A new balancing approach in Balanced Scorecard by applying cooperative game theory

Transcription

1 IEOM 011 A new balanng approah n Balaned Soreard by applyng ooperatve game theory M. Jafar-Eskandar Department of Industral Engneerng Iran Unversty of Sene and Tehnology, Narmak, Tehran , Iran E-mal: Mesam_Jafar@ust.a.r A.R. Alahmad, M.Hedar and GH.H.Khalegh Department of Industral Engneerng Iran Unversty of Sene and Tehnology, Narmak, Tehran , Iran Abstrat: Balane soreard s a wdely reognzed tool to support manager n performane of work. Balane Sore Card (BSC has many advantages but t also suffers from some drawbaks. In ths paper, we develop a new balanng approah based on game theory. We propose an nteraton method among dfferent strateg agents of soreard as players provdng a methodology for ollaboraton among dfferent players to redue any nonssteny. We mplement four-person ooperatve game theory to balanng n BSC. Keywords: Balaned Soreard (BSC, Balaned Soreard (BSC, ooperatve game theory. 1. Introduton 1 Durng the past few years, balaned soreard (BSC has been wdely used among aademans and researhers nvolved n strateg management and manageral aountng. The BSC, desgned by Kaplan and Norton [1], uses four perspetves whh reflet frm value reaton atvtes: Learnng and growth perspetve, nternal/busness proess perspetve, ustomer perspetve, and fnally fnanal perspetve. The BSC methodology reates an nfrastruture for strateg management atvtes and ntrodues four new management proesses ontrbutng to lnkng long-term and short-term strateg objetves separately and smultaneously and use tools for dong balane n organzaton. BSC helps managers understand numerous nterrelatonshps and ausal effets n among perspetves []. Ths understandng an help managers transend tradtonal notons regardng funtonal barrers and ultmately mprove deson-makng and problem solvng. Strategy and exeuton revews an help management teams revew the strateg plans, the plannng proess, nludng BSC metrs and strategy maps [7, 8]. Although BSC has proven a powerful tool for strateg plannng and ommunatng strategy that asssts n strategy mplementaton but there are some lmtatons on usng ths method. One bas ssue to be surmounted s the dffulty of determnng Balanng among dfferent 194

2 BSC perspetve. In ths artle, We use ooperatve evolutonary game theory to make predtons about fourperson oorporaton games. The rest of ths artle s organzed as follows. In the followng seton, we provde an ntroduton to balane sore ard and the ooperatve evolutonary game theory and the model. In Seton 3, we present oalton formaton. In Seton 4 one balanng system defned by the use of game theory and Fnally, the onluson remarks are gven n seton 5 to summarze the ontrbuton of the paper. Lterature revew.1 Lterature on the balaned soreard (BSC Frst devsed by Kaplan and Norton, the balaned soreard approah omprses four perspetves: learnng and growth perspetve, nternal proess perspetve, ustomer perspetve, and fnanal perspetve [1, 8, 9] whh seeks to offer managers a system that would help them turn strategy nto aton. Ths system arranges the vson of organzaton nto themes that are dsaggregated and detaled top-down n strateg maps. Presently, a large number of organzatons are urrently suessful usng BSC. In fat, Nven [14] mentons that reent estmates suggest that 50% of the 1000 largest Fortune Organzatons use BSC. There s onsderable evdene that organzatons are nreasngly adoptng BSC n ther strateg proess and that methodologal sope does exst to usng t, wth ase study desrptons showng that ts applaton alls for a degree of nnovaton n order for BSC deas to be really benefal to the organzaton. The BSC s just a few numbers or performane ndators need to be heked. Also t serves as a brdge between dfferent felds (fnanal and non-fnanal felds, but t must be noted that there are some lmtatons : 1. Undretonal ausalty too smplst: The use of ausal-loops alone s seen as problemat beause these loops do not apture the noton of strateg fators aumulatng and depletng [17].. Does not separate ause and effet n tme: The tme dmenson s not part of the BSC, beause n some ause-and-effet relatonshps a tme lag exsts between ause and effet [17,18]. 3. No mehansms for valdaton : The BSC onept provdes no mehansm for mantanng the relevane of defned measures [18,19]. 4. Insuffent lnks between strategy and operatons: State that the BSC fals to dentfy performane measurement as a two-way proess [17, 18,19]. 5. Too nternally foused : A BSC may be too narrowly defned [18,19].. Bakground of the evolutonary game and the model Game theory s often desrbed as a branh of appled mathemats and eonoms that studes stuatons where multple players make desons n an attempt to maxmze ther returns. Generally, the publaton of the Theory of Games and Eonom Behavor by Morgenstern and Von Neumann n 1944 symbolzes the foundaton of Game Theory system [0]. But the modern Game Theory has lttle relatonshp wth ths book. The modern Game Theory developed from 1950s- 1960s, and n 1970s the modern Game Theory beame popular eonom theory [1]. The bas onept of game theory nludes: player, aton, strategy, nformaton, nome, equlbrum. Player an be ndvdual or groups suh as manufaturer, government, and naton. The bas model of formal game theory []: 1, Are the atons of player1 and player; P s the payoff funton of every player n dfferent strategy { assoaton. Set s the set of players strateges. If 1, } satsfed the followng: 195

3 1 1 P ( 1, max P ( 1 1, 1S P ( 1, max P ( 1, S ( Then strategy set 1, s Equlbrum. For game set ( 1, V, f there s no strategy set ( 1, satsfyng the followng at the same tme: 1 1 P ( 1, P ( 1, P ( 1, P ( 1, Then t s alled Pareto optmalty. 3. Applyng ooperatve evolutonary game theory n BSC Ths mght be far-fethed to defne the proportonal probablty of playng the ooperaton strategy as the ollaboraton effort. Ths problem an be solved by ntrodung the ontnuous-strategy ooperatve game. Aordng to Doebel and Knowlton (1998, Doebel et al. (004, Kllngbak and Doebel (00, Wahl and Nowak (1999a, Wahl and Nowak (1999b, t s natural to assume that players adopt ontnuous strateges n SD games. Smlarly n an ooperatve evolutonary game, t s natural to assume that players an make ontnuously varyng ollaboraton effort. In a four-player ooperatve game, we assume that eah player has a maxmum resoure budget, x, x, x, x, respetvely. However four players mght determne ther m m m m ollaboraton effort durng the ooperatve proess. Let p1, p, p3, p4 be the effort ndex of Player ( 1,,3,4. Aordngly, p xm s the total ollaboraton effort of Player ( 1,,3, 4. We denote B( p1x1 m, pxm, p3x3m, p4x4m as ommon beneft of four B( p x, p x, p x, p x, whh players. Beause of the effeny of dfferent players, we adopt allows asymmetr effeny between players as the beneft funton. Let C( p x four players respetvely. Thus, Player, s payoff funton an be wrtten as follows. ( p, p, p, p B( p x, p x, p x, p x C( p x m m 3 3m 4 4m m m m m m m be the ooperaton osts of Here we would lke to emphasze that we are dsussng an asymmetr ontnuous ooperaton game. Frst, xm ould be dfferent from another and p ould be dfferent. Player may not be as effent as Player j n ontrbutng to the ollaboraton result (, j 1,,3, 4 ; j. If Eqs.above are onave and we obtan a vetor of p, p, p, p where 0 p 1, then p 1, p, p 3, p 4 s a unque equlbrum for ths asymmetr ontnuous ooperaton game. We frst fous on ase where the payoff funtons are lnear to the ollaboraton efforts. We have the followng observaton

4 Table 1 : The players effort matrx Player 1 Defet Player Defet Player 4(Defet Player 4(Defet Player 3 (Defet, Player 3 (Defet, Player 4(Defet Player 3 (Defet, Player 3 (Defet, Player 4(Defet Player 4(Defet Player 4(Defet Player 3 (Defet, Player 3 (Defet, Player 4(Defet Player 3 (Defet, Player 3 (Defet, Player 4(Defet Player Defet Player 1 Defet p1 p p3 p4 p1 p(1 p3 p (1 p 4 1 p p3 p4 (1 p1 p (1 p3 p4 p p p 1 3(1 p4 p1 p p3 p4 p p p p 1(1 3 4 p1 (1 p(1 p3 p4 (1 (1 (1 p1 p p3 (1 p4 (1 p1 p(1 p3 (1 p4 (1 p1 (1 p p3 p4 (1 p1 (1 p (1 p3 p4 p1 (1 p p3 (1 p4 p1 (1 p (1 p3 (1 p4 (1 p1 (1 p p3 (1 p4 (1 p1 (1 p (1 p3 (1 p4 Proposton. A four-person dsrete-strategy ollaboraton game wth mxed strateges an be desrbed equvalently by a four-person ontnuous-strategy ollaboraton game wth a payoff funton lnear to ther ollaboraton efforts and a orrelated tem p xm. 4 1 Proof of Proposton. We show that the payoff of a player n a speal ontnuous-strategy ollaboraton game an be used to desrbe the payoff of the player n a dsrete- and mxed-strategy ollaboraton game. For a dsrete-strategy game, we argue that the mxed strateges mght be onsdered as a ontnuous effort that a player s wllng to ontrbute to the ollaboraton. Thus, we an onsder a mxed strategy essentally as an effort matrx (see Table. To study the dsrete-strategy game for four players, we start wth the ntutve symmetr model as shown n Table. In ths artle, we onglomerate a sngle fator alled soal punshment, whh s denoted by. In ths ollaboraton game, we assume that a player wll be punshed, e.g., hs/her reputaton gets hurt, et., f he/she dedes to defet whle the other ooperates. As a result, the defetor s payoff dereases due to the mpat of. We model a symmetr ollaboraton as shown n Table

5 Player Defet Table : A symmetr ollaboraton game Player 1 Defet b, b, b, b,,, b b b b b, b, b, b b, b, b, b b, b, b, b b, b, b, b b, b, b, b b, b, b, b,,, b b b b b, b, b, b b, b, b, b b, b, b, b b, b, b, b b, b, b, b b, b, b, b 0,0,0,0 Thus, Player, 1 s expeted payoff s gven by : 1( p1 p1 p p3 p4( b p1 p(1 p3 p4( b (1 p1 p p3 p4( b (1 p1 p(1 p3 p4( b 4 3 p1 p p3(1 p4( b p1 p(1 p3(1 p4( b (1 p1 p p3(1 p4( b (1 p1 p(1 p3(1 p4( b 3 p1 (1 p p3 p4( b p1 (1 p(1 p3 p4( b (1 p1 (1 p p3 p4( b 3 (1 p1 (1 p(1 p3 p4 ( b p1 (1 p p3 (1 p4 ( b p1 (1 p(1 p3(1 p4( b (1 p (1 p p (1 p ( b Let ( p 0 p ( 1,,3,4 and we obtan the optmal soluton. We use an example to show the mplementaton of our proposed method. We assume the exstene of an adaptve effet that takes plae as the ollaborators use a partular medum. The effet essentally s that the more the ollaborators use the same medum, the more effetve they beome at usng the medum. Hene, we assume a pee-wse lnear learnng 1 j urve for the ollaborators as a result of the adaptve effet, whose slope s denoted by, for the spef medum and ollaborators prevously. We defne,0 0, where stands j stands for the umulatve frequeny of Medum beng utlzed by the. The sum of j for all meda equals the total number of omponent games played untl the urrent round (omponent game. Suppose the overall ollaboraton tasks are dvded nto a seres of omponent games, n whh ollaborators mght hoose dfferent meda for eah omponent game. Thus, the expeted payoff of Player n the tth omponent game of ths dynam ollaboraton game an be expressed as : t ( P, max (1 B ( p x, p x, p x, p x C ( p x ( P, j p,,0 1 m1 m 3 m3 4 m4 j m j t j 198 5

6 4. Conluson Game theory, n the last deades has emerged as a powerful method to desrbe and to gve way-outs when fang nteratve problems solvng. However, one bg onstrant to make t more applable seemngly s n determnng alternatve pay-offs. Espeally when the problems are domnated by qualtatve onsderatons lke what usually happens n strateg problems. Qualtatve nputs annot be proessed dretly by game theory. They should be translated frst nto quanttatve nputs (pay-offs. As run the model by MATLAB software, I see that s Nash equlbrum pont n p 0.5 1,,3, 4 Fg. 1: Error of run model Fg.: Nash equlbrum pont Ths paper shows how game theory an be used to balane that perspetve of BSC. The researh found that the best Equlbrum pont for the four players n BSC s by p 0.5 1,,3, 4. To deal wth that, they need to unte ther efforts and to support one another. Referenes [1] Kaplan, R.S., Norton, D.P.: The balaned soreards: measures that drve performane. Harvard Bus Rev 70(1, 71 79, (199. [] Andrews, K. Z. Two knds of performane measures. Harvard Busness Revew, 74(1, 8 9, (1996. [3] Banker, R. D., Potter, G., & Srnvasan, D. An empral nvestgaton of an nentve plan that nludes nonfnanal performane measures. Aountng Revew, 75(1, 65 9, (000. [4] Frgo, M. L. Nonfnanal performane measures and strategy exeuton. Strateg Fnane, 84(, 6 8, (00. [5] Sad, A.A., HassabElnaby, H. R., & Wer, B. An empral nvestgaton of the performane onsequenes of nonfnanal measures. Journal of Management Aountng Researh, 15, 193 3, (003. [6] Banker, R. D., Chang, H., & Pzzn, M. J. The balaned soreard: Judgmental effets of performane measures lnked to strategy. Aountng Revew, 79(1, 1 3, (004. [7] Kaplan, R.S., Norton, D.P.: The strategy-foused organzaton: how balaned soreard ompanes thrve n the new busness envronment. Harvard Busness Shool Press, Boston (001. [8] Kaplan, R.S., Norton, D.P.: Strategy maps: onvertng ntangble assets nto tangble outomes. Harvard Busness Shool Press, Boston (

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