THE CONSTITUTION OF THE NONPROFIT ENTERPRISE: IDEALS, CONFORMISM AND RECIPROCITY #

Transcription

1 Luc Papers n. 5, Sere Etca, Drtto ed Economa 8, novembre 00 THE CONSTITUTION OF THE NONPROFIT ENTERPRISE: IDEALS, CONFORMISM AND RECIPROCITY # Ganluca Grmalda *, Lorenzo Saccon **. Introducton Studes dealng wth the economc and socal functon of the nonproft enterprse can be traced back nto two maor strands of lterature. The frst emphasses the pecular falures manly medan voter and asymmetry of nformaton - of both the poltcal and the market system n the provson of publc or welfare goods (respectvely esbrod, 988; Hansmann, 980), thus argung for the necessty of new types of organsatonal forms of productve actvty n those sectors. However, these models do not actually explan what n the pecular nsttutonal nature of the nonproft should help to solve ths knd of neffcency. The second approach does offer a postve explanaton for the nonproft frm, whch draws on the dea that the agents nvolved n the nonproft sector have other-regardng motvatons such as altrusm, wll to conform to the establshed system of norms, a dsposton to recprocate the perceved farness of others acton (for a revew, see Rose-Ackermann, 987). However, n our vew ths approach does not provde a sound theoretcal foundaton for these atttudes, whch rsks makng the whole explanaton vod. Moreover, such a theory s at odds wth evdence on the conflcts of nterests that affect the agents nvolved n the nonproft actvty, as hghlghted by the frequent practse of self-mposng norms nvolvng fducary dutes and codes of conduct even n the nonproft sector. In fact, the realty of the nonproft sector appears much more varegated than what would result from ths approach. The model we develop n ths paper seeks to address both shortcomngs that we perceve n the receved theory. Frst, t takes on the queston of ndvdual motvatons to choce, provdng a general model of choce n whch a varety of possbly conflctng motves to acton s weghed up by an agent. In ths settng, a seemngly altrustc behavour s not a mere atttude of the ndvdual, but s one of the # Support receved by the MIUR and the CARIPLO Foundaton under the natonal research proect Economc comparatve analyss of nsttutons and nsttutonal complexty of governance forms, n the perspectve of ncomplete contracts s gratefully acknowledged. * Department of Economcs, Unversty of Trento and Unversty of Southampton ** Department of Economcs, Unversty of Trento and CELE, Centre for Ethcs, Law and Economcs, Unversty Cattaneo-Luc, Castellanza

2 Luc Papers n. 5, novembre 00 possble outcomes emergng from a process of ratonal evaluaton of dfferent motves to acton. In the applcaton of ths model to the case of the nonproft enterprse, we shall assume that agents preferences are represented by a comprehensve utlty functon, n whch two basc motves to acton are consdered: the frst s a (standard) self-nterested motvaton, whereas the second s a condtonal wllngness to conform to an deology, or a moral prncple, whch for brevty we shall call a conformst, or deal, motve to acton. Ideology, or moralty, s shaped as a normatve crteron of evaluaton for collectve modes of behavours, whch provdes the agents wth a rankng of the states of affars based on ther greater or lesser correspondence wth the fulflment of ths normatve prncple. The deology s seen as the result of a (possbly hypothetcal) contract between the agents nvolved n the nteracton n an ex-ante phase. Ths sets on a normatve prncple that offers an assessment n the ex-post phase of the socal outcomes, broadly descrbed, n terms of the fulflment of the prncple tself; that s to say, the normatve prncple bols down to a socal welfare functon that measures the correspondence of the outcome wth the normatve prescrptons provded by the deology. Agents, therefore, use such a shared prncple n order to measure ther own and any other s degree of conformty wth t, and we assume that one s own motvaton to act n conformty wth the prncple ncreases wth others (expected) conformty. In other words, ndvdual complance wth the deology s condtonal on others complance wth t, as perceved by the agent. Ths pecular feature of recprocty over others behavour calls for an extenson of the usual equpment of decson theory, whch s provded by the theory of Psychologcal Games (Geanakoplos et al., 989). Second, we propose a possble way n whch the model s capable of accommodatng for the pece of evdence mentoned above, namely the possblty of conflct of nterests wthn the nonproft. In fact, the nonproft s one of the possble outcomes n a game of producton where some relevant agents settng up the productve actvty, deally an entrepreneur and a worker, determne the nature of the organsaton through ther decsons. Snce the structure of the nteracton turns out to be that of a coordnaton game, then codes of ethcs and self-mposed rules of conduct can be ustfed as devces extendng the structure of the game n order to select the outcome correspondng wth the nonproft organsaton, or, as we suggest for future extensons of the work, nvestments made to reveal the true type of the frm to external agents, e.g. donors, n a context of asymmetrc nformaton. Overall, two are the features that are needed to turn the nature of the frm from proft to nonproft orented n the producton game. Frst, agents must attach a suffcently hgh weght to the conformst motve to acton n comparson wth the materal loss that ths may brng about. Second, the deology that agents ncorporate nto ther system of ends s shaped as the result of a (possbly hypothetcal) socal contract between the relevant fgures partcpatng n the venture. In partcular, deology s nclusve n that not only does t take nto account the nterests of the agents actve n the productve enterprse, but also the nterests of other benefcares and stakeholders of the good produced. Ths addtonal category s represented n the model by the presence of a thrd agent, the consumer, who does not have an actve role n the after-consttutonal phase;.e. she s a dummy player n the stage game of producton. By conformng to the deology, therefore, the promoters are aware that they are gvng voce to some categores otherwse excluded from socal consderaton. Moreover, the deology s assumed to apply a

3 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty far and effcent dstrbuton of the surplus n accordance wth a contractaran crteron, snce the nterests of each partcpant consumer ncluded - are symmetrcally accounted for (Brock 979, Saccon 99, 000). Gven such an mpartal perspectve that characterses the ex-ante stage of agreement on the set of dstrbutve prncples, the resultng choce can also be sad to embody a pecular moral character. On an operatve ground, the Nash barganng soluton s taken as the functon representng ths deology. Overall, the nonproft organsatonal form s seen as the result of a - possbly hypothetcal nternal contract agreed upon by the relevant fgures settng up the enterprse, whch brngs n the nterests of the stakeholders external to the frm n an equtable manner. Therefore, deology stands out as a crucal asset for the nonproft organsaton. The frst part of the paper s devoted to the development of the ndvdual model of choce. Secton ntroduces the dstncton between consequentalst and conformst ndvdual preferences. The materal and deal game are then presented as representatons of the same nteracton though assessed from dfferent standponts, whch adopt the self-nterested consequentalst and the conformst atttude respectvely. Fnally, a general verson of the comprehensve utlty functon s presented. Secton 3 offers a specfcaton of the conformst motve to acton, ntroducng a pecular noton of recprocty n complance wth the deology, whch s based on an extenson of Rabn s model of farness (993). The second part of the paper ams to apply such a model of behavour to the account of the nonproft enterprse as a pecular organsatonal form. Secton 4 llustrates the settng of the producton game, where both the actve players have one acton mprovng the qualty of the good and another one that leaves t unaltered wth respect to a free market standard. The surplus of the consumer s drectly lnked wth the number of agents performng the qualty-mprovng acton. It s then shown how ths stage game leads to dfferent solutons dependng on whether t s evaluated from the self-nterested standpont (materal game) or from the deal one (deal game). Secton 5 explores the fnal soluton of the producton game when the two conflctng atttudes are blended nto the comprehensve utlty functon. e show how an equlbrum s possble that leads both actve agents to perform the qualty-mprovng soluton, provded that the weght attrbuted to the deologcal motvaton s suffcently hgh. However, we observe that under the same condtons there exsts another equlbrum n whch agents perform the non-qualty-mprovng acton, besdes a thrd equlbrum n mxed strateges. Notcng that the structure of such a psychologcal game resembles that of a coordnaton game, we suggest that the ssung of codes of ethcs by the frm may act as a cogntve devce able to generate determnate expectatons for the agents over the qualty-mprovng equlbrum. e fnally nterpret ths result as a man underpnnng for the nonproft frm.. The System of Choce of the Agents.. Self-Regardng and Other-Regardng Motves to Acton: an Overvew The dea that ndvduals take nto account a large number of reasons to acton when makng decsons, whch extend well beyond the stereotypcal self-nterested motve, s now largely accepted 3

4 Luc Papers n. 5, novembre 00 among students of ratonal choce. As Bnmore puts t (994: 9), not even n Chcago are the vews [that homo-economcus strctly abdes by her own self-nterest] gven credence any more. Ths set of supplementary motvatons may nclude altrusm, the wllngness to act n accordance wth the receved sense of moralty, or the want to conform to the behavour or the expectatons of the other members of the communty. In prncple, every type of motvatons, even those dctated by a person s whms, or by selfdestructve and ant-conformst desres, can be ncluded n one s system of ends. Therefore, accordng to ths vew, the range of the agent s possble motves to acton s left as ample as possble. In other words, there s no constrant on the set of ends that the agent may lke to pursue, but the correspondent choces need to satsfy requrements of nternal consstency n order to be called ratonal. In partcular, when a sequence of choces made under dfferent crcumstances that s, under dfferent values of the parameters that frame the context of choce fulfls the basc axoms of transtvty, completeness, reflexvty, and possbly some others, then the nternal consstency and thus the ratonalty of the acton can be sad to hold. The utlty functon does not have any ntrnsc meanng f not for actng as a formal devce to represent such a coherent system of choce. In partcular, ndvdual ratonalty s not assessed on the grounds of the agent s effectveness n pursung some noton of selfnterest, but rather on the logcal nternal coherence of her choces wth respect to her ends: even the behavour of a sant can be assessed n terms of ratonalty n much the same way as that of a homoeconomcus. Ben Ner and Puttermann (998) provde a theoretcal underpnnng for such a model of ndvdual choce, by dstngushng between self-regardng, other-regardng and process-regardng motvatons. The dfference between them depends on whether the agent s concerned wth the consequences of her acton on herself, on others, or on the way outcomes are brought out, respectvely. e shall expand on ths pont n the next secton. Another way of representng these deas has been put forward by Copp (997), who assocates dfferent reasons to acton to dfferent standponts that can be adopted n assessng a partcular socal outcome. In partcular, a self-regardng motvaton stems from the adopton of a standpont that s nternal to the ndvdual, where the standard of assessment s some form of her wellbeng. In the case of the other-regardng motvatons, the agent uses a perspectve external to that of her own self. In ths case, she may adopt the standpont of a sngle agent dfferent from her, whch may lead to altrusm, or that of the team she s part of (Sugden, 000), or the pont of vew of an mpartal observer sympathetc to each member of the group of agents (Harsany, 977). Only recently have some contrbutons been put forward that buld on ths background theoretcal framework to provde workng models of choce. In partcular, Bernhem (994) and Sugden (998a, 998b) add to the self-nterested motvaton a second one gven by the desre to obtan the commendaton and avod the dsapproval of others wth respect to one s own actons. In these models the other-regardng motve s thus assocated wth the desre to lve up to others expectatons, whch s the reason why these approaches are generally referred to as normatve expectatons models (Sugden, 999). Another strand of contrbutons s connected wth the flourshng body of lterature n Expermental Economcs, where the evdence gathered n laboratory experments on ndvdual behavour, somewhat unaccountable by relyng only on self-nterested motvatons, have spurred the elaboraton of new 4

5 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty hypotheses n choce models. Fehr and Schmdt (00) dstngush theores where agents are endowed wth socal preferences - that s, ther utlty functon also depends n some way on the payoffs dstrbuton amongst them and theores where agents are motvated by ntentons-based recprocty; that s, the ndvdual s spurred to replcate the ntenton perceved n others actons. In partcular, the socal motves taken nto account n the frst approach nclude averson to nequalty n surplus dstrbuton, or some form of altrusm, or concern for the ndvdual poston wthn the payoffs rankng. The second approach bulds on Rabn s semnal model of farness (993). The man dea s that the agent may assgn a dfferent value to others actons dependng on how she perceves ther ntentons n brngng them out. For nstance, an acton may be deemed as knd when t brngs about an extra utlty wth respect to what expected n relaton wth some standard of behavour, or t may be perceved as nasty when t leads to an unexpected loss. As a matter of fact, accordng to nvestgatons n Psychology, a key trat n human behavour s to recprocate the ntenton perceved n others behavour wth an acton of the same sgn. On ths vew, Rabn s model s a formal devce to ncorporate these observatons nto ndvdual choce theory. The theory of Psychologcal Games provdes wth some tools to embody these consderatons nto a formal analyss. In fact, t ntroduces belefs, of every possble order, on each other behavour nto the utlty functon (Geneakoplos et al (989)). In ths fashon, t s possble to model the dea that an agent can be more or less satsfed dependng on how others actual acton correspond to her ntal expectatons. In partcular, for smplcty restrctng the analyss to the case of two-person nteractons, Rabn consders a par of kndness functons, whch measure the extent to whch the agent s and her counterpart s actons ncrease or dmnsh one another s expected payoff. Ths estmate s used by each agent to apprase the kndness of the other party to herself, on the grounds of her second order expectaton, and the kndness of the subect herself toward the other agent, as perceved on the bass of her frst order expectaton. The way n whch these functons are constructed s to consder the best and the worst payoff that each agent can cause to the other on the bass of the recprocal expectatons, and then to consder how the payoff actually brought about les between those two extremes 3. Other models have been developed n whch agents socal preferences and ntenton-based recprocty atttudes are both present n ndvdual motvatons. For nstance, n Charness and Rabn (999) the weght that each ndvdual attaches to each other ndvdual n her own socal preference depends on the dsesteem wth whch the agent herself thnks of the others, whch s apprased n terms of the dstance of others behavour from a purely dsnterested one. Lkewse, n Falk and Fschbacher (999) each agent computes a benevolence term for any other agent, whch depends on the degree to whch any other agent s acton has ncreased or dmnshed the nequalty n the overall dstrbuton. Ths term s then multpled by a recprocty term that s postve or negatve n relaton to the other agent s acton beng perceved as knd or hostle. Fnally, another parameter measures the relatve weght attached to materal utlty wth respect to that of recprocty on the socal dstrbuton. The model that we ntend to buld s smlar to those now llustrated n that the aspects of recprocty are related to some forms of normatve evaluaton of the socal states. However, as we shall argue n secton 3 and 5., t dffers from them n the content of the normatve functon. 5

6 Luc Papers n. 5, novembre 00.. Conformst Preferences... Consequentalst Preferences Vs. Deontologcal Reasons to Prefer In the present paper we shall embrace the vew outlned n the prevous secton that the number of motvatons that agents consder extends beyond the standard self-nterested reasons to acton. However, we beleve that pror to the dstncton between self-regardng and other-regardng reasons to acton there exsts an even deeper dstncton between consequentalst and conformst types of preferences of the ndvdual, on whch our model wll be grounded. Gven the mportance of the matter, we devote the present secton to put forward n detal the theoretcal underpnnngs of the ndvdual system of preference. Smply stated, preferences can be sad to be consequentalst when they are defned over the consequences of the agents actons. Consder a stuaton of strategc nteracton nvolvng many agents. Ths generates states of affars that can be dfferently descrbed accordng to ther dfferent characterstcs. If these are meant as consequences, they are understood as what happens to the decson maker n a state.e. as the consequences to the decson maker herself - or what happens to any subset of ndvduals or to every ndvdual that s the consequence to anyone n the same state. In the frst case the characterstcs under consderaton would be an attrbute of the sngle agent herself such as her wealth, lesure, effort, etc. - and they are the result of a one to one mappng between the state set and the consequence set held by one partcular ndvdual (the decson maker). In the second case the characterstcs under consderaton would be attrbutes of some set of ndvduals (possbly all of them), and they could be defned by a one to many correspondence between the state set and the consequences sets held by all the concerned ndvduals. The dstncton between self-regardng and other-regardng consequentalst preferences thus depends on whether the lst of characterstcs takes nto account only self-referred consequences, or also consequences to other agents. In the former case we have self-regardng consequentalst preferences. hen nstead the agent takes account of the consequences of socal nteracton on other ndvduals, other-regardng consequentalst preferences obtan. Notce that ths defnton does not necessarly mply a benevolent dsposton of the self towards other people, but only that ndvdual preferences are affected by the outcomes occurrng to other people as well as thers. For nstance, even a sentment of hate towards another person would be regarded as mplyng an other-regardng preference for the very fact that the set of consequences that the agent consders ncludes that of other agents. To be sure, however, otherregardng preferences are the natural source for ndvdual moral preference of a consequentalst type - namely, preferences over every ndvdual s consequences mpartally weghted. In partcular, we have utltaran moral preferences f, besdes accountng for everyone s consequences, we further requre that each agent s consequences are assessed from the pont of vew of each agent s preferences, thus mplctly callng for nterpersonal comparsons of utlty, n addton to the requrement of summng up each agent s utlty. Altrustc preferences are another specal case, n whch the agent attaches a hgh, weght to the consequences for other agents, as assessed from the pont of vew of ther own self-referred preferences, rather than from her own. 6

7 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty Let us now come to the second basc type of preferences of the self, whch we call personal conformst preferences as opposed to personal consequentalst preferences. As well as the frst type of preferences, conformst preferences are defned over states of affars, but nevertheless they are not descrbed n terms of consequences occurrng to any ndvdual, but as patterns of ndvdual, nterdependent or collectve behavours, and as belefs about such modes of behavour. e put a deontologcal element at ther bass, snce these preferences are grounded on some ntrnsc characterstcs of the agents actons rather than on ther consequences. In other words, agents are motvated to act by the awareness that ther actons satsfy some formal propertes rather than from the mere outcomes of ther actons 4. For nstance, the agents may attach utlty to the knowledge that the decson procedure they follow s far accordng to some defnton. Agan, t s possble to draw a secondary dstncton between self-regardng and other-regardng conformst preference, where the former refers to the case n whch the agent only cares about the ntrnsc characterstc of her own acton, whereas the latter ponts to the characterstcs of both her own and the others partcpants actons. In order to better understand the dstnctons between the two basc concepts of preferences, the followng elements are to be consdered n sequence: ) the relevant descrpton of states of affars (sec...), ) the preference orderng over states of affars as t depends on the relevant descrpton of the states (sec...3), ) the nduced preferences orderng over the actons set of each ndvdual player, v) the numercal representaton of such preferences by an utlty ndex that we call deal utlty(sec...4) The Relevant Descrpton of States of Affars States of affars are now prmarly descrbed as sets of nterdependent actons - to whom each player belefs over the other s actons are appended. These are consdered wth respect to ther conformty (or lack of conformty) to a gven abstract prncple of ustce. Under ths descrpton states are modes of deontologcal ndvdual or collectve behavours performed by the players. e may fx a pattern of behavours (a vector of strateges) that s meant as perfectly deontologcal because t fully conforms to an abstract prncple of farness or to a far crteron of benefts dstrbuton amongst the concerned partes. Call such a state the deal. Then we may look for the degree of conformty to the deal dsplayed by each state of affars resultng from the ndvdual choces actually performed by all the players (or by each player s choce gven other players choces.) In other words, we allow for the possblty that agents experence dfferent levels of utlty - that s, dfferent degrees of motvatonal strength - n relaton to the degree to whch the normatve prncple can be sad to be fulflled. In partcular, n order to defne the character of mutualty of the preference (see next secton), t wll be mportant to sngle out the ndvdual contrbuton to the accomplshment of the deal state and, conversely, the ndvdual responsblty n the devaton from t. Another pont deserves some comments. The prncple of ustce to whch agents desre to conform ther actons, may well be a prncple of dstrbutve ustce, and ths wll ndeed be the case n our model. Therefore, the outcomes for the agents have to be taken nto account n order to check the degree of farness of the surplus dstrbuton. Ths does not reduce the second type of preferences to the frst. Frst type utltes are no more than the rough materals of the second type. e must know about outcomes where utltes for consequences are allocated amongst the players n order to descrbe whether they 7

8 Luc Papers n. 5, novembre 00 correspond to the deal dstrbuton defned accordng to an abstract prncple. A prncple of farness (some gven far barganng soluton to a socal contract model) accounts for each state accordng to a dstrbuton crteron. Ths enables us to say whether the occurrng vector of strateges n each state determnes a payoffs dstrbuton consstent wth the abstract prncple of farness. But what matters for the relevant descrpton of the states of affars are not consequences or materal payoffs as such, but the descrpton of a dstrbutve property of the payoffs. Under ths descrpton there s no ndvdual to whom the relevant state of affars happens as a consequence. e smply have a dstrbuton statng the rato accordng to whch a pe, whch provdes an amount of overall surplus as hgh as possble, s parttoned amongst dfferent players. Consequently, we may say that the concern for outcomes s n ths case only ndrect, as the nterest of the agents les n the complance wth the deal prncple of ustce rather than on the consequences that ths brngs about. The content and the features of such a prncple wll be specfed n more detal n secton..4 and Mutual Conformty Preferences are then defned not drectly over consequences, but over acts n the grounds of ther conformty to an abstract norm,.e. a dstrbutve prncple. It s apparent that the preference orderng over states depends on an obectve measure of conformty of any vector of actons to the abstract prncple of farness as t s bult nto the descrpton of each state of affars (as seen through the belefs of the players over the others actons). The more a state of affars s expected to conform to the deal, the more t s preferred by a player,.e. the degree of expected recprocal conformty s used as the bass for defnng each player s preference orderng over states. Therefore, conformty s the characterstc that we assume s consdered by players n order to say how desrable a state s. In partcular, besdes allowng for the measurablty of the extent to whch the set of nterdependent actons fulfls the abstract normatve prncple, we also assume that the expectaton of greater conformty by other agents spurs a greater ncentve n the agent to conform as well. In ths sense, at the bass of conformst preferences les a measure of how much deontology s bult nto the expected pattern of behavour dsplayed by all the players n each state. Ths type of preference may be deemed as conformst, n that t conssts of the desre to have the rules ex-ante accepted by an agent to be obeyed by everyone else. The type of conformsm we are descrbng s nonetheless moral, n that the prncple whose general observance trggers utlty s, n our model, the result of an ex-ante unanmous and mpartal ratonal choce. In ths aspect there les the maor dfference between approaches lke Sugden s and ours: n Sugden (000) there does not exst an ndependent normatve condton shapng the rule that agents are requred to conform to: n fact, agents pay a dsutlty (a penalty) for not lvng up to anyone else s expectaton. Ths mples that vrtually any outcome of the game can emerge as the moral rule to be followed, snce every conventon can fnd support by means of the motvatonal force engendered by the expectatons of the communty members (Grmalda, 00). Hence, the heurstc power of such an approach can appear questonable, snce t seems that every norm can command conformty for the very fact of havng come nto exstence. In our model, we take a dfferent route n modellng conformsm n that the rule must reflect an abstract prncple of ustce, whose only requrements are to be ratonally acceptable and far n an ex-ante perspectve. In other words, not all of the patterns of mutual conformty, but only those 8

9 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty satsfyng ex-ante propertes of ratonal acceptablty, are those embraced by the agents. e shall take the Nash soluton to barganng games, and the correspondng socal welfare functon, to represent such a prncple (see secton 5.). One mportant feature of our approach s that, despte the deontologcal element put at the bass of conformsm, we must not gve up the ultmately subectve nature of preferences over states of affars, meant as some sort of subectve affecton of the players (Gauther 986). In fact there s no reason to conclude that the preference crteron should be based on some obectve value havng an ontologcal realty out there, completely ndependent on the affectons or the udgement of those who are asked to express ther preference. Notce that whle conformst preferences depends on degrees of conformty - whch are an obectve measure of the levels of deontology bult n the descrpton of states - nonetheless deontology s meant as conformty of actons to a far dstrbuton prncple that we have smply ratonally agreed upon. As we shall llustrate n secton 5., ratonally agreed prncples of far dstrbuton are n our model meant as what players would accept n an hypothetcal barganng stuaton amongst symmetrcally ratonal barganers, who are all equally drven by ratonalty postulates derved from the same prncple of utlty maxmsaton under strategc nteracton, but as well equally ncapable to dentfy ther own partcular name and role n the game. 6 To clear up the matter, let us state the herarchy wthn whch the dfferent peces of the argument should be understood so far. Frst of all, for each player t s taken for granted the exstence of some frst order utlty functon defned on states, whch are ntally descrbed n terms of the consequence that each player gets from feasble surplus allocatons. Second, players accept some terms of agreement concernng surplus dstrbutons. Ths agreement s worked out accordng to a fundamentally subectve noton of unanmous ratonal choce under deally symmetrcal barganng condtons. Moreover, t defnes a norm for dstrbutng benefts n any game stuaton of the knd under consderaton. Thrd, ths prncple s adopted as the deal term of reference n order to measure conformty of states of affars - descrbed as vectors of nterdependent actons - to a prncple of farness, and ths ntroduces a deontologcal assessment of states of affars. The result s a preference orderng defned over states of affars, whch we hold not merely because of our prmtve psychologcal desres for materal payoffs or preferred consequences, but because t conforms to a ratonally agreed abstract prncple. That conformst preferences are based on a prncple derved n turn from a ratonal barganng model (over payoffs dstrbutons), does not make less deontologcal the reason of preference at ths second level of the argument. Nonetheless the deontologcal nature of these second order preferences does not make them dependent on values (ontologcally) obectve n nature or completely ndependent of the decson maker s affectvty or udgment. Dutes are smply those we have ratonally agreed upon n a hypothetcal barganng stuaton...4. Preference Orderngs and Ideal Utlty In the end, what really matters are each player s preferences over her own actons. As consequentalst preferences nduce personal preferences over the actons sets of every player, ths must also be true for conformst preferences. Smply, these are nduced by the conformst preferences over states descrbed so far. If a player thnks that a strategy combnaton conformng to the prncple of farness s currently the 9

10 Luc Papers n. 5, novembre 00 most probable state of affars, then she wll prefer her acton that conforms to the duty call t the deontologcal acton exactly because t contrbutes to brng about a state of affars conformng to the duty. To state t a bt formally, agent A conformstcally prefers acton X to acton X f A observes an acton Y by the other player B that would brng about a state of affars S (a strategy vector) that conforms to the prncple P f chosen together wth acton X more than together wth acton X. Ths defnton however hdes how mportant belefs are to the defnton of personal conformst preferences. e must account for the fact that a player, whle he does not observe vectors of actons as such, on the contrary holds belefs over other players actons and over other players belefs over hs own acton. Thus he holds preferences over actons accordng to whether these actons, along wth what she beleves other players wll do and what she beleves other players wll beleve about what she does, contrbutes to brng about states of affars that conforms to a ratonally agreed prncple of farness. To gve agan a formal defnton, agent A conformstcally prefers acton X to acton X f she beleves that agent B wll adopt the acton Y, gven that he (B) beleves that A chooses acton X, so that by choosng acton X (together wth act Y) agent A beleves to brng about a state of affars S that conforms to prncple P more then by choosng acton X. Ths defnton makes t natural explanng personal conformst preferences of agent A as restng on a herarchy of mutual belefs, wthn whch any layer of belefs of each party s ustfed by a hgher order layer of belefs. 7 Snce conformst preferences are also two-place relatonshps, by assumng that they satsfy the usual condtons of completeness and transtvty, we can derve a standard preference orderng over the strategy set of an agent 8. Thus, even f conformst preferences are defned over characterstcs of ont actons, rather than on ther consequences, ths does not mpede to represent them by means of a utlty functon, whch would satsfy n addton the usual axoms of expected utlty. e call t ndvdual deal utlty of actons as t s based on the agent s conformst preference orderng on actons. In what follows, we wll provde an example of a utlty functon that addtvely compounds the selfnterested consequentalst motve to acton and the deontologcal-conformst one. The two wll be assocated wth what we call a materal and a conformst, or deal, (source of) utlty, whch, under a reasonable assumpton of separablty, make up the ndvdual comprehensve utlty functon. The exstence of ths par of dfferent atttudes calls for two dfferent types of analyss, comng down to two dfferent concepts of soluton of the same basc game stuaton under scrutny. e call the frst type of analyss the materal game, n whch the self-nterested atttude s domnatng and agents are only concerned wth ther materal utlty: ths wll be gven a formal llustraton n sec..3. The second s the deal game, where nstead the deontologcal source of preference s the relevant one and agents are concerned wth ther deal utlty, as shown n secton.4. The fnal choce of the agent wll be based on how these two prompts to acton are combned n the comprehensve utlty functon, and n partcular on the weght that the agent assgns to one rather than to the other prompt to acton. 0

11 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty.3. The Materal Game It s gven a game G, made up as usual by a trplet of elements: a set I of players, a set of strateges S and a utlty functon U for each agent. Formally, G { I, S, U} =, where S = S defnes the set of feasble strateges profles, and lkewse U s the set of vectors of utltes. Allowng for the use of mxed strateges by the agents, we can further ntroduce the operator (X) to express the randomsatons over a set of elements X. e can thus defne the set of possble randomsatons over the strategy sets of the agents: Σ = ( S ) ; fnally, we can consder the vector ncludng a randomsaton for each agent: I : Σ : = Σ, where the generc element s ndcated wth Σ σ. In the game G, the utlty functons represent a measure of the self-nterest of the agents, thus reflectng the frst type of motvatons llustrated n secton.. They are defned, as customary, frstly over the outcomes of the games - that s over the consequences to any player attached to a gven way of playng the game, such that they are functons of the profles of pure strateges: U (S). 9 Furthermore, takng on standard assumptons regardng expected utlty, we ntroduce Von Neumann-Morgestern utlty functons defned over mxed strateges profles, (Σ) I U, where U ( σ ): = P ( s) U () s. () s represents the probablty that the pure strategy profle s s played accordng to the mxed strategy profle σ. Provded that the nature of ths game does not dffer from the standard, the relevant concept of soluton would be the Nash s one. s S σ P σ.4. The Ideal Game The deal game dffers from the prevous one n that agents evaluate the socal stuaton from a dfferent standpont than the self-nterested consequentalst one, possbly ncludng the evaluaton of the materal payoffs of other agents who are affected by ther actons but cannot affect the fnal outcome. Hence, we ntroduce an deal game G* as an extenson of the materal game G, n whch the set of players s possbly larger than n the materal game thus modfyng the correspondng set of utltes. Formally, ths game s defned by the trplet: * { I*, S, U *} G =., wth I I * and U* U =. Notce that the set of actons S s left unaltered wth respect to the materal game: by defnton the players now ncluded n the game are dummy players n the orgnal one. Restng upon ths constructon, we can now ntroduce the noton of a normatve prncple used to apprase socal state of affars resultng from strategc nteracton. Ths generates a rankng of the strategy combnatons made on the grounds of the deology, or the moral prncple, whch s ex-ante accepted by the agents. Notce that ths rankng s establshed accordng to the level to whch the vectors of materal utltes (the standard payoffs vectors) satsfy a gven formal dstrbutve property, that s whether, attached to any outcome, a dstrbuton of the materal utltes does materalse that satsfes a normatve property T. Consequently, we are assumng that t s possble to measure on some scale the I *

12 Luc Papers n. 5, novembre 00 correspondence of the socal states of affars to an deal norm of assessment, whch s represented by a functon of the socal outcomes. Ths s analogous to an ndvdualstc socal welfare functon n that t s dependent on the materal utltes of the agents nvolved n the nteracton and establshes a certan formal property of the materal utltes dstrbuton amongst the agents themselves: T : = * I U ( S) R Therefore, such a normatve prncple permts the creaton of an orderng over the possble states of affars (strategy vectors lke s S), whch represents the assessment that an mpartal spectator would gve to the dfferent socal stuatons on the bass of the relevant normatve crteron of dstrbuton. A hgher value of the functon T, defned over outcomes, mples that the assocated socal state of affars satsfes to a hgher degree the normatve crteron. Of course, takng the structure of the game as granted, t s possble to make the functon drectly dependent on the pure strategy profle set S, and, also, on the mxed strateges of the game: [ ] ( ) = P ( s) T U () s T σ :. s S σ In analogy wth ndvdual expected utlty, the expected normatve functon s smply a weghed sum of the ndexes of welfare dstrbuton under all possble pure strateges profles, wth weghts gven by the probabltes that each outcome s actually played..5. The Comprehensve Utlty Functon As already ponted out, we allow for an agent havng varous, possbly conflctng, motves to acton n her own system of delberaton. The frst s gven by the usual self-nterested motvaton, whereas the second hnges upon the orderng of the socal outcomes that s carred out by means of the normatve prncple T ntroduced n the prevous secton. It conssts of the utlty derved from the knowledge that the acton performed by the agent, gven her expectaton on others players acton, satsfes, to some extent, the normatve prncples T wth respect to the assessment of the socal states of affars based on the rankng of the correspondng outcomes. e now ntroduce what we call a comprehensve utlty functon, whose components are gven by the materal and deal utlty. In what follows we shall assume that the agents are able to fully compare ths par of reasons to acton and to take a decson, thus leavng asde the ssue of commensurablty of dfferent sources of value 0. The comprehensve utlty functon wll then have the followng form: V ( σ ) U ( σ ) λ f [ T ( σ )] = I* + The frst term U represents the materal utlty and s shaped n accordance wth the agent s selfnterested consequentalst preferences. The second term s the deal utlty and reflects the agent s concern wth other types of reasons to acton, meant n general as the degree of conformty of the socal state of affars - the agent s and the others partcpants behavours - to the normatve prncple of welfare dstrbuton T. Ths s expressed as a functon f, shared by all agents, of the socal normatve crteron T.

13 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty For smplcty, the two components enter the functon addtvely, and the parameters λ, possbly dfferent for the agents, measure the weght attrbuted to ther deal rather than materal source of utlty. The functon f may be specfed n dfferent ways n order to account for varous possble forms of the moralty-grounded motve to acton. In the followng secton we shall provde a partcular specfcaton based on an dea of expected mutualty n conformng to the normatve prescrptons. 3. Mutual Conformsm 3.. A Recprocty-Based Account of the Ideologcal Motve The model that we wsh to develop emphasses the aspects of recprocty n actng n accordance to a shared normatve prncple embodyng an deology, as represented by the welfare dstrbuton functon T. In partcular, the dea we want to capture by means of our model s germane to the common approach n the lterature on moral phlosophy that sees agents as avalable to sustan a ust acton, but possbly detrmental n terms of self-nterest, only nsofar they expect other agents to do the same. Indeed, ths s a restatement of the usual noton of recprocty, where ths s now ntended n a general sense and wth respect to a normatve prncple, rather than n a two-sde relatonshp where agents are concerned wth each other s payoffs. e model ths account of recprocty by buldng on Rabn s model of farness (see sec..). In partcular, Rabn s kndness functons are substtuted by functons of expected conformty wth the normatve prncple, so that each agent s ncentve to perform an acton satsfyng the moral prncple, and possbly contrastng the self-nterested reason to act, s postvely lnked wth the extent to whch the opponent s expected to perform an acton consstent wth the same normatve prncple. In ths way, we model the dea that agents derve utlty from ther expected recprocal conformty to a shared normatve prncple, rather than from an expectaton about how knd they are one toward the other n terms of the satsfacton of ther own consequentalst preferences Expected Conformty to the Ideology To model these deas, we need a further extenson of the analytcal structure of ndvdual preferences, derved from the approach of Psychologcal Games (Geneakoplos et al, 989). In prncple, the formal apparatus requres the constructon of herarches of belefs of nfnte order, but ths aspect s much smpler here snce, for our purposes, belefs of the frst two orders are all of what s needed n order to gve an account of recprocty. A frst order belef for player s a probablty measure over the other players mxed strategy set, namely B := ( Σ ) ; thus the generc element b ndcates the probablty wth whch beleves B that the other players are gong to mplement the profle of strateges σ -. In the same fashon we can defne B := ( B ). Obvously, when there are ust two actve players, we have B := ( Σ ) B = : B. A second order belef for player s a conecture over the belef of over s strateges. Therefore, t conssts of a probablty measure over the Cartesan of other players belefs of frst order: and 3

14 Luc Papers n. 5, novembre 00 B ( B ) =. Thus the generc element of ths set, b : of over s strateges s B b. e shall ndcate wth ( b, b,...), represents s probablty that the belef b = the nfnte-dmenson vector collectng the belefs of each order for player. e now restrct our attenton to a two-person game, even though a generalsaton to the case of n players would be straghtforward. In analogy wth Rabn s par of kndness functons, measurng the mutual mpact of one s actons on the other s ndvdual utlty, we can now ntroduce functons computng the degree of conformty to the deal -.e. a moral prncple (we call t thereafter the deology). e frst defne s conformty to the deology n the followng way: MAX T ( ) ( σ, b ) T ( b ) f σ, b = MAX MIN T ( b ) T ( b ) MAX MIN where T ( b ) = arg maxt ( σ, b ) and T ( b ) arg mnt ( σ, b ) T MAX ( b ) and MIN ( b ) Σ =. In other words, T are respectvely the maxmum and mnmum value that the welfare dstrbuton functon, representng the normatve prncple or deology, can assume, dependng on s acton, gven s frst order belef ( MIN ( b ) order belef. ( b ) b over the acton that s gong to perform. Therefore, f T MAX ( b ) T s obtaned, then agent s maxmsng (mnmsng) the welfare functon gven hs frst T σ s nstead the value of the welfare functon correspondng to s actual choce σ,, gven what he expects from player. Hence, (, b ) satsfes the normatve crteron assocated wth the functon T. hen ( b ) f σ s an ndex varyng between - and 0 expressng the extent to whch s acton Σ, f σ s equal to 0 (-) t means that s exactly performng the strategy maxmsng (mnmsng) the welfare functon, gven s frst order belef, and ths proves that hs acton s consstent wth the normatve prescrptons at the maxmum (mnmum) degree. In other words, conformty to the agreed upon normatve prncple s measured by the extent to whch one s acton reduces the dstance between the actual state of affars and the deal one, that s the state where the value of the welfare dstrbuton functon s maxmsed over the agent s strategy set, gven the expected choce by the counterpart. To model the concept of recprocty n the ndvdual motvatonal system, we need to ntroduce a functon symmetrc to that set out above. Ths s the esteem that player forms about s complance wth the deology: MAX ~ T ( ) ( b, b ) T ( b ) f b, b = MAX MIN T ( b ) T ( b ) MAX MIN where T ( b ) = arg maxt ( b,σ ) and T ( b ) arg mnt ( b,σ ) T MAX ( b ) and MIN ( b ) Σ =. Therefore, T are the value that the welfare functon takes when player respectvely Σ 4

15 G. Grmalda, L. Saccon, The Consttuton of the Nonproft Enterprse: Ideals, Conformsm and Recprocty maxmses or mnmses t, gven the second order belef of player. In other words, those functons ndcate the maxmum and mnmum values that player can attrbute to the welfare functon, gven the belef he has about s acton as perceved by hmself. In fact, recall that such a functon measures the esteem of s complance to the deology as measured from s standpont. Thus, f player has formed a belef b about the player s belef over s acton, she wll udge s actons from ths pont of vew. She wll then consder the best and the worst value that can do wth respect to the welfare functon, and then compare these values wth T ( b, b ) ~ accordng to hs belefs. Alke the twn functon f ( σ b ), a value of ( b, b ), whch s the actual value that expects the welfare functon to take, f equal to 0 (-) ndcates the maxmum (mnmum) degree of conformty by player to the deology as emboded n the welfare functon T The Comprehensve Utlty Functon e can now ntroduce the fnal verson of the utlty functons. Notce that, as n every psychologcal game, the utlty of an agent depends on her belefs over the dfferent possble outcomes (strategy vectors). e assume the followng representaton, whch blends the two functons of complance to the deology: The fact that V [ ] ( ) ~ ( σ b, b ) = U ( σ, b ) + λ + f ( b, b )[ + f σ, b ], b now substtutes σ depends on the fact that only n equlbrum the two are assumed to concde. The deal utlty, agan weghted by the coeffcent λ, conssts of the product of the two conformty functons augmented by. The dea we wsh to capture through ths specfcaton s twofold. On the one hand, the agent s utlty depends postvely on the realsaton of the best socal state of affar, n terms of the satsfacton of the normatve crteron; ndeed, the deal utlty s ncreased when an agent performs an acton ncreasng the value of T, whoever she s. The second aspect s the character of recprocty n the complance wth the ~ normatve crteron: n fact, the (esteemed) conformty of the other player, as expressed by ( b, b ) f, may be seen as the margnal ncentve that the subect has n pursung her deal motvatons, as represented by f ( σ b ),. Therefore, the deal utlty ncreases as the counterpart s acton s perceved as more consstent wth the deology, thus elctng a smlar behavour n the agent herself. In the extreme ~ case n whch ( b, b ) f s equal to, whch denotes the worst acton that agent can perform n terms of the normatve prncple, the coeffcent of the deologcal motve gets equal to zero, thus leavng the ~ self-nterest as the only relevant motve to acton 3. Conversely, when + ( b, b ) f s postve and suffcently large, then agent may accept to pursue an acton that s contrary to her self-nterest but conform to the normatve prncple 4. In general, the evaluaton of the opponent s conformty to the normatve prncple magnfes or shrnks the ndvdual motvaton to act n accordance wth the normatve prncple as well. 5

16 Luc Papers n. 5, novembre The Psychologcal Nash Equlbrum The pecular nnovaton ntroduced n the comprehensve utlty functon, that s the ncluson of belefs n the arguments of the functon, calls for an extenson of the standard concept of soluton of games, namely the Nash equlbrum. e shall adopt the orgnal noton of Nash psychologcal equlbrum put forward by Geanakoplos et al. n ther semnal contrbuton, although some refnements of ths noton have been suggested (Van Kolpn, 99) and others appear possble. The underlyng dea of ths concept s that, f we are n equlbrum, then the belefs of ratonal players must be coherent wth the strateges that are there beng played. As an example, f n equlbrum I observe my opponent playng the (possbly mxed) strategy σ Σ, then my frst order belef must assgn probablty one to that partcular strategy and 0 to all of the others. Ths s tantamount to sayng that once an equlbrum has been reached, all of the frst order belefs must be sngle-pont dstrbutons assgnng probablty one to the equlbrum strategy. The hgher order belefs are then generated upon a condton of coherence wth ths ntal condton (Geanakoplos et al, 989: 64). e shall call β ( σ ) the dstrbuton of belefs assocated wth the dstrbuton that s coherent wth assgnng probablty to the strategy σ, and wth β ( σ ) = ( β ( σ ),... β ( σ )) B n the profle of such belefs for the n players. Recallng the defnton of b as the vector collectng the belefs of each order for player, and consequently of b= (b, b n ) as the profle of belefs for each of the n players, we are now able to provde the defnton of Psychologcal Nash equlbrum (Geanakoplos et al, 989: 65): A psychologcal Nash equlbrum for a n-person normal form psychologcal game G s a par ( b, σˆ ) B Σ ˆ such that: ) b ˆ = β ( ˆ σ ) ( ) V ( bˆ, ˆ σ ) σ, V bˆ,( σ, ˆ σ ) ) for each I and Σ Condton () s a smple restatement of the standard Nash equlbrum condton, affrmng that for each player the equlbrum strategy must confer a payoff not smaller than what attaned by any other feasble strategy, gven the opponents strateges and the belefs 5. Condton () restrans the belefs to be coherent wth the equlbrum strategy. Notce that f belefs are not part of the utlty functon then condton () becomes redundant and the defnton bols down to the standard Nash equlbrum defnton. 4. The Game of Producton After the phlosophcal and analytcal underpnnngs of the system of choce of the agents have been set out, we can now apply ths model of choce to the analyss of the nonproft enterprse (NPE hereafter). Frst, we depct a stuaton of nteracton n the producton of a good (secton 0), whose outcomes correspond to a varety of dfferent behavour of a frm correspondng n turn to dfferent organsatonal form. Ths game s analysed n accordance wth the two atttudes that make up the utlty functons of the 6