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Religion, Longevity, and Cooperation: The Case of the
Craft Guild.
Gary Richardson
Department of Economics
University of California, Irvine
Michael McBride
Department of Economics
University of California, Irvine
This version: 27 September 2006.y
Preliminary draft. Comments welcome.
Please notify authors of citations.
Abstract When the mortality rate is high, repeated interaction alone may not sustain cooper- ation, and religion may play an important role in shaping economic institutions. This insight explains why during the fourteenth century, when plagues decimated popula- tions and the church promoted the doctrine of purgatory, guilds that bundled together religious and occupational activities dominated manufacturing and commerce. During the sixteenth century, the disease environment eased, and the Reformation dispelled the doctrine of purgatory, necessitating the development of new methods of organiz- ing industry. The logic underlying this conclusion has implications for the study of institutions, economics, and religion throughout history and in the developing world today. JEL ClassiÖcations: C70, D23, D43, D71, L10, N83, N93. Keywords: craft guilds, Christianity, purgatory, Reformation, rational-choice, free rider.
Corresponding author: Gary Richardson, Department of Economics, University of California, Irvine, 3151 Social Science Plaza, Irvine, CA 92697-5100, [email protected]. y We thank participants in workshops UC Irvine, Stanford University, and George Mason University as well as participants in the Spiritual Capital, German Cliometrics, ASREC, and Western Economics Association conferences for comments, advice, and encouragement.
1 Introduction
Religious beliefs ináuence economic activity. A large literature establishes that fact.^1 Why religion matters remains the subject of debate. Recent research elucidates how economic incentives shape the organization of congregations, why religious sects specialize in particular niches, and when economic opportunities induce trade-o§s between spiritual and secular activities.^2 This research extends earlier scholarship that explores the ináuence of religion on individualsítastes, desires, proclivities, and habits and emphasizes how religion shapes both preferences for and constraints upon human action.^3 The earlier literature grew from Max Weberís work on The Protestant Ethic and the Spirit of Capitalism.^4 Weber argued that in Protestant nations, the Reformation changed preferences for labor relative to leisure, for savings relative to consumption, and for physical goods relative to emotions such as acceptance by peers and fear of damnation, encouraging the accumulation of capital and expansion of industry. Weberís thesis emerged from his dis- sertation on The History of Commercial Partnerships in the Middle Ages, which established a baseline from which to assess how the Reformation ináuenced commerce and industry.^5 Comparing recent and earlier research reveals a line of argument analogous to Weberís, in the sense that it explains the symbiotic evolution of religious and economic institutions during the centuries crucial for the formation of the modern market economy, and complementary to Weberís, in the sense that it illuminates an additional channel through which religion a§ected the economy. Religious beliefs shaped the evolution and ináuenced the e§ectiveness of occupational organizations. Our analysis of this observation begins at the same point as Weberís. We examine the organization of industry in late medieval England, a society where artisanal activity occurred in organizations called craft guilds. These associations of artisans dominated economic ac- tivity for centuries, during which the foundations of modern economic progressó including industries such as clothmaking, metallurgy, and manufacturing, which took o§ during the (^1) Larry Iannaccone, 1998. Robert Barrow and Rachel McLeary, 2003; Joel Mokyr, 1990. (^2) Ran Abramitzky 2005; Eli Berman 2000; Laurence Iannaccone 1992, 1994, and 1998. (^3) McClearly and Barro, 2006. See also David Hume, 1993; Adam Smith, 2003; and Richard Tawney, 2000. (^4) Max Weber 1930. (^5) Weber 2003
an afterlife. The late-medieval Christian church promoted the doctrine of purgatory, which stated that after death, individuals experienced excruciating pain, which purged them of sins in preparation for entrance into Heaven, where one experienced ecstasy. Purgatorial pain could be lessened by the prayers of the living, particularly by pious people who knew one well, such as family, friends, and colleagues. Guilds were organized to provide prayers for the souls of deceased members. Guilds threatened to punish members caught breaking the rules by excluding them from intercessory services. This threat became more salient when belief in the doctrine spread and mortality rates rose, enabling guilds that bundled together religious and occupational activities to sustain occupational cooperation in environments where purely secular associations employing folk-theorem threats could not. This logic provides a new understanding of the rise, decline, and changing nature of guilds in medieval and early modern England. During the twelfth and thirteenth centuries, when industrial activity initially expanded in towns, urban residents formed organizations focused on secular, economic, and legal concerns. During the fourteenth century, as the doctrine of purgatory spread and the disease environment deteriorated, craftsmen organized increasing numbers of guilds that prayed for the souls of deceased members. Guilds that engaged both in religious and occupational activities proved especially e§ective at facilitating cooperation. During the sixteenth century, mortality rates fell, religious reformation swept aside the doctrine of purgatory, and new methods of organizing industry evolved. This logic builds a bridge between hitherto unrelated literatures. The Örst employs game theory to study economic institutions. Avner Greif pioneered this line of research.^9 His work reveals how reputations, repeated relationships, and folk-theoretic interactions fostered the rise of anonymous exchange during the later Middle Ages. The second employs club theory to study religious institutions. Laurence Iannaccone pioneered this line of research.^10 His work reveals how the imposition of sacriÖces and the threat of exclusion shape the behavior of congregations. We study groups that operated both as Greif-style economic cooperatives and Iannaccone-style religious cooperatives. Our model shows how social, cultural, economic, and demographic factors determined when guilds operated according to the principles outlined (^9) Greif 1992, 1993, 1994, 1998, 2006. Greif, Paul Milgrom, and Barry Weingast 1994. (^10) Iannaccone 1992, 1994, and 1998
by Greif, when guilds operated according to the principles outlined by Iannaccone, and when guilds operated according to an amalgamation of both. The remainder of this paper develops our argument, that exogenous shocks on two fronts, mortality rates and religious beliefs, shaped the structure of industrial organization in late medieval and early modern Europe, when guilds of craftsmen used spiritual sanctions to sustain occupational cooperation in settings where purely economic threats could not do so. Section 2 summarizes the essential historical evidence. Section 3 presents a game theoretic model that illustrates how religious sanctions fostered cooperation among groups of craftsmen in a single industry. Section 4 uses the model to describe how changes in religious doctrines and the disease environment ináuenced an economy consisting of numerous independent industries. Section 5 considers how changes in doctrines and disease ináuenced the level of cooperation within organizations. Section 6 relates our Öndings to the broader literature and discusses the implications of our analysis. Religion can form a foundation for cooperation in environments where folk theorems function poorly.
2 Historical Background
In England from 1275 to 1550, an era often called "Industrial Revolution of the Middle Ages," cooperatives formed the foundation of industry and society. Three kinds of cooperatives existed in the largest numbers: those engaged principally in occupational activities, which we refer to as a occupational cooperatives; those engaged principally in praying for the souls of deceased members, which we refer to as intercessory cooperatives (or chantries); and those engaged in both activities, which we refer to as a combined cooperatives. Past scholars typically referred to these organizations as craft guilds, chantries or parish guilds, and craft guilds respectively. Here, we use new terminology to highlight these organizationsísimilar structures and di§erent objectives.^11 These three ubiquitous organizations are the subject (^11) Note: Medieval men and women referred to these organizations by a wide variety of names including brotherhoods, companies, confraternities, chantries, crafts, fraternities, guilds, and mysteries. Modern his- torians typically refer to all of these organizations as guilds, often prefacing the term with an adjective indicating the leading members or principal activity of the organization (e.g. merchant guild, craft guild, social guild, parish guild, or religious guild). Modern theorists often refer to organizations like these as cooperatives. Since our study analyzes dimensions of these organizations that have hitherto escaped acad- emic attention and since we wish to avoid the often bitter battle over appropriate terminology, we employ
Combined cooperatives bundled together the functions of intercessory and occupational cooperatives. All three of these organizationsó occupational, intercessory, and combined cooperativesó provided members with collective goods. Examples include reputations for quality, manufacturing technology, low prices for inputs, high prices for outputs, shared re- ligious rituals, and prayers from a pool of pious persons. All three required members to contribute to the costs of these collective endeavors. For example, manufacturing coopera- tives required members to bear the costs of using high-quality inputs, rather than cheaper alternatives. Chantries required members to contribute time, emotion, exertion, and en- ergy; to participate in religious rituals; to attend funerals; to regularly pray for the souls of the deceased; and to pay period dues (which paid salaries of priests and purchased pious paraphernalia). Chantries also required members to abstain from pleasures of the áesh and material temptations of secular life. Because a key task for all three organizations was to induce members to bear their share of the collective costs and to discourage free riding, all three organizations possessed mechanisms for monitoring membersícontributions, encouraging cooperation, and punishing defection. Manufacturing cooperatives, for example, employed o¢ cers known as searchers who scrutinized membersímerchandise to make sure it met guild standards and inspected membersíshops and homes seeking evidence of attempts to circumvent the rules. Chantries employed o¢ cers who monitored membersíbehavior to ensure that they lived piously and prayed faithfully. Members of chantries, guilds, and cooperatives who failed to fulÖll their obligations faced punishments of various sorts. Punishments varied across transgressions, guilds, time, and space, but a pattern existed. First time o§enders were punished lightly, perhaps su§ering public scolding and paying small monetary Önes, and repeat o§enders pun- ished harshly. The ultimate threat was expulsion. These voluntary organizations could do nothing harsher because laws protected persons and property from arbitrary expropriations and physical abuse. Table 1 summarizes evidence concerning the scope and scale of these organizationsíac- tivities during the later Middle Ages. From the revival of urban life (circa 1000) to the initial spread of doctrine of purgatory (circa 1275), occupational cooperatives existed in many Eng- lish towns. The greatest concentration existed in clothmaking industries. Some towns and
industries lacked cooperatives of craftsmen; in all towns and industries, many craftsmen worked outside of cooperatives. During the three generations following the introduction of the doctrine of purgatory to England (roughly 1275 to 1350), the number of occupational cooperatives and chantries grew gradually. The Örst combined cooperatives were formed. Growing numbers of craftsmen belonged to these organizations, but many craftsmen con- tinued to work independently. Following the Black Death (circa 1348 to 1350), the number of chantries skyrocketed. Within a generation, almost all adults in England belonged to an intercessory organization. Many intercessory societies evolved into combined cooperatives. The number of combined cooperatives increased exponentially. Almost all urban artisans belonged to an organization that provided both intercessory and occupational services. After the Reformation (circa 1547), the number of combined cooperatives plummeted. Within a generation, combined cooperatives ceased to exist. Some of these pious and proÖtable orga- nizations shed their religious dimensions and survived as purely occupational cooperatives. In many industries, however, new organizational forms arose. The putting-out system be- came increasingly popular. Mutual insurance societies began constructing the Örst actuarial tables. Industry shifted from the towns where it had been centered for centuries to villages where it began to expand.
Table 1: Evidence of Medieval English Cooperatives by Type and Time Period Period Years Occupational Intercessory Combined Before Doctrine of Purgatory pre 1275 Purgatory to Black Death 1275 to 1350 Black Death to Reformation 1350 to 1550 Post-Reformation post 1550 Sources: Richardson 2000, 2001, 2004, 2005. Richardson and McBride 2006. Notes: An open circle indicates that during the time period, evidence demonstrates that cooperatives of this type existed. The cooperatives were rare to common. Some craftsmen belonged to them, but other craftsmen operated independently and/or outside of these organizations. A Ölled circle indicates that during the time period, evidence demonstrates that cooperatives of this type were ubiquitous. All individuals living in urban areas belonged to organizations of this type. Few if any craftsmen operated independently. A blank space indicates that during the period, cooperatives of that type did not exist. Figure 1 depicts trends in the two exogenous variables which, we argue, propelled the changing nature of economic cooperation in late medieval England: the mortality rate and the
model, craftsmen manufacture cloth for export. With minor adjustments to the proÖt func- tion, our hypothetical cloth exporters could be victuallers acting as Cornout oligopolists, master craftsmen monopsonizing markets for journeymen and apprentices, a guild of gold- smiths lobbying authorities for favorable policies, or a group of pewterers jointly developing a new technology for manufacturing lead-free áatware.
3.1 Occupational Equilibrium
Our occupational cooperative depicts a typical situation in the largest medieval industry. A group of clothmakers manufacture textiles for export to the wider market. The craftsmen live in the same town, own their own workshops, employ identical technologies, and manufacture indistinguishable merchandise. The craftsmen develop a collective reputation for product quality. They di§erentiate their wares from textiles made in other towns by giving their cloth a conspicuous characteristic, such as a unique weave or color, which outsiders cannot copy. The conspicuous characteristic and collective reputation provide pricing power. When our clothmakers manufacture high-quality merchandise, they sell their wares at premium prices and earn large proÖts. When they manufacture shoddy merchandise, consumers refrain from purchasing their products. They sell limited quantities at low prices, and earn small sums. The occupational cooperative consists of a group of n craftsman, labeled i = 1; 2 ; 3 ; :::; n, who interact during periods labeled t = 1; 2 ; 3 ; :::; 1. Each period consists of a sequence of three moves in the following order. One, each craftsman simultaneously decides the quality, qit 2 fqH ; qLg, of the cloth that he manufactures. H stands for high quality, L stands for low quality, and qH > qL. Two, nature chooses which craftsmen die. The mortality rate m, 0 < m < 1 , is the probability that craftsman i dies. This probability is independently and identically distributed across craftsmen. Three, period t ends and payo§s are received. Craftsman i chooses fqitg^1 t=1 to maximize his expected present discounted payo§, Uit.
Uit =
X^1
t=
(1 m)t^ it (qit; q it) ; (1)
where it (qit; q it) is iís proÖt in period t given the qualities chosen by all craftsmen in that period. A craftsmanís proÖts, it (qit; q it), increase as the average quality (^1) n^ Pnj=1 qjt of the cloth made by other members of the cooperative increases because the craftsmen share a
collective reputation for product quality. But, a craftsmanís proÖts decrease as the quality of his own cloth, qit, increases, because manufacturing high-quality cloth costs more than manufacturing low-quality cloth. To solve the model, three single-period proÖt levels must be deÖned. Denote iís single- period proÖt level as C , the cooperative level of proÖts, if all craftsmen choose qH in period t. Denote iís single-period proÖt level as D, the defectorís proÖt level, if all craftsmen other than i choose qH in period t but craftsman i chooses qL. Denote iís single-period proÖt level as N E , the single-period Nash Equilibrium proÖt level, if all of the craftsmen including craftsman i choose qL in period t. Our assumptions about it imply D > C > N E. Additional assumptions complete the model. First, all choices are publicly observable, i.e., at the end of step 1, all of the craftsmen know the quality levels chosen by all of their colleagues in that and all previous periods. This assumption seems reasonable, since the occupational cooperatives under investigation were small (10 to 50 members), close-knit associations of individuals interacting on a frequent (daily or weekly) basis with periodic (quarterly or annual) administrative meetings attended by all members where the organi- zation reviewed the conduct of its members and o¢ cers. In addition, these cooperatives devised rules, established revelation mechanisms, invested in technology, and employed ad- ministrators for the explicit purpose of illuminating membersíquality choices. Second, each craftsman who dies in period t is replaced by a new, identical craftsman at the start of period t + 1. This assumption simpliÖes the analysis and is consistent with the structure of these organizations. Occupational cooperatives (as well as chantries) recruited new members continuously and screened them intensively. Occupational cooperatives possessed ranks of journeymen and apprentices awaiting promotion to the rank of master. These provisional members participated in the social and ritual life of the organization. So, they had the am- ple opportunity to observe events that transpired and learn the history of the organization. Often, when a master died, one of his subordinatesó typically either his son, senior jour- neyman, or former apprenticeó inherited his workshop, paying his widow for the privilege of taking over the productive capital. In this situation, the cooperative can maintain high-quality production if all the craftsmen play the trigger strategy: ìproduce high quality in period 1; in period t > 1 , produce high
scientists studying religious organizations.^15 Our chantry consists of a group of n craftsman, labeled i = 1; 2 ; 3 ; :::; n, who interact during t periods, labeled t = 1; 2 ; 3 ; :::; 1. Each period consists of a sequence of moves in the following order: One, all craftsmen simultaneously decide whether to join , jit = 1, or not join jit = 0, the chantry. Joining/re-joining entails paying membership fee f. Two, nature chooses which craftsmen die. The mortality rate m, 0 < m < 1 , is independently and identically distributed across craftsmen. Three, surviving chantry members vote on how to spend the chantryís resources, bntf , where bnt is the number of craftsmen who joined the chantry in step 1 of period t. The surviving members may spend the resources on prayers for the souls of deceased chantry members, or divide the resources among surviving members, or some combination of both. Four, period t ends and payo§s are received. Craftsmen iís Bellman equation is Uit = maxfmI (pray) vit (prayer expenditures) I (jit = 1) f + (1 m) (rit + Ut+1)g: (3)
I (pray) takes the value 1 if i dies and is prayed for in t by the surviving chantry members and takes the value 0 otherwise. The prayer value function, vit (), represents iís valuation today (i.e. before step 3 in time t) of the prayers that he believes will be said on his behalf after he dies. vit is increasing in the amount (of money and/or e§ort) expended on prayers and is non-rivalrous. I (jit = 1) is an indicator function that has value 1 if i joins in t but takes value 0 otherwise. rit is the amount of club resources redistributed back to i in step 3. Additional assumptions complete the model. First, all actions are publicly observable. Second, any member who dies in period t is replaced in the next period by an identical individual. These assumptions appear realistic and reasonable for the reasons indicated in our description of an occupational cooperative. Third, the spending option with most votes in step 3 is chosen. If there is a tie among options, then the option outlined in the club by-laws is chosen. The chantryís by-laws consist of two edicts. First, in step 3 of period t, the chantry includes a member on the prayer roll if he joined the chantry in all prior periods of his life (^15) Iannaccone (1998) describes why religious activities should be modelled as club goods.
and died in period t. Second, in step 3 of period t, the chantry spends all resources from fees collected in step 1 on prayers for members who are on the prayer list from by-law 1. These by-laws encapsulate an assumption that simpliÖes the mathematics of the model because a craftsman that does not join the chantry in one period never receives prayers in future periods, and therefore, has no incentive to cycle in and out of the organization. These by-laws also reáect the by-laws of the typical medieval chantry, which stated that the association would pray only for the souls of members who died in good standing. Those names were inscribed on rolls of parchment read during intercessory services. To simplify our analysis, we assume for now that these by-laws are contractually binding. In a subsequent subsection, we explain why these by-laws are self-enforcing. The chantry exists as an equilibrium when all craftsmen join the chantry in step 1 of period t and in all future periods. This equilibrium exists when all craftsmen play the strategy: ìin each period t; join the club in step 1 and vote according to the by-laws in step 3.îChoosing this strategy given that all others choose this strategy yields the utility Uit
Uit = mvit (nf ) f + (1 m) Ut+1:
Since the strategic situation repeats itself in all periods, Uit = Uit+1: Therefore,
Uit = vit (nf ) (^) mf:
A craftsman will follow this strategy when all other craftsmen follow this strategy if doing so yields a higher expected payo§ than all possible deviations. The only deviation for i in t is to not join the club, which yields payo§ normalized to 0 in round t and all future periods. Therefore, choosing the strategy "join the chantry now and forever after" is optimal when
Uit 0 ) vit (nf ) (^) mf 0 ) vit (nf ) (^) mf v. (4)
Inequality (4) states that craftsmen form chantries when the spiritual beneÖts that one expects to receive after death, vit (nf ), are equal to or greater than membership costs that
yields the Bellman equation for the ith^ member of the combined cooperative.
Uit = maxfmI (pray) vit (prayer expenditures) I (jit = 1) f + (1 m) (it (qit; q it) + rit + Uit+1)g: (5)
Members choose contributions to the religious and occupational aspects of this organization to maximize their expected utility functions. The organizationís by-laws consist of two ordinances. First, in step 4 of period t, add to the prayer list any individual that (a) participated in the organizationsíreligious activities in that and every prior period of his life, (b) chose qit = qH in all prior periods of his life, and (c) died in period t. Second, in step 3 of period t, spend all resources from fees collected in step 1 on prayers for the salvation of the souls of the persons on the prayer list. These by-laws link the cooperativeís religious and occupational endeavors by promising spiritual beneÖts only to those who cooperated professionally. Economic cooperation is sustained by threats of religious, rather than economic, retaliation. We assume that the organization operated in this manner because by-laws of this type are the only ones observed historically. In the next subsection of the essay, we explain how such by-laws could be sustained as an equilibrium. Given these by-laws, we can determine the payo§ from following a strategy of cooperating religiously and economically. ìIn each period, join the chantry in step 1; set qit = qH in step 2; and vote according to the by-laws in step 4.î If all craftsmen follow this strategy, then craftsman iís expected payo§ is
Uit = mvit (nf ) f + (1 m) (C + Uit+1) ) Uit = (1^ m^ m )C + vit (nf ) (^) mf: (6) A craftsman has two potential deviations from this strategy. First, craftsman i can deviate in step 1 by not joining the chantry. Under this deviation, he will forever be excluded from the religious beneÖts. Moreover, since all others continue to choose qH , he can set qit = qL and receive D in every period. The present value of this deviation is P^1 t=1 (1 m)t^ D, which equals 1 mm D. Second, after joining the chantry in step 1, craftsman i can deviate in step 2 by choosing qit = qL. This deviation yields a lower expected payo§ than the Örst deviation since the deviating craftsman pays the membership fee f in step 1, but never
receives religious beneÖts. Since it is a dominated strategy, to determine when the guild can be sustained as an equilibrium, we only need to compare the present value of the payo§ in (6) to the payo§ from deviations of the Örst type. The comparison indicates that pursuing the cooperative strategy when all other craftsmen do also is optimal for i when
(1 m) m C^ +^ vit^ (nf^ )^ ^
f m ^
1 m m D^ ) vit (nf ) 1 m^ m (D C ) + (^) mf ) vit (nf ) 1 m^ m (D C ) + v^ v: (7)
Inequality (7) states that joint religious and economic cooperation can be sustained in equi- librium if the value of the religious beneÖts is su¢ ciently high. Figure 2(c) plots combinations of m and v(nf ) in (m; v (nf ))-space for which (7) holds as an equality. The parameters are the same as those in Figures 2(a) and (b). The area along and above the curve, v, indicates combinations of m and v(nf ) for which joint cooperation exists as an equilibrium. The shape of the v-curve is similar shape to the v-curve, but lies above it, because the potential beneÖts from deviating from a combined religious and economic cooperative are larger than the potential gains from deviating from single-task organization. The combined cooperative, therefore, needs a greater threat to deter deviation. As the mortality rate, m, increases, v^ converges to v. The curves converge because as life expectancies fall, the economic incentive to deviate diminishes, and the punishment needed to sustain combined religious and economic cooperation approaches that needed to sustain religious cooperation alone. In addition, for m > m, the beneÖts provided by membership in a combined coopera- tive, determined by v, are strictly larger than the beneÖts of provided by membership in a chantry, determined by v. This relationship exists for a simple reason. Combined coop- eratives provide both religious and economic services, and therefore, provide both religious and economic beneÖts. Figure 3 reveals the types of organizations that exist at di§erent points in our parameter space. At mortality rates below m, an occupational equilibrium will exist. The value of
men die, or only craftsman i survives, or nobody ever dies) and all possible deviations in those states. We simplify the presentation of our model by imposing by-laws that directed craftsmen to behave during extreme states as they behaved during typical times. The substantive results presented in our paper remain unchanged. The reason is that when the value of intercessory prayers is su¢ ciently large, their denial becomes an excruciat- ing punishment, and when the mortality rate rises high enough, defection from occupational organizations becomes irresistibly enticing. That said, several subtle di§erences are worth mentioning. First, if the mortality rate is extremely high (m close to 1), then there is a chance that all members will die. No members will survive to spend club resources on prayers. SpeciÖcally, the probability of receiving vit (nf ) is no longer m but is instead (m mn), which approaches 0 as m approaches 1. For the expected beneÖts of membership to be su¢ ciently high when m is close to 1, vit (nf ) must then be very large. This results in U-shaped v^ and v-curves. The upward turn of the v^ and v-curves occurs at an extremely high value of m. Above that value, as m approaches 1, no type of cooperation can be sustained. This intriguing subtlety may explain the breakdown of both religious and economic institutions during the Örst few years of the Black Deathís initial onslaught into Europe, when many people believed the end of the world was at hand. Second, if the mortality rate is very low (m close to 0), then there is a high probability that no member of the organization will die, and no money needs to be expended on prayers. Allowing the club to reward living members, either in the form of a refund of club fees or by producing a club good to be consumed by living members, will lower the expected cost of joining the club. This áattens the v^ and v-curves at low mortality levels. However, both v^ and v^ will remain downward sloping at low m, as long as surviving chantry members cannot refund resources in their entirety and must spend some on prayers. There are many reasons to believe that contributions to chantries were not completely refundable. First, chantries, like all clubs, had Öxed operating costs that consumed a portion of the resources. Second, a substantial portion of contributions to chantries were time, e§ort, emotion, and energy put into religious rituals and e§orts to lead pious lives. Those non-monetary sunk costs could not be refunded.
In sum, the model with binding by-laws presented earlier is equivalent to a model with self-enforcing by-laws where mortality rates are bounded away from 0 and 1. Since this interior range corresponds to the range of actual mortality rates observed (with the possible exception of a few years around 1350), the model with binding by-laws elucidates the essential issues. Punishment Mechanism: Exclusion versus Nash Reversion. A ubiquitous fea- ture of late-medieval guilds was their reliance on individually-targeted religious sanctions to enforce rules regarding occupational activities. Other game-theoretic options existed, of course. Guilds could have punished uncooperative members by taking actions with wider consequences. Members of a manufacturing guild who caught one of their own passing o§ shoddy merchandise under the guildsígood name could have punished the o§ender by col- lectively lowering the quality of their products for a prolonged period. That would lower the o§enderís income, albeit at the cost of lowering the income of all other members as well. Similarly, members of a guild that caught one of their brethren shirking on prayers and sinning incessantly could have punished the o§ender by collectively forsaking the Lord and descending into debauchery. Then, no one would or could pray for the soul of the o§ender, and his period in purgatory would be extended. In broader terms, cheaters could have been punished by any action that reduced the average incomes of all guild members or increased the pain that all members expected to endure in purgatory. The combination of these punishments could have sustained cooperation for a wider set of parameter values than when relying on either Nash reversion or religious exclusion alone. In our basic model, where monitoring and enforcement are perfect and Nash threats are free, we can deÖne joint punishment strategies and by-laws that sustain cooperation for all vit (nf ) v, where v^ is the dual-threat version of v^ deÖned in inequality (7). SpeciÖcally, we calculate
vit (nf ) ^1 m^ m (C N E ) + v^ v.
Because C > N E , v^ < v^ for all m. Thus, the parameter space in which dual-threat guilds exist is a strict superset of the parameter space in which exclusion-only guilds exist. In theory, such threats could have convinced even the most recalcitrant members to
