A SIMULATION APPROACH TO A WORLD WITH LEARNING

Transcription

1 Workng Paper WP-886 October, 2010 A SIMULATION APPROACH TO A WORLD WITH LEARNING Rafael Andreu Josep Rverola Josep M. Rosanas Rafael de Santago IESE Busness School Unversty of Navarra Av. Pearson, Barcelona, Span. Phone: (34) Fa: (34) Camno del Cerro del Águla, 3 (Ctra. de Castlla, km 5,180) Madrd, Span. Phone: (34) Fa: (34) Copyrght 2010 IESE Busness School. IESE Busness School-Unversty of Navarra - 1

2 A SIMULATION APPROACH TO A WORLD WITH LEARNING Rafael Andreu 1 Josep Rverola 2 Josep M. Rosanas 3 Rafael de Santago 4 Abstact The man objectve of the frm n economcs-based models s to mamze proft. Droppng ths objectve n order to make the models more realstc complcates the analyss and s seldom done, thus leavng management acton out of the pcture. In ths paper we try to understand how management decsons gve rse to aggregate results. In partcular, we develop a smulaton model of an economy n whch emphass s placed on managers decson-makng crtera. The key decson managers have to make s whch projects ther frms wll undertake. Project selecton has an mpact on the frm, as the frm s profle may change through learnng. Keywords: Management and Economcs, Learnng, Smulaton. 1 Professor, Strategc Management and Informaton Systems Departments, IESE 2 Emertus Professor, Producton, Technology and Operatons Management Department, IESE 3 Professor, Accountng and Control Department, IESE 4 Assocate Professor, Manageral Decson Scences Department, IESE IESE Busness School-Unversty of Navarra

3 A SIMULATION APPROACH TO A WORLD WITH LEARNING In economcs-based models the objectve of the frm s to mamze proft or, n a more modern formulaton, to mamze frm value. Under certan assumptons (unbounded ratonalty beng a crucal one), mcroeconomc theory s able to show that mamzng frm value mamzes socal welfare (see, for eample, Jensen, 2000, for a bref statement of the argument). Droppng the proft mamzaton assumpton n order to make the models more realstc complcates the analyss and s seldom done, and so management acton out s left of the pcture. Although frm value, as a decson-makng crteron, s supposed to refer to companes long-run value, n practce the decson-makng process s heavly nfluenced by fnancal analysts emphass on short-run varables such as quarterly earnngs. In ths paper we depart from the economcs-based approach by postng that a company's longrun value depends on ntangble varables related to learnng and motvatonal captal. In partcular, we develop a smulaton model 1 of an economy n whch emphass s placed on managers behavor, n such a way that aggregate results depend on actual busness decsons. In Secton 1 we descrbe the model and gve some ntuton regardng ts most relevant features. In Secton 2 we make eplct the nterconnecton between the decsons of the agents nvolved, as well as other techncal aspects. In Secton 3 we present the results of the smulated scenaros, and n Secton 4 we draw some conclusons. 1. A World wth Motvaton and Learnng We study the short and long-term behavor of a populaton of companes that have aspratons (goals) as to what type of company they would lke to be n the future. Managers of these companes make decsons based on ther (possbly naccurate) understandng of the company s characterstcs. The key decson they have to make s whch projects ther frms wll undertake. Interacton among companes takes place n successve rounds, representng perods n whch a project can be selected and completed. In addton to carryng out projects (whether successfully or unsuccessfully), companes and managers can learn from eperence,.e., ther behavor may change dependng on observed results. In order to evaluate the performance of the companes operatng n the economy, we use the number of successfully completed projects as an ndcator of the total (aggregate) value 1 See Davs et al. (2007), Harrson et al. (2007), Glbert (2008), Mller and Page (2007). IESE Busness School-Unversty of Navarra

4 created. At the same tme, companes changng profles are taken an ndcator of the economy s potental, understood as companes ablty to successfully undertake better projects n the future Company Value Followng Pérez López (1993), we characterze frms accordng to the followng attrbutes, whch correspond to three types of motves: a) Effectveness, or the degree to whch a company acheves suffcent measurable (usually fnancal) results to adequately compensate ts members n economc terms (etrnsc motves); b) Attractveness, or the degree to whch employees develop professonally and enjoy ther jobs (ntrnsc motves), and c) Unty, or the degree to whch employees dentfy wth the organzaton s goals and values, and wth the other members of the organzaton (transcendent motves, as defned by Pérez López). 2 A frm s profle s descrbed by a trplet (U,A,E), where the frst element ndcates whether the frm has Unty (U), the second, whether t has Attractveness (A), and the thrd, whether t has Effectveness (E). A 1 ndcates the presence of an attrbute, a 0 ts absence. We use the letter to desgnate a generc company. For nstance, =(0,1,1) represents a frm that has effectveness and attractveness, but no unty. Lkewse, the profle of a frm that has attractveness and unty, but no effectveness, wll be (1,1,0); and so forth. 3 Throughout ths paper we wll use the terms profle and type nterchangeably. There are seven meanngful types of frms =( 1, 2, 3 ), namely, (0,0,1), (0,1,0), (1,0,0), (0,1,1), (1,1,0), (1,0,1), and (1,1,1). 4 We shall refer to these types or profles by nteger numbers (from 1 to 7), n such a way that the nteger s bnary representaton corresponds to ( 1, 2, 3 ) Project Potental Projects, too, are characterzed n terms of effectveness, attractveness, and unty, and are represented by y=(y 1,y 2,y 3 ). If a project has a 1 n a partcular attrbute, a company that has that attrbute s more lkely to succeed n eecutng that project. In other words, the probablty that a frm succeeds when carryng out a partcular project wll be hgher f there s a match between the company profle and the project profle. For eample, f a project has the profle y=(0,1,1), a frm that has effectveness and attractveness s more lkely to succeed wth the project than a frm that lacks those attrbutes. At the same tme, a 1 n a partcular project attrbute means that the project has the potental to facltate the development of that attrbute n companes that undertake t. If a company undertakes a project wth y 2 =1, the frm s more lkely to develop attractveness durng that round, even f t does not ultmately succeed wth the project. For eample, a company that lacks attractveness wll know that ts chances of succeedng wth y=(0,1,1) are slm, yet ts managers may decde to undertake the project as a means of developng attractveness n ther frm. 2 In the termnology of Pérez López, transcendent motves refer to the satsfacton of other people s needs. 3 Ths s of course a smplfcaton, ntended to avod unnecessary techncal completes. A natural etenson of the model would be to nclude dfferent ntenstes for each attrbute, between 0 and 1. 4 Profle (0,0,0) s not meanngful for obvous reasons. 5 The nteger number assocated wth type ( 1, 2, 3 ) s For eample, by type 1 we mean =(0,0,1); by type 4, =(1,0,0); profle 5 wll be =(1,0,1); and profle 7, =(1,1,1). 2 - IESE Busness School-Unversty of Navarra

5 1.3. Project Selecton and Learnng At the begnnng of each perod, companes select the projects they would lke to develop. Once selected, the projects are carred out and ether succeed or fal. Project selecton takes nto account: () () () Managers knowledge of the company s current profle. Managers knowledge of a project s probablty of success. Managers goals regardng the type of company they would lke to be n the future. Each management team has preferences wth regard to the type of company they would lke to be. These preferences are descrbed by γ = ( γ1, γ 2, γ3, γ 4, γ5, γ6, γ7 ) (1) where each component represents the relatve mportance that managers assgn to each of the seven company types. The values of these parameters reman fed throughout successve rounds. We assume that managers allocate ther tme, resources, and efforts n such a way that the results satsfce (but do not necessarly mamze) ther goals or epectatons. We eplctly assume that managers are wllng to forego short-term results n echange for learnng and the future development of the frm s potental. Whle the target profle γ remans fed throughout the smulatons, the knowledge mentoned n () and () above may evolve through tme. Companes and managers can and do learn. On the one hand, managers learn about what type of company ther company s. Ths process takes place by lookng at each perod s results and updatng, n a Bayesan way, the probablty dstrbuton that descrbes ther mperfect knowledge about the true profle of ther frm. 6 On the other hand, managers also learn about the success probablty of the dfferent types of projects. 7 We mplement ths learnng va a neural network that s traned ntally and learns from eperence thereafter. The network does not fully eplot the nformaton estng n the observatons, as n the Bayesan case; nstead, t takes an appromate pont of vew, more consstent wth managers bounded ratonalty (see Secton 2). Fgure 1 shows the basc structure of the model. In the net secton we make eplct the nterconnecton between the decsons of the agents nvolved, as well as other techncal aspects. 6 Managers may thnk they are runnng an attractve company (.e., one n whch employees enjoy ther jobs), but t may be that employees thnk otherwse. If, as a consequence of ther (wrong) belefs, managers take on a project that requres attractveness, the company s lkely to fal, although at the same tme t may develop attractveness. Managers can learn by revsng ther belefs about the company s profle. 7 As an eample, managers may observe the performance of frms that undertake projects wth the profle (1,y 2,y 3 ), that s, projects that have the potental to develop unty. Based on ths nformaton and ther knowledge of ther own company s profle, managers can select the projects that are most lkely to contrbute to developng unty n ther frm. IESE Busness School-Unversty of Navarra - 3

6 Fgure 1 Smplfed Model Structure 2. Structure of the Model The process by whch managers select projects depends on three elements: the type of company they would lke to be n the future; the (ncomplete) knowledge they have about the company s profle, whch s updated along the way; and the (ncomplete) knowledge they have about a project s chances of success, whch s also updated along the way. The nterplay of these elements gves rse to a rch varety of decson patterns. As an llustraton, note that managers may thnk they are runnng a partcular type of company, when n fact they are runnng some other type. As success depends on what the company s actually able to do (ts true profle), managers have an nterest n learnng about that profle. At the same tme, some managers may not be nterested eclusvely n mmedate fnancal results, but also n long-term goals, such as mprovng the satsfacton of ther employees, or developng the company so that t can undertake more challengng projects n the future. 8 The fact that, after workng on a partcular project, a company s profle may change (.e., t may acqure an 8 Another etenson of the model would be to allow for the envronment becomng more demandng wth the passng of tme and generatng more projects that requre, say, unty. We have not ncluded ths possblty so far. 4 - IESE Busness School-Unversty of Navarra

7 attrbute t dd not have before, or t may lose an attrbute) means that decson patterns may change along the way, makng the model qute rch and more realstc Knowledge of Company Profle A key element of the model s the way n whch managers form ther belefs about the type of company they run. As they do not know the true profle of the frm, we endow managers wth a pror (a probablty dstrbuton), π, defned as follows: π ) = π (,, ) = ( P ( true profle of the companys ( 1, 2, 3 )) We assume that the ntal dstrbuton s unform over all possble profles, whch s a nonnformatve pror dstrbuton and a reasonable assumpton n decson makng under uncertanty (whch may be easly modfed at a later stage, on the bass that management s supposed to know better than that). As new nformaton becomes avalable, the probablty dstrbuton s updated n a Bayesan way Probablty of Success Another mportant element s the way n whch managers form ther belefs about the possblty of success n a gven project. Let P T (,y) be the true probablty of success, defned for all pars (,y) as P T (, y) = P( success company =, project = y). (2) Managers subjectve percepton of (2) wll be denoted by P S (,y). Note that whle managers make ther decsons based on P S, the actual frequency of successes and falures n the smulatons wll be determned by P T. The process by whch managers form ther subjectve perceptons s modeled by means of a neural network. In partcular, the system makes publc all quadruples {Intal Profle of frm; Project Type; Success or Falure; Fnal Profle of frm} generated durng each round. Based on ths nformaton, companes update ther knowledge (thus smulatng the learnng process of ther management teams). For smplcty, we assume that the learnng process s the same for all companes, n the sense that t s the same type of neural network that processes the nformaton n all frms. We thus deal wth three probablty measures: () () () P T (,y) s the true probablty that a company wth profle succeeds when t undertakes a project wth profle y. Ths probablty s assumed to be a feature of the envronment, determned by the modeler. P S (,y) s the subjectve estmate that a company of type wll succeed f t undertakes a project of type y. Ths measure s updated as new nformaton s generated by the envronment n each round, and should converge to P T (,y). P F (,y) s a frequency. It tells us how often a project of type y has actually succeeded when undertaken by a company of type durng the dfferent rounds. As tme goes by, t should converge to P T (,y). IESE Busness School-Unversty of Navarra - 5

8 2.3. Evoluton of Profles A thrd key element of the model s the fact that, after workng on a project, a company may develop a desred attrbute, or t may lose t (because ts choce of project was short-sghted or napproprate). The modfcaton of profles s modeled by means of a transton matr, whch specfes the probablty that, n a gven perod, a company wll evolve from one profle to another as a consequence of undertakng a partcular project. Consder a company wth the profle =( 1, 2, 3 ) that undertakes project y=(y 1,y 2,y 3 ). The company s profle at the end of the round wll be denoted by =( 1, 2, 3 ): ( y, y, y ) ( 1, 2, 3) ( 1, 2, 3 ) The new profle s modeled by drawng from the probablty dstrbuton P [ =,, ) = (,, ), y = ( y, y, ( y3 where we eplctly assume that the new value of each attrbute s ndependent of the new value of the other attrbutes. The probablty that, after one round, 1 =1 (that s, that after havng worked on a project, the company has acqured unty) wll be denoted by g 1 ( 1,y 1 ). In an analogous way, g 2 ( 2,y 2 ) and g 3 ( 3,y 3 ) wll denote the probablty that the company has acqured attractveness ( 2 =1) and effectveness ( 3 =1). In general, g (, y ) = P( = 1, y ), (3) where g [0,1]. Gven the ndependence of the attrbutes, f a company chooses to undertake project (y 1,y 2,y 3 ), each attrbute of the company (each ) wll evolve accordng to a controlled Markov chan 9, wth transton matr A : ) ] A = P( P( = 0 = 0 = 0, y ) = 1, y ) P( P( = 1 = 1 = 0, y ) = 1, y ) Usng (3), ths matr can be wrtten as A = 1 g (0, y ) 1 g (1, y ) g (0, y ) g (1, ) y (4) Note how t s the project that determnes the matr. Note also that the matr s unknown to managers (as ts components are a characterstc of the envronment, determned by the modeler). 9 See Chung (1982), Taylor and Karln (1998), or Heyman and Sobel (2003). 6 - IESE Busness School-Unversty of Navarra

9 In order to smplfy notaton, we let λ denote the probablty that a company lackng an attrbute acqures t after workng on a project wth that attrbute. That s, for =1,2,3, λ = g ( 0,1) = P( = 1 = 0, y = 1) Lkewse, we let μ denote the probablty that a company loses an attrbute after workng on a project that does not have t: μ = 1 - g (1,0) = P( = 0 = 1, y = 0) for =1,2,3. We mpose the followng condtons on these parameters: 1) Invarance, whch requres that attrbutes cannot change when the ntal company value and project value are the same. In partcular, for =1,2,3: g ( 1,1) = P( = 1 = 1, y = 1) = 1 and = P( = 1 = 0, y = 0) = g ( 0,0) 0 2) Entropy, whch means that a weak project attrbute s less determnant of the fnal result than a weak company attrbute. For =1,2,3, we assume that g (0,1) g (1,0) 3) Dffculty, whch states that mprovng effectveness s easer than mprovng attractveness, and ths n turn s easer than mprovng unty. We also requre that losng unty s easer than losng attractveness, and ths n turn s easer than losng effectveness. We wrte: 2.4. Decson Makng λ and 1 λ2 λ3 μ1 μ2 μ3 Two crtera are used to choose projects. One captures the dea that managers would lke to choose the project that mamzes epected NPV. Ths, however, would requre them to compute the success probablty P T (,y), whch s not observable. A soluton could be to use the subjectve percepton P S (,y), but the problem s that managers do not know the true profle of ther frm. We thus consder the followng verson of the Epected NPV, 10 V ( y) = NPV ( y) PS (, y) π( ) As we are assumng that the fnancal value of all projects s the same, we may assume NPV(y)=1 for all y, whch yelds: all 10 Note that the summaton has seven terms, as there are only seven company profles. IESE Busness School-Unversty of Navarra - 7

10 The other crteron has to do wth managers aspratons (goals) regardng the type of company they would lke to have n the future. The dea we try to model s that managers choose the project that wll brng them closer to ther goal. We proceed n two steps: frst, we take nto account the wshes or desres of the management team, represented by γ ; second, such desres are tempered by the mtaton effect, whch s the attracton that managers may feel toward the projects that successful companes chose n the past. In order to make thngs concrete, note that V ( y) = PS (, y) π( ) all s an estmate of the success of a company wth profle. As P T (,y) s not observable and P S (,y) s dfferent for each company, we wll use the frequency measure P F (,y). If one consders the epected net present value of a project as a measure of success, snce all projects are alke, the above epresson s a proy for the total value earned by a company n a gven smulaton round. In an analogous way, s a proy for the total value earned by all companes of type. The functon G wll be used to model the nclnaton to mtate companes that have been successful n the past. Note that G() can be computed wth the data generated by the system n each round. Managers preferences regardng future company profle were gven by (1), where the components, γ, represented the relatve mportance that managers assgn to each company type. These preferences, whch reman fed throughout successve rounds, should be combned wth the fact that managers are not blnd to what goes on n ther envronment (mtaton effect). 11 How to combne the two varables s open to dscusson, but n lne wth the tradton of System Dynamcs (see, for eample, Meadows, 2008), we adopt a multplcatve approach. We therefore defne γ = γ G() ), so that γ = ( The second crteron used by managers to choose projects s thus: = γ (, ) ( ) P y π where the probablty s to be understood as an (observed) frequency. T all projects y undertaken by P (, y) G ( ) = P (, y) all companes of type F all projects y undertaken by γ1g( 1), γ 2G(2), γ3g(3), γ 4G(4), γ5g(5), γ6g(6), γ7g(7) W ( y ) = γ P ( y ) ) 11 Ths approach goes beyond the concept of mmess n neo-nsttutonal theory (D Maggo and Powell, 1983). 8 - IESE Busness School-Unversty of Navarra

11 Note that we have developed two ndces, V(y) and W(y). Whle the former relates to the project s effcency (ts capacty to generate short-term profts), the latter captures how closely the project s algned wth managers preferences regardng the future of the company. We combne the two ndees as follows: D( y) = (1 α) V ( y) α W ( y) where α s the managers wllngness to sacrfce short-run profts n echange for a better company profle n the future. Managers do not mamze ths nde; rather, they f a threshold, T, and choose the frst project for whch D(y) T. 12 If α=1 (complete wllngness to sacrfce mmedate profts), the decson crteron becomes D(y)=W(y), meanng that the weght n the decson-makng process s carred by the managers long-term vson of the type of company they would lke to be n the future. If α=0, the decson nde would be D(y)=V(y), meanng that managers eclusvely seek short-term profts. Fgure 2 shows the detaled structure of the model. Fgure 2 Detaled Model Structure 12 Projects of dfferent types are successvely offered to each company n a random order. IESE Busness School-Unversty of Navarra - 9

12 3. Smulatons and Prelmnary Results In ths secton we report the results of the smulatons. The objectve s to llustrate the knd of output that the model can produce and ts potental to provde nsght nto the dynamcs of an economy that takes account of learnng, as well as decson makng at the frm and management level. Unless otherwse stated, we consder N=1000 companes, whch we allow to nteract for H=300 perods. For smplcty, we assume that all projects take one perod to complete, and that frms undertake only one project per perod. We also assume that all projects have the same economc value and requre the same nvestment condtons, ndependent of whch company undertakes them. For eample, f the NPV of a project s 10 mllon, we assume that ths s so no matter what company carres out the project. 13 Ths means that the number of successful projects n a round s a measure of the aggregate value generated n the economy. As a consequence of the projects t undertakes, a company s profle may change, makng the company better or less well prepared to successfully undertake projects n the future. We may therefore consder the dstrbuton of company profles at the end of a round as a measure of the future potental of the economy. 14 Ths does not mean that managers wll necessarly undertake more demandng or challengng projects; whether they do so wll depend on: () Ther target profle ( γ ). () () How boundedly ratonal they are (the threshold T). How wllng they are to forego mmedate results n order to develop attractveness and unty n ther frms (α). We start wth the followng assumptons, some of whch are modfed later on: 1) The ntal dstrbuton of frms s unform. 2) All frms have the same preferences regardng target profles ( γ s the same for all companes). 3) All management teams have the same ntal percepton regardng the profle of ther frm (same prors). 4) Each company has the same degree of bounded ratonalty (the threshold T s the same for all companes). 5) Each frm has the same wllngness to forego mmedate economc results n favor of better future profles (α s the same for all companes). 13 A way to epress ths fact s to assume that the NPV of all projects s The dea s that the capacty of a company to successfully undertake any type of project s hgher as ts profle approaches =(1,1,1) IESE Busness School-Unversty of Navarra

13 6) Changes n profle are governed by the same transton matr for all companes (the matrces A of secton 2.3). Ths assumpton can be nterpreted as dependng on the envronment, rather than beng decded by managers. We ntally adopt the followng values: λ1 = 0.1, λ2 = 0.2, λ3 = 0.3 μ1 = 0.9, μ2 = 0.8, μ3 = Parameters related to project selecton (α, T ) (a) Case 1: α=1 and low values of T For these values the evoluton of the dfferent types of companes quckly stablzes (n fewer than 50 perods) to 40% of (1,1,1)s, and lower percentages of other profles. In partcular, profle (1,0,0) stablzes at 10% of the populaton. 15 The complete evoluton s shown n Fgure 3, where tme (number of rounds) goes n the horzontal as and the percentage of each company type goes n the vertcal as (the red curve corresponds to (1,1,1)s, the yellow to (1,0,0)s, and so forth): Fgure 3 Evoluton of company profles for α=1 and low values of T (b) Case 2: α=1 wth ncreasng values of T. 15 The 40% of type-7 companes s due to the structure of the matrces A (see equaton (4)). IESE Busness School-Unversty of Navarra - 11

14 If we hold α=1 and ncrease the value of the threshold T, the proporton of type-7 companes quckly goes up to 100%. The stuaton s more or less the same even for T=1, as can be seen n Fgure 4. Fgure 4 Evoluton of company profles for α=1 and T=1 (c) Case 3: α=0. When α=0, t takes hgh values of T to get to 100% of type-7 frms. For lower values of T, stablzaton occurs at 40% of (1,1,1)s, although wth ncreasng nstablty. 16 In Fgure 5 one can see that the proporton of (1,1,1)s can even reach 100% durng transtory perods of false stablzaton, then fallng back to 40%. Note how a longer tme s needed to converge to 40%. In the smulatons that follow we wll let the model run for more than 300 perods n order to ensure that we do not mss potental changes that may not be observable n the shorter run. Fgure 5 Evoluton for α=0, T=0.9 and T=0.99 For T=1 stablzaton happens at 100% of (1,1,1)s: 16 Gven the model confguraton, gettng to 40% of (1,1,1)s s the standard low IESE Busness School-Unversty of Navarra

15 Fgure 6 Evoluton for α=0 and T=1 The behavor s analogous f 0<α<1. For a fed value of α, the fnal proporton of type-7 companes s 40% f the value of T s low, whle for hgher values of T t rses to 100%. As the fed value of α gets hgher, the transton from 40% to 100% takes place at lower values of T (as would be epected). The evoluton path, however, s sometmes unstable and slow, as can be seen n Fgures 7 and 8. Fgure 7 Evoluton of company profles for α=0.66, T=0.395 and 0.4 IESE Busness School-Unversty of Navarra - 13

16 Fgure 8 Evoluton of company profles for α=0.7, T=0.315 and α=0.74, T=0.29 (d) Interpretaton Combnatons of coherent values of α and T (lke hgh values of both parameters) tend to produce more stable evolutons. However, t s possble to compensate for a lmted wllngness to forego mmedate profts (a low value of α) wth a more demandng threshold (hgher values of T ) n order to get a populaton of companes wth greater future potental. In other words, a company wth a short-term culture can end up havng a long-term culture f ts managers are more demandng wth regard to project selecton (postve learnng may take place as a result of undertakng hgh qualty projects). 17 We can also see that once the evoluton starts to deterorate, t s dffcult to turn t around. Furthermore, transtons from a stable stuaton to a worse one seem to be trggered by acceptng an unusually bad project, or undertakng a sequence of not-so-good projects that start an epsode of dysfunctonal learnng Parameters related to the envronment (matrces A ) To further llustrate the model s behavor, we carry out addtonal eperments n dfferent envronments. These new envronments are generated by changng the values of the probabltes n the transton matrces A. a) Envronment 1: Easer to lose unty (hgher μ 1 ) 17 Ths phenomenon can also be nterpreted as an nterestng nterplay between eploraton and eplotaton n the March tradton (March, 1991) IESE Busness School-Unversty of Navarra

17 If we set μ 1 =0.99 we obtan that, for α=1 and T=0, the fnal proporton of type-7 companes goes to 40%, as before (see Fgure 9). Fgure 9 Evoluton of company profles for μ1=0.99, α=1 and T=0 However, f we ncrease the value of T, the fnal proporton quckly goes to 100%: Fgure 10 Evoluton of company profles for μ1=0.99, α=1, and T=0.1 IESE Busness School-Unversty of Navarra - 15

18 If we now let α=0 and choose low values of T, an equlbrum s reached at 40% of (1,1,1)s. For hgher values of T<1, the 40% equlbrum s stll reached, but at a slower pace and wth ncreasng nstablty. See Fgure 11, where one can observe how the proporton of (1,1,1)s stays at 100% for longer perods of tme. Fgure 11 Evoluton of company profles for μ1=0.99, α=0, and T=0.8, 0.95 and 0.99 Only for T=1 does the proporton of (1,1,1)s become stable at 100%. All these changes n behavor mmc closely the results obtaned wth the ntal value (μ 1 =0.9). Increasng μ 1 to 0.99 dd not generate substantal changes. b) Envronment 2: Harder to acqure unty (lower λ 1 ) 16 - IESE Busness School-Unversty of Navarra

19 If we set λ 1 =0.001 we obtan that, for α=1 and T=0, the fnal proporton of type-7 companes also goes to 40%, but t never goes above 40%, and the evoluton s slower (see Fgure 12). Fgure 12 Evoluton of company profles for λ1=0.001, α=1 and T=0 For hgher values of T the proporton reaches 100%, but through a slower evoluton. If we let α=0 and choose low values of T, the proporton of (1,1,1)s goes to 40%, but wth a dfferent dynamcs, as can be seen n Fgure 13. Fgure 13 Evoluton of company profles for λ1=0.001, α=0 and T=0.1 IESE Busness School-Unversty of Navarra - 17

20 As T becomes hgher, nstablty appears and the stable state occurs at a lower proporton of type-7 companes, close to 29% (see Fgure 14). Fgure 14 Evoluton for λ1=0.001, α=0, T=0.4 and 0.75 If T gets closer to T=1, the same sort of nstablty appears, although reachng a mamum around 51% of type-7 companes (well below the 100% attaned before), eventually stablzng at around 22% (see Fgure 15). Note that n ths case the (1,1,1) profle s not the one wth the largest share of the whole populaton. Fgure 15 Evoluton of company profles for λ1=0.001, α=0, T=0.85 and IESE Busness School-Unversty of Navarra

21 Only for T=1 does the proporton of (1,1,1)s domnate n a stable manner, although t does not reach 100%, but rather 54%. Fgure 16 Evoluton of company profles for λ1=0.001, α=0, and T=1 c) Interpretaton If the changes n parameter values are not large, the behavor does not change sgnfcantly, allowng us to conclude that the model s robust, n a way that wll facltate future research. Also, the parameters that defne the envronment make up what may be understood as a baselne for the future potental of the economy, a sort of benchmark aganst whch managers cannot fght. Ths can be understood as the underlyng culture or socal ethos, whch can only be modfed through more fundamental acton (e.g., generatng a socal envronment n whch unty s apprecated). 4. Conclusons The model we have presented attempts to eplan, usng smulaton technques, the aggregate behavor of a populaton of frms n terms of ther managers motvatons and wllngness to sacrfce short-term measurable results for qualtatve varables that affect the future. The key elements of our model are bounded ratonalty, satsfcng behavor, and a learnng process that can change the nature and behavor of frms. Although the model s stll n the development stage, t provdes a structured settng n whch these ssues whch are often dscussed nformally can be rgorously analyzed. An mportant characterstc of our approach s the feasblty even easness of modelng a complcated process of enterprse evoluton based on management atttudes and values. A farly smple and parsmonous descrpton of realty leads to emergent behavor whch s not obvous at all. 18 The model ncludes the (almost) mnmum number of features that characterze real-lfe enterprses, gong far beyond the stylzed versons of economcs-based models. Up to now, most modfcatons of mamzng behavor have been ntroduced n a pecemeal fashon, as addenda to the mamzng manager, who s almost always lurkng n the background. We have shown that features such as learnng, bounded ratonalty, concern for the welfare of others, 18 In lght of the work of the Santa Fe Insttute (see, for eample, Mller and Page, 2007), one would epect from our smple assumptons the appearance of sgnfcant emergng propertes. Ths s n fact the case, as we have seen n Secton 3. IESE Busness School-Unversty of Navarra - 19

22 uncertanty, and so on can be analyzed and modeled smultaneously. No harm arses from t and the eplanatory power of the model ncreases notceably. We would lke to pont out the mportance of bounded ratonally for our results. Wthout t, the optmal behavor of managers would quckly converge to type-7 companes, whch would consstently domnate the others. Bounded ratonalty does away wth ths, snce the manager s satsfed wth the frst project that eceeds the threshold, makng t reasonable for companes to undertake projects other than (1,1,1). 19 Dversty s good, and n our model t emerges from the bounded ratonalty feature. Managers uncertan knowledge about ther company type may have a catastrophc effect on ther company s evoluton, n the sense that a large change may arse from a small modfcaton n the parameters. The reason s smple but nterestng. The manager has a pror on the company type. Unless the pror s very sharp around the true value, the dstrbuton gves weght to the other types. Assume you have a type-7 company. We argue that these companes can be very unstable whenever management has naccurate knowledge of ther true state. As managers estmate company type by computng the epectaton over the pror, the epected company type wll come to less than 7. Ths leads to the selecton of other than type-7 projects, whch, n turn, gves a postve probablty of losng attrbutes. And f you lose attrbutes, t wll be dffcult to recover them, leadng to a decrease n the number of type-7 companes, whch reflects what happens n real lfe when managers have a dstorted percepton of the state of ther company. In practce, managers who have a dffuse knowledge about ther company make poor decsons. And obvously, everythng wll be much worse f they consder only the effcency attrbute, gnorng attractveness and unty. Fnally, t s worth nvestng n learnng about one s own company profle. Assume that, at a gven stage, companes of type-7 abound. By the mtaton effect, I would lke to be lke the leaders. But, f I want to carry on beng a type-7 company, I must select type-7 projects. A type-7 company dong a type-7 project has a probablty of success equal to one, and wll contnue to have a (1,1,1) profle. Assume that my preferences are for type-7 companes but my company s not type-7. What happens? By mtaton I wll tend to select (1,1,1) projects and so wll set myself up for falure, whch may lead to a downgrade n company type. The wdespread tendency to follow the leaders entals the rsk of overreachng, unless managers have an accurate assessment of ther company profle. Elusve concepts such as attractveness and unty are dffcult to measure objectvely. Estmatng them s therefore the responsblty of general management. The tendency to delegate ths task to the HR department solates general management and reduces the chances of a correct dagnoss, thus ncreasng rsks. One possble dffculty wth the model stems from the fact that, n ts current form, t s not easy to antcpate behavor for values of the parameters n reasonable domans. The only way to learn about behavor s by runnng the model and observng the outcome. In our further work we wll try to eplan observed behavor, buldng on the fact that the dynamc evoluton of the model s controlled by a Markov chan, a class of well known processes. We also ntend to add some of the enhancements suggested n prevous sectons. 19 Under some condtons a majorty of frms become type-7 (whch s obvously the deal stuaton). But we have seen that learnng can be dysfunctonal: after the proporton of (1,1,1)s reaches 100%, t can decrease substantally as tme goes by IESE Busness School-Unversty of Navarra

23 References Chung, K. L. (1982), Lectures from Markov processes to Brownan moton, New York: Sprnger-Verlag. Davs, J., K. Esenhardt, and C. Bngham (2007), Developng theory through smulaton methods, Academy of Management Revew 32(2), pp DMaggo, P. J. and W. W. Powell (1983), The ron cage revsted: Insttutonal somorphsms and collectve ratonalty n organzatonal felds, Amercan Socologcal Revew 48, pp Glbert, N. (2008), Agent Based Models, Quanttatve Applcatons n the Socal Scences, Thousand Oaks, CA: Sage Publcatons. Harrson, J. et al. (2007), Smulaton modelng n organzatonal and management research, Academy of Management Revew 32(4), pp Heyman, D. P. and M. J. Sobel (2003), Stochastc Models n Operatons Research, New York: Dover Publcatons. Jensen, M. (2000), Value Mamzaton, Stakeholder Theory and the Corporate Objectve Functon, n Breakng the Code of Change, M. Beer and N. Nohra, (eds.), Boston: Harvard Busness School Press, also n Journal of Corporate Fnance, Fall March, J. G. (1991), Eploraton and Eplotaton n Organzatonal Learnng, Organzaton Scence 2(1), pp Meadows, D. H. (2008), Thnkng n Systems: A Prmer, Whte Rver Juncton, VT: Chelsea Green Publshng Company. Mller, J. H. and S. E. Page (2007), Comple Adaptve Systems: An Introducton to Computatonal Models of Socal Lfe, Prnceton, NJ: Prnceton Unversty Press. Pérez López, J. A. (1993), Fundamentos de la dreccón de empresas, Madrd: Ralp. Rosanas, J. (2008), Beyond Economc Crtera: A Humanstc Approach to Organzatonal Survval, Journal of Busness Ethcs, DOI /s ld. Taylor, H. M. and S. Karln (1998), An Introducton to Stochastc Modelng, 3rd ed., San Dego, CA: Academc Press. IESE Busness School-Unversty of Navarra - 21