maret s large and that demand uncertanty s an mportant element n coopetton studes. Keywords: Coopetton, Insurance agent, ame theory. Introducton It s well nown that nsurance can realze more effcent rs allocaton and enhance effcency. The author would le to acnowledge fnancal support by the Mnstry of ducaton, Culture, Sports, Scence, and Technology n the form of a rant-n-d for Young Scentsts (), and

3 However, because nsurance products are nvsble and complex, some problems may be encountered. For example, ndvduals may purchase unnecessary and/or unsutable nsurance products because of ther nsurance agents napproprate actvtes. Such actvtes lower consumers confdence n nsurance maret, nsurance frms, and the nsurance ndustry. Thus, from the perspectve of mantanng confdence, the tranng of nsurance agents s one of the most mportant ssues facng nsurance frms. In the real world, tranng of nsurance agents s conducted not only by each nsurance frm but also by the nsurance ndustry as a whole. Thus, the nsurance maret contans both cooperatve tranng and compettve sales systems. In other words, the nsurance maret s nether perfectly cooperatve nor perfectly compettve, that s coopettve. Furthermore, every maret, ncludng nsurance, has some nds of uncertanty. For example, the amount of demand s changng every day. If the nsurance maret faces demand uncertanty, we examne how that affects the effectveness of the coopetton n an nsurance maret. To answer the above queston, ths artcle bulds a game-theory model that combnes tranng nvestments for nsurance agents n an nsurance maret wth demand uncertanty. The remander of ths artcle s organzed as follows. Secton explans why game theory s a powerful tool for analyzng a coopettve maret stuaton. Secton 3 bulds the model and derves some results. Concludng remars are presented n Secton 4.. Methodology number of artcles apply game theory to coopetton studes. For example, randenburger and Nalebuff (6, 5 8) argue for the usefulness of game theory n understandng a coopettve stuaton. Lado et al. (7, 3) show how game theory explans behavor assocated wth nterfrm relatonshps. Oura (007, 008, 00a) argues that game theory can be a powerful tool to nvestgate coopetton. Pesamaa and rsson (00, 67) descrbe how game theory can be a useful tool for analyzng and predctng actors nterdependent decsons. In coopetton studes, there are three advantages of use of game theory. Frst, game theory can analyze nteractons between frms n an olgopolstc maret. It s natural that coopetton cannot be realzed n a monopolstc maret. lso, we cannot consder coopetton n a perfectly Oura (00b) analyzed the relatonshp between nsurance agents sales effort and wage schedules by a prncpal-agent model. The followng explanatons are a summary of the descrptons n Oura (007).

4 compettve maret because the defnton of perfect competton precludes strategc choces. Thus, coopetton only arses n olgopolstc marets and game theory s the prncpal method used for analyzng that maret structure. 3 ctually, the nsurance maret n many countres ncludng Japan can be consdered to be olgopolstc. For example, n the case of Japan s nsurance ndustry, there are 83 nsurance frms (43 lfe nsurance and 40 nonlfe (drect) nsurance frms at the end of 0), whch means that game theory can be an approprate tool to analyze an nsurance maret wth coopetton. Second, game theory s a rgorous analytcal method. In partcular, game theory s the prmary tool for nvestgatng a multstage process, because t can be treated as an extensve-form game, and the equlbrum of ths game can be derved by the bacward nducton used to compute the equlbrum. Thrd, game theory permts us to dstngush much more easly between the cooperatve and compettve aspects n a coopettve maret. Coopettve stuatons have a tendency to be complex because they contan elements of both cooperaton and competton. However, game theory can be used to buld a smple model by separatng the cooperatve and compettve aspects n a coopettve maret stuaton. 3. The Model Suppose that there are two nsurance frms named nsurance frm and nsurance frm, respectvely, n the maret. They sell ther nsurance products through nsurance agents. Our model develops the followng three-stage game. In the frst stage, both nsurance frms compettvely decde on the amount of ther tranng nvestments for nsurance agents to mantan maret confdence. represents the amount of tranng nvestment by the nsurance frm for {, }. The amount of tranng nvestment depends on the level that mantans the confdence of the nsurance maret. The nvestment functon s quadratc and s assumed to be specfed by ( ). In the second stage, the nature determnes the stuaton wth regard to confdence n the nsurance maret. There are three possble cases as follows. The frst case can be called the good confdence case n whch all (potental) consumers are credble to the nsurance maret. In ths case, the form of the demand 3 For example, Shy (5, ) argued that [ ] game theory s especally useful when the number of nteractve agents s small. 3

5 functon s p a q q, () where superscrpt means the good confdence case, a denotes the ntercept of the demand functon that represents nsurance maret sze, p represents the nsurance premum, and q and q are the quanttes of nsurance products sold by nsurance frm and, respectvely. The probablty of realzng the good confdence case s. The second case s the bad confdence case. Ths case ndcates that the actvtes of the nsurance agents of ether nsurance frm tend to lower confdence n both of them. lthough not all nsurance agents choose napproprate actvtes, t s assumed that (potental) consumers lose confdence not just n ndvdual agents but n the whole nsurance maret. Thus, the demand functon n ths case s p a q q, () where superscrpt means the bad confdence case. ( 0,) represents the degree of lowerng the confdence. In other words, the nsurance maret s dmnshed by nsurance agents napproprate actvtes. The probablty of realzng the bad confdence case s ( ) ( ). The thrd case can be called the worst confdence case. Ths case ndcates that the nsurance agents of both nsurance frms actvely lower confdence n the nsurance maret. The demand functon n ths case s p a q q, (3) where superscrpt means the worst confdence case. The sze of the nsurance maret reduces more than n the bad confdence case because ( 0,) ( )( ).. The probablty of realzng the worst confdence case s In the thrd stage, after both nsurance frms observe whch case s realzed, they smultaneously decde the quanttes of nsurance products. t that tme, the sze of the nsurance maret, represented by a, has some uncertanty but s assumed to be dstrbuted by the normal dstrbuton functon N (, ) [ ] [ a] represents the mean, and ( ), where a represents the varance of the sze of the nsurance maret. ecause each nsurance frm taes ts decsons n the frst and thrd stages, we analyze these stages by 4

6 bacward nducton. Frst, we consder the thrd stage. 4 oth nsurance frms can choose ther quanttes of nsurance products n accordance wth a demand functon and ts uncertanty. In the good confdence case, both nsurance frms are assumed to be rs neutral and ther proft functons can be wrtten as π p q ( a q q ) q, (4) where π represents the proft of nsurance frm n the good confdence case. From equaton (4), we derve the equlbrum quanttes of nsurance products as q a a ( ), (5) where the asters () means that value s the equlbrum value. Substtutng equaton (5) nto equaton (4), the equlbrum proft of each nsurance frm shows that π ( a ). (6) 3 3 From equaton (6), the equlbrum expected proft of each nsurance frm s [ ] ( ) π. (7) In the bad confdence case, the proft functon of each nsurance frm can be wrtten as where ( a q q ) q π p q, (8) π represents the proft of nsurance frm n the bad confdence case. From equaton (8), we derve the equlbrum quanttes of nsurance products as q a a ( ). () Substtutng equaton () nto equaton (8), the equlbrum proft of each nsurance frm becomes π ( a ). (0) 3 3 From equaton (0), the equlbrum expected proft of each nsurance frm s 4 The analyss n the thrd stage orgnates entrely from Saa (, Chapter 3), whch nvestgated broader cases such as the monopolstc nformaton case. 5

7 6 [ ] ( ) π. () Smlarly, the equlbrum quanttes of nsurance products and expected profts n the worst confdence case can be derved as 3 a q, () [ ] ( ) 4 π, (3) where π represents the proft of nsurance frm n the worst confdence case. Next, let us consder the frst stage. The expected proft of each nsurance frm n the frst stage, whch s denoted by [ ] Π, can be wrtten as [ ] [ ] ( ) ( ) { } [ ] ( )( ) [ ] π π π Π. (4) Substtutng equatons (7), (), and (3) nto equaton (4), we obtan [ ] ( ) ( ) { } ( )( ) [ ]( ). 4 Π (5) From equaton (5), the optmal amount of tranng nvestment may be derved as ( )( ) ( ) ( ). (6) From equaton (6), the equlbrum expected proft of each nsurance frm s [ ] ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ). 8 4 Π (7) To evaluate the equlbrum amount of tranng nvestment that s denoted n equaton (6), the optmal amount of tranng nvestment when both nsurance frms cooperatvely choose ther amount of tranng nvestment s derved by maxmzng total expected proft, defned as [ ] [ ] [ ] ~ Π Π Π, (8) where tlde (~) means that value s derved n a cooperatve tranng nvestments stuaton. From equaton (8), the equlbrum tranng nvestment of each nsurance frm are derved by

8 ( )( ) ( ) ( ) y comparng equatons (6) and (), t s easy to derve ~. () ~ >. (0) Ths equaton (0) mples that both nsurance frms choose a lesser amount of tranng nvestment when they are n competton. In other words, the equlbrum amount of tranng nvestment runs nto the prsoners dlemma stuaton because both nsurance frms want to be free rders on ther rval s tranng nvestment when actng compettvely. To avod realzng such Pareto-nferor outcome, t s better f each frm cooperatvely chooses ts tranng nvestments. Thus, n practce, nsurance frms tran ther nsurance agents not only for themselves exclusvely, but n effect for all the other nsurance frms. For example, Japanese nsurance agents cannot sell some nds of nsurance products that are rsy and complcated unless they have had some tranng and pass the examnaton requred to demonstrate nowledge of the nsurance laws and products. Such tranng for nsurance agents s conducted by some nsurance assocatons such as The Lfe Insurance ssocaton of Japan and The eneral Insurance ssocaton of Japan. Moreover, educatonal actvtes and enhancement of qualty of agents and solctors are lsted n the actvtes of The Lfe Insurance ssocaton of Japan and The eneral Insurance ssocaton of Japan, respectvely. 5 Thus, from the results of our analyss, these assocatons can be evaluated as coordnators seeng to avod the prsoners dlemma stuaton. ecause both nsurance frms n our model are clearly compettve n the thrd stage, the game ncludng a coordnator contans both compettve and cooperatve aspects. In other words, the exstence of nsurance assocatons promotes a coopettve nsurance maret and ncreases ncentves to rase tranng nvestments by all nsurance frms. Furthermore, we analyze whether such coopetton becomes more effectve when demand uncertanty become large. To now how the effectveness of coopetton changes n accordance wth changes n demand uncertanty, we defne the followng measure, whch represents the effectveness of coopetton n the nsurance maret. 6 5 These man actvtes can be confrmed from each assocaton s webste. See and (accessed prl 30, 0). 6 The followng results are the same f the effectveness of the coopetton n the nsurance maret s defned 7

9 ~ θ ( )( ). () In the equaton (), θ > s always satsfed, and means the effectveness of coopetton s larger f θ s larger. To nvestgate the effect of demand uncertanty on the effectveness of coopetton, by partally dfferentatng equaton () wth respect to θ, we obtan 8 ( ) ( )( ) > 0. () quaton () mples that effectveness of coopetton n the nsurance maret becomes larger when demand uncertanty ncreases. Ths result shows that realzng the coopettve stuaton s more mportant f demand uncertanty n the nsurance maret s large. From that perspectve, we fnd that demand uncertanty s an mportant element n coopetton studes. 4. Concludng Remars Ths artcle consdered tranng nvestments for nsurance agents n terms of coopetton. e derved the followng results from our analyss. Frst, nsurance frms undertae less tranng nvestment f t s determned compettvely by nsurance frms. From ths result, we showed how some assocatons n the nsurance maret coordnate the amount of tranng nvestment and produce a hgher amount of tranng nvestment. Second, we showed how the effectveness of coopetton becomes larger when demand uncertanty s larger. e confrmed from that fndng that realzng the coopettve stuaton s more mportant f the demand uncertanty n the nsurance maret s large. lso, we concluded that demand uncertanty s an mportant element n coopetton studes. References. randenburger,. M., and Nalebuff,. J., 6, Competton, Doubleday, New Yor. ~ as. 8

10 . Lado,.., oyd, N.., and Hanlon, S. C., 7, Competton, Cooperaton, and the Search from conomc Rents: Syncretc Model, cademy of Management Revew,., pp Oura, M., 007, Compettve Strateges of Japanese Insurance Frms: ame-theory pproach, Internatonal Studes of Management and Organzaton, 37., pp Oura, M., 008, hy Isn t the ccdent Informaton Shared? Competton Perspectve, Management Research, 6.3, pp Oura, M., 00a, Compettve Strateges to Lmt the Insurance Fraud Problem n Japan, In Dagnno,.., and Rocco,., eds. Competton Strategy: Theory, xperments and Cases, Routledge: London, pp Oura, M., 00b, n nalyss of the Unpad Insurance enefts Problem n Japan, Journal of Clam djustment,., pp Pesamaa, O., and rsson, P.., 00, Competton among Nature-based Toursm Frms: Competton at Local Level and Cooperaton at Destnaton Level, In Yam, S., Castaldo, S., Dagnno,.., and Le Roy, F., eds. Competton: nnng Strateges for the st Century, dward lgar Publshng, Massachusetts, pp Saa, Y.,, The Theory of Olgopoly and Informaton, Toyo Keza Shnpo-sha, Toyo (n Japanese).. Shy, O., 5, Industral Organzaton: Theory and pplcatons, The MIT Press, Cambrdge.