A Theory of Community Formation and Social Hierarchy

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A Theory of Community Formation and Social
Hierarchy

Susan Athey
Stanford GSB

Emilio Calvano
Bologna U. and CSEF

Saumitra Jha
Stanford GSB∗

August 15, 2016

Abstract

We analyze the classic problem of sustaining trust when cheating and
leaving trading partners is easy, and outside enforcement is difficult. We
construct equilibria where individuals are loyal to smaller groups– com-
munities– that allow repeated interaction. Hierarchies provide incentives
for loyalty and allow individuals to trust agents to extent that the agents
are actually trustworthy. We contrast these with other plausible institu-
tions for engendering loyalty that require inefficient withholding of trust
to support group norms, and are not robust to coalitional deviations. In
communities whose members randomly match, we show that social mobil-
ity within hierarchies falls as temptations to cheat rise. In communities
where individuals can concentrate their trading with pre-selected members,
hierarchies where senior members are favored for trade sustain trust even
in the presence of proximate non-hierarchical communities. We link these
results to the emergence of trust in new market environments and early
human societies.

author);

∗athey@stanford.edu

(corresponding

saumi-
tra@stanford.edu. We would like to thank David Baron, Avinash Dixit, Avner Greif,
Jim Fearon, David Laitin, Pedro Miranda, Ian Morris, Josiah Ober, Paul Seabright, Adam
Szeidl and participants in the Berkeley development seminar, Harvard-MIT organizational
economics seminar, Nobel Symposium on Foundations of Organization (Stockholm), 4eme
JEC workshop (Paris), and across Stanford for helpful comments. Gleb Romanyuk provided
much valued assistance. Athey thanks the Toulouse Network for Information Technology for
support.

emilio.calvano@unibo.it;

1

1

Introduction

A long-standing puzzle in economics concerns how individuals maintain trust
despite short-term incentives to cheat. Almost every type of exchange involves
some sort of moral hazard problem, whereby the individual providing a good or
a service may shirk on quality or effort, or fail to deliver the good. An enor-
mous literature seeks to use the theory of repeated games to suggest solutions
In long-term bilateral relationships, the breakdown of future
to this problem.
cooperation provides an incentive for cooperation. However, in larger groups, the
probability of future interaction with the same individual may be small, and even
worse, it may be possible for a cheater to make choices (such as relocating) to
actively avoid those he has cheated in the past.

In the face of such fundamental challenges to cooperation in large groups, sev-
eral natural alternatives can be considered (in Section 2, we review the literature
in more depth). The first, which do not consider in this paper, is the rule of law.
Here, we focus on settings where legal institutions are limited in their ability to
enforce trust. The second is community enforcement: all individuals in a soci-
ety agree to jointly punish defectors. This type of approach has limited value
when individuals have the opportunity to cheat and leave, and the community
enforcement technology does not extend across all potential trading partners. A
third class of alternatives recognizes the crucial role of loyalty: strategies that
provide incentives for individuals to concentrate their trust relationships with
known partners over time. Our paper fits into this category.

Several perspectives on loyalty exist. One is that individuals differ in their
innate propensity for good behavior, and individuals attempt to signal their type
by cooperating. Loyalty is engendered because new trading partners are not
known to be honest, and the signaling process takes time. In this paper, we set
aside unobserved individual heterogeneity, and instead analyze other forces that
can support loyal relationships.

We build a very simple model of a large population playing bilateral trust
games. We consider several assumptions that enable rich and realistic behavior
to emerge. First, we allow players to form communities. Technically, we allow
players to choose a location, a choice that limits their ability to play trust games
to other players that also chose that location in that period. However, indi-

2

viduals can relocate in every period, capturing the idea that players can cheat
and leave. Second, we consider various technologies for record keeping within a
community. The record keeping is limited, however; all current members of a
community can see how long others have attended that community, as well as
a uni-dimensional status which depends on public randomization but not in any
way on any individual’s trading history.

Third, a key exogenous parameter of the model, which we refer to as trading
selectivity, is the extent to which a subset of community members can serve all of
the trading needs of the community. This parameter is motivated by differences
in the kinds of trust exchanges that could occur in the real world. Taking the
location analogy literally, in a town or a neighborhood, you sometimes encounter
people randomly, and have the opportunity to create value through trust. A
neighbor can hold the door for you, help you carry your bags, warn you of a
pothole ahead, sign for your package and deliver it to you, or call a doctor if
you faint on the street. These trust opportunities arise due to proximity, and
individuals cannot easily make choices to only interact within a small set of
established relationships. By choosing your location, you inherently choose to
interact with community members. A second type of interaction entails more
choice in the selection of partners. For example, an individual may need advice
or information, or they may need to procure goods or small amounts of labor
where quality is difficult to contract upon. Then, an individual might be able
to choose to interact with only certain individuals in a community; in such cases
some individuals might engage in more trade than others. In our model, the only
publicly observed characteristics of individuals are the length of their attendance
and their status (the outcome of public randomization that depends on their
attendance) so it is natural to consider that high status individuals would be
selected more often for trade. Our paper analyzes only two polar cases, full
trading selectivity and no trading selectivity, where in both cases trade must
take place within a community. We compare the types of equilibria that can
be sustained and their robustness properties across these two polar cases, noting
that most real-world environments entail a range of trust interactions including
both types of trading selectivity as well as intermediate cases.

Using our model, we proceed in several steps. First, we examine equilibria
of a type that have been considered in the literature in the past in the context

3

of our model. In these identity investment equilibria, individuals are forced to
make costly (and wasteful) investments of either time or resources in order to
start trading in a community. These investments may take a number of forms,
including culture-specific investments or the costs of traveling to a specific phys-
ical location. Identity investment equilibria serve as a benchmark for the novel
equilibria we introduce in our paper. Though natural, we critique these equilibria
on several grounds. First, focusing on the no trading selectivity case, individuals
artificially withhold trust from certain agents. They fail to trust certain individu-
als and thus lose out on valuable opportunities to create surplus, not because the
individuals cannot be trusted (that is, not because it is impossible for their coop-
erate rather than cheat and leave incentive constraints to be satisfied), but rather
to uphold a social convention. Furthermore, upholding that convention does not
benefit a community itself: the community as a whole would create more ex-
pected surplus if it abandoned the convention of requiring new members to make
investments. An individual community sustains trust because other communities
impose entry costs, not because they play any role in the community itself. Thus,
a coalitional deviation where all members of a community abandoned the initial
investment requirement would benefit the community. On the other hand, if any
single community did that, trade would break down in other communities.

This motivates us to propose several alternative structures for equilibria that
sustain cooperation. We begin with the no trading selectivity case. There we
develop what we call a maximal trust hierarchical equilibrium. In this equilibrium,
when a trading opportunity arises between two individuals, trust–which in our
model can occur at different scales– is always maximal :
individuals trust one
another up to the point where an agent is just indifferent between working and a
cheat and leave strategy. The equilibrium is also hierarchical : agents with higher
status are trusted more. As we will develop in the paper, a key feature of the
equilibrium is that advancement to higher status– which can be thought of as
social mobility– is probabilistic.

Once we have established conditions under which maximal trust hierarchical
equilibria exist, we analyze more deeply the structure of the equilibria, as well as
compare different equilibria in the class. We analyze the distribution of income,
and look at tradeoffs between equality and efficiency.

Next, we turn to analyze the trading selectivity case. In this setting, we look at

4

equilibria where trades are concentrated on agents with higher status. Newcomers
to a community on average have low status. We show that communities that
employ these structures are robust in an interesting and novel way. Even if
another community adopts a more egalitarian structure, individuals will still
choose to join the communities with a hierarchical structure. This contrasts with
identity investment equilibria, where the existence of a community that trusts
newcomers undermines trust in other communities.

After developing the theoretical results, we then relate these results to three
real-world applications. We apply our results to understanding the puzzling emer-
gence of hierarchies among early human societies, to the development of imper-
sonal citizenship, illustrated by the Roman Republic, and to the sustenance of
trust in settings as different as marketplaces in modern Nigeria and in online
communities. Though separated by time and geography, all our examples share
the commonality of a challenging contracting environment, with increasing pop-
ulation sizes and the possibility of cheating and leaving for alternative venues.
We trace how hierarchies emerged in each environment, and how hierarchies may
be interpreted as providing a means of facilitating trust.

2 Existing Theoretical Perspectives

Our paper builds upon literatures on the importance of trust in economic de-
velopment, on social networks and in historical political economy. The issue of
cooperation based on reciprocity has attracted the attention of both social scien-
tists (e.g. Kranton, 1996b) and evolutionary biologists (see Nowak and Sigmund
(2005) for a survey.) The problem of sustaining trust in particular has long been
seen as a fundamental question in economic development, and economics more
generally (Arrow, 1974, McMillan, 2002).

Beyond the classic folk theorems, theorists traditionally focus on two types
of mechanisms that overcome the trust problem: those that signal reputations
and those that require third party enforcement.
In reputation-based models,
players learn about the others’ type as honest or opportunistic as the relationship
progresses. Equilibria in which more senior individuals are accorded more trust
emerge as a result of these inferences (eg Sobel, 1985, Watson, 1999, Ghosh and

5

Ray, 1996)). Our formulation exhibits an analogous equilibrium dynamic without
any unobserved individual heterogeneity. We also differ from an important line of
research on cooperation in groups that employs multi-lateral enforcement among
delimited coalitions, following Greif (1993) and Kandori (1992), by examining
settings where multi-lateral enforcement is not possible and populations can be
arbitrarily large.1

Dixit’s (2003) study of trade expansion and enforcement is similar in motiva-
tion to ours. He uses a circular world as a geographical analogy for the costliness
of information flows across distances, and examines how much cooperation can
be sustained as the circle grows in size. He finds that small and large worlds
can sustain greater trust than their intermediate counterparts. In small worlds,
partners to a transaction are likely to know third parties in common, and thus
are able to share information about defectors. In large worlds, developing a legal
system becomes economical. In contrast, our model focuses on the case where
information sharing about behavior within bilateral relationships is not possible.

Beginning with Klein and Leffler (1981), the role of specific investments or
“cultural capital” has assumed an important role in research into trust. For ex-
ample, Iannaccone (1992) applies the notion of specific investments to cults that
provide club goods. There is an incentive to free-ride upon others’ zealousness.
In order to limit participation to the truly committed, religious practices, such
as stigma and self-sacrifice develop to act as screening devices. Similarly, Fryer
(2002) allows for identity-specific investments among African Americans and com-
pares their effects on within-market trust with that of investing in general human

1For example, Woodruff (1998) finds that Mexican footwear manufacturers were also able
to maintain trust through third party enforcement mechanisms and information sharing. In
a manner analogous to Greif (1993)’s classic example of the Maghribi medieval traders, such
trust is supported by multilateral enforcement among small, culturally homogeneous groups,
underpinned by the threat of ostracism from the community or business coalition.

A feature of such identity-based mechanisms, as we will show, however, is that such groups
fail to support cooperation when group sizes are large, there is limited information sharing that
prevents third party enforcement and where the availability of alternative trading partners
make it easy to cheat and leave, and thenceforth avoid the cheated party.

Furthermore, even when there some random chance of re-encountering a cheated party, such
mechanisms require high degrees of coordination to sustain– coordinated barriers to entry in
each group are raised to prevent cooperation failing in other groups. The relaxation of such
barriers by any group coalition will lead to a failure in cooperation in all. Indeed, as Woodruff
describes, third party enforcement and cooperation among Mexican footwear manufacturers
appeared to break down as new opportunities to trade with the US emerged with trade liber-
alization, allowing alternative trading partners outside the coalition.

6

capital or “acting white.”2 These works, however, take both the set of identities
and prescriptions to be exogenous.

The intuition underlying the identity-investment equilibrium– using barriers
to entry such as costly “gifts” into new relationships to sustain cooperation in
old relationships– has been noted by a number of important studies (eg Kranton,
1996a, Carmichael and Macleod, 1997, Ramey and Watson, 2001)). The focus of
these studies has however chiefly been two-agent partnerships rather than broad
groups.

Research has also begun to examine the role of such conventions for sustain-
ing cooperation in groups. The role of membership fees in engendering loyalty
to “insiders” with whom such costs have not been incurred has been explored
by Board (2008), and the role played by time in acting as such a membership fee
has been explored by Friedman and Resnick (2001) in the context of internet chat
rooms. Sobel (2006) analyzes a model where individuals in a large population
form bilateral relationships. He contrasts relational contracts with formal con-
tracting as mechanisms for sustaining trust. As in our model, it can be inefficient
for partnerships to be exclusive in every period. Sobel’s model has relationships
that permanently “grow stale.”In his model, relationships based on relational
contracts may last inefficiently long, because the institutions that support coop-
eration must entail costs of starting new relationships. In contrast to this model,
and the literature on cooperation in social networks, in which ties are based upon
individual trading histories (eg Jackson, 2003, Bloch, Genicot, and Ray, 2008),
the social hierarchies we construct are “impersonal” in the sense that the actual
agents in the hierarchy can change but they inherit the incentives of their rank
and thus fully efficient exchange can be sustained. This is a distinct advantage of
social hierarchies that has not to our knowledge been explored in the economics
literature.3

2In using the term “identity” we follow Akerlof and Kranton (2000). We differ, however,
in the form that identity takes. In their formulation, group “identity” enters into individuals’
utility functions. These identities and the associated “prescriptions” for behavior result in
individual and group sanctions for violators of the group “code of conduct.”

3The key distinction between an agent’s rank and their personal identity naturally has a long
tradition in sociology. In particular, we build on and further work, at least as early as White
(1970), on mobility in hierarchical organizations and “chains of vacancies” created by openings
at higher ranks of hierarchies (see also Gibbons (2005)). Specific identity investment also has
parallels in an important literature, beginning with Kreps (1990), on the role of “corporate
culture”. Culture can create value for the firm through variety of means, including reducing

7

Thus, cooperative equilibria based upon the existence of barriers to form new
relationships occupy a prominent role in theories of trust.4 An important focus
of our study is to analyze the robustness properties of such identity investment
equilibria in environments where some groups adopt social hierarchies and there
may be insurgent egalitarian groups that lower barriers to entry entirely.5 Our
analysis also differs from much of the existing literature on trust in its focus on
endogenous group formation, hierarchical structures, and the problems associated
with increasing population size.6 It links and contributes instead to important lit-
eratures looking at cultural transmission (eg Boyd and Richerson, 1994, Bisin and
Verdier, 2011, Doepke and Zilibotti, 2013) and the origins of hierarchy and forma-
tion of state-like institutions (Bates, Greif, and Singh, 2002, Besley and Persson,
2009, North, Wallis, and Weingast, 2009, Bowles and Choi, 2013, Seabright, 2013,
Dow and Reed, 2013, Boix and Rosenbluth, 2014, Mayshar, Moav, Neeman, and
Pascali, 2015), as we describe below.

3 The Model

We take as our departure point the classic Shapiro and Stiglitz (1984) model
of moral hazard and unemployment in the job market, a useful benchmark for
examining trust in trade relationships (Greif, 1993).

costs of coordination and communication and improving commitment by managers (see also
Hermalin (2010).) Homogeneity within firms can happen through selection and through learning
and indoctrination (Van den Steen, 2005) which can also be thought of as specific investments
in the firm culture or identity. Thus, though we abstract from the potential productive roles
of identity investment, our discussion of the relative robustness of hierarchies and identity
investment equilibria can shed light on the relative robustness of trust-enhancing aspects of
corporate culture as well.

4A notable exception to the focus on entry barriers to sustain trust is work by Lindsey,
Polak, and Zeckhauser (2003), who incorporate the notion of itinerant temptations into their
study of long-term bilateral, exclusive relationships between individuals where there is “free
love”: no barriers to a new start. Existing relationships gain value the longer they exist. This
makes them robust to break-ups. However, this occurs for different reasons in our model: in
the social hierarchies we construct, senior agents engender more trust.

5In comparing the competitiveness of alternative forms of social organization, our paper has
natural links to research in organizational ecology (e.g. Hannan, Polos, and Carroll (2007)) as
well as reciprocity in traditional societies exposed to the market (Kranton, 1996b).

6The role played by subgroup defection in limiting patterns of cooperation in larger com-
munities has also been studied by Genicot and Ray (2003) in the context of risk-sharing. We
abstract from the risk-sharing advantages of having larger groups in our study.

8