metadata: authors: 0: author: Robinson,James Alan
1: author: Vostroknutov,Alexander
2: author: Vostroknutova,Ekaterina
count: World
docna: 0: docna: Endogenous Institutions and Economic Policy
docty: Policy Research Working Paper
abstracts: cdata!: This paper proposes a new framework to
            model institutions and institutional change. It shows how
            moral agents, who strive to cooperate with others, can form
            institutions that facilitate cooperation. The framework
            makes it possible to model informal as well as formal
            institutions as games played by moral agents: when the
            quality of the government is low and agents are not willing
            to use its services they will create informal institutions
            that allow them to cooperate outside the official channels.
            It is also possible to conceptualize institutions as
            inclusive or extractive and model institutional change as a
            consequence of the choice of moral agents among available
            institutions as time unfolds. With a series of examples of
            clientelistic networks, the paper shows that the framework
            can be useful for understanding how and why such networks
            form and persist. The framework can be used to model any
            interactions among moral agents, thus giving rise to a wide
            variety of possible institutional settings.
display_title: Endogenous Institutions and Economic Policy
listing_relative_url: /research/2023/11/34193594/endogenous-institutions-economic-policy
topicv3: Institutions and Growth m1327406 1276,Economic Growth Policy m1327634 1070,Social Norms and Poverty m1503846 3751
publishtoextweb_dt: 2023-11-08T00:00:00Z
dois: 10.1596/1813-9450-10600
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 644534
1: author_key: NA
2: author_key: 687122
model_extractions: Policy Research Working Paper 10600 Endogenous Institutions and Economic Policy _James A. Robinson Alexander Vostroknutov Ekaterina Vostroknutova_ Macroeconomics, Trade and Investment Global Practice November 2023
Policy Research Working Paper 10600

# **Abstract**

This paper proposes a new framework to model institutions and institutional change. It shows how moral agents, who strive to cooperate with others, can form institutions that facilitate cooperation. The framework makes it possible to model informal as well as formal institutions as games played by moral agents: when the quality of the government is low and agents are not willing to use its services they will create informal institutions that allow them to cooperate outside the official channels. It is also possible to conceptualize institutions as inclusive or extractive and model institutional change as a consequence of the choice of moral agents among available institutions as time unfolds. With a series of examples of clientelistic networks, the paper shows that the framework can be useful for understanding how and why such networks form and persist. The framework can be used to model any interactions among moral agents, thus giving rise to a wide variety of possible institutional settings.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at evostroknutova@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Endogenous Institutions and Economic Policy<sup>∗</sup>

**James A. Robinson**<sup>†</sup> **Alexander Vostroknutov**<sup>‡</sup>

**Ekaterina Vostroknutova**<sup>§</sup>

Topics: _Institutions and Growth, Social Norms and Poverty, Economic Growth Policy._ Keywords: _endogenous institutions, social norms, inclusive/extractive institutions, growth, institutional policy._ JEL Classification: _E61, E71, H20, O11, O17, O43._ ∗All mistakes are our own. The findings expressed in this paper are those of the authors and do not necessarily represent the views of the World Bank or its member countries. We would like to thank Milan Brahmbhatt, Frederico Gil Sander, Norman Loayza, Stephen Ndegwa, Hannes Rusch, Gaute Solheim and the seminar participants in IMT Lucca, DECIG Seminar Series at the World Bank, and MBEES and MLSE at Maastricht University for valuable comments.

> †Harris School of Public Policy and Department of Political Science, University of Chicago. e-mail: jamesrobinson@uchicago.edu.

> ‡Department of Microeconomics and Public Economics (MPE), Maastricht University, The Netherlands. e-mail: a.vostroknutov@maastrichtuniversity.nl.

- §The World Bank. e-mail: evostroknutova@worldbank.org. Corresponding author.
# **1 Introduction**

In the past decades, neoclassical economics has been rather successful in accounting for the process of economic growth in industrialized countries using the Solow-Swan model and its extensions [Solow, 1956, Swan, 1956, Aghion and Howitt, 2008]. However, it has failed to predict the slow catch up in income per capita by developing countries [North et al., 1993, Keefer and Knack, 1997, Caselli, 2005, Rodrik, 2013]. While recent methodological breakthroughs allow concluding that significant welfare gains from eliminating structural distortions can be achieved [Baqaee and Farhi, 2020], the literature does not explain the staggering proportions of these “distortions” or suggest policies to reduce them. For example, the informal sector employs the majority of workers and produces more than half of GDP in many parts of the world [Loayza, 2018, Perry et al., 2007], while political institutions in transplanted democracies are often overwhelmed with clientelism and corruption to the detriment of growth [Stokes, 2011]. The attempts to eliminate these distortions directly have failed [Floridi et al., 2020], suggesting that they are structural in the sense of being ”the way of life” in many developing countries [De Soto et al., 1989], and need to be taken into account in policy making.

Chief among possible explanations of these failures has been the importance of economic institutions [North, 1990, Ostrom, 1990, Hall and Jones, 1999]. Historically, the formal institutions of the Western world (such as democratic political systems) have been shown to create long-term growth in income per capita [Fukuyama, 1995]. However, multiple studies have shown that transplanting Western institutions to other countries does not necessarily lead to a commensurate welfare improvement [Putnam et al., 1992, Raiser, 1997]. One potential reason is that institutional change is a long-term process, where institutions need to grow organically based on the existing economic system including the informal institutions and social norms already in place [Acemoglu and Robinson, 2020].

Indeed, Acemoglu and Robinson [2020] have argued that building and maintaining institutions conducive to economic growth requires enormous effort from governments and societies. Such _inclusive_ institutions are located in the “narrow corridor” between a fully disorganized “state of nature,” or Warre, and an all-controlling Leviathan of a powerful government. Acemoglu and Robinson painstakingly collect evidence of institutional design and historical path-dependence that have led countries to or away from this narrow corridor. But while this analysis clarifies what features the desired inclusive institutions possess that makes them so effective in creating growth, in practice only a handful of developing countries have been able to properly engineer such institutions to create some convergence to the narrow corridor. The majority of developing countries suffer through what Acemoglu and Robinson call _extractive_ institutions, where a small proportion of the population enjoys the benefits that all workers of the economy create, and are not therefore conducive to long-term economic growth per capita.

The general consensus across various literatures is that institutions arise to support _cooperation_ of economic agents [e.g., Nee, 1998, Ostrom, 2000, Keefer and Knack, 2008, Henrich, 2015a]. Cooperation is also an important feature of inclusive institutions. As Acemoglu and Robinson [2020] note, “in the corridor [of inclusive institutions] the state and society do not just compete, they also cooperate. This 1
cooperation engenders greater capacity for the state to deliver the things that society wants and foments greater societal mobilization to monitor this capacity.” Yet, in neoclassical economics transactions are costless, agents are only interested in maximizing their own consumption utility, and firms—or collectives of agents who create surplus—are treated as exogenously given production functions. The fact that standard models do not account for cooperation is mainly the reason they are unable to model emergence of firms and other institutions [Coase, 1937].

Alternative approaches that tried to modify the neoclassical paradigm to incorporate institutions also did not produce a general, viable framework for policy applications. For example, according to views expressed in institutional economics, models of institutions have lagged the intuitive and historical understanding of their importance [Williamson, 2000, Furubotn and Richter, 2010]. With a majority of models being at the country level and including exogenous variables to account for the quality of institutions, institutional economics has not yet arrived at the practicality of how to induce positive institutional change or orchestrate a shift from extractive to inclusive institutions. To obtain a workable model of institutional change, there is a need for a more fundamental bottom-up approach to understanding the formation and evolution of institutions that takes into account the motivation of individual agents to self-organize into cooperative “units” or firms [Sala-i Martin, 2002]. Such an approach can lead to a framework where institutions arise _endogenously_ and where policies can be devised to change them. To our best knowledge, no such framework currently exists.

Our study aims at filling this long-standing gap in the understanding of economic institutions and policies directed at changing them. We propose a parsimonious framework of how institutions arise and how they function within an economic environment defined by other institutions. In the version of the model described here, many of the “distortions” mentioned above (such as informality, clientelism, or corruption) appear organically and can be changed through appropriate policies suggested by the model. More importantly, the model can be adapted to various forms of institutions and economic environments, which can make it indispensable for applied and policy-oriented work related to institutional change.

Conceptually, our framework is different from the neoclassical approach in only one small but fundamental aspect. While neoclassical economic agents are assumed to have a _single motivation_ , namely the desire to have more consumption utility, we assume that agents trade off _two motivations:_ the standard preference to have more consumption and _the desire to cooperate with others_ . While the introduction of the latter motivation in the utility function is novel, large swaths of literatures in various social sciences have been converging on the view that humans are a social species that has evolved special mental capacity for cooperation.<sup>1</sup> According to this view, the innate preference for cooperation is operationalized through the desire to adhere to _social norms_ , or common beliefs about how things ought to be done. In economics, this second motivation is modeled as an additional term in the _norm-dependent utility function_ that was first introduced by Kessler and Leider [2012]: norm-following agents maximize the sum of their consumption utility and a measure of social appropriateness defined on outcomes (the agents 1 The reason this capacity has evolved is that cooperation is more profitable than no cooperation [e.g., Bicchieri, 2006, Henrich, 2015a, Fehr and Schurtenberger, 2018, Laland, 2018].

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prefer more socially appropriate outcomes to less socially appropriate ones).

The introduction of the cooperative motivation dramatically changes the way agents behave and helps understand how institutions emerge. To be more specific, in neoclassics the concept of a cooperative enterprise (a firm) and the concept of an agent are necessarily separated because selfish agents by definition are unwilling to cooperate in social dilemmas and thus have no motivation to self-organize into firms. Firms however do exist in reality and therefore are simply brought in as production functions.<sup>2</sup> In our framework, the norm-following agents care about the social appropriateness of their actions, which tends to be the highest when agents successfully cooperate with each other. This is the motivational force that pushes them to find ways to create new cooperative enterprises, and leads to the formation of institutions.

We assume that the desire to cooperate is not negligible and has a tangible effect on preferences. Therefore, we should expect that norm-following agents are comparatively as willing to enter cooperative relationships and form institutions as they are willing to maximize their consumption utility. This implies that institutions for cooperation should emerge in all economic environments, even those in the “state of nature,” similarly to how we expect humans to strive for more consumption in all economic environments. In this view then, informality is not a distortion, but rather an attempt of norm-following agents to self-organize and cooperate in the absence of other means to do so [Perry et al., 2007]. This view also suggests that government plays a crucial role of a facilitator who helps agents to fulfill their desire to cooperate. With strong government that provides good and efficient services for doing business (e.g., in the form of enforceable laws), we should then expect that agents will prefer to cooperate legally through government rather than through informal institutions that are far less efficient given their internal structure. This argument provides a flavor of institutional policy that comes out of our framework: agents are attracted to institutions that give them the best available options to cooperate; while this is happening, the less attractive institutions die out thus bringing about institutional change.

The paper is structured as follows. In Section 2 we describe our general methodology based on the new framework to study the emergence of social norms by Kimbrough and Vostroknutov [2022a], further KV, and embed it in various literatures. This framework allows us to talk about social norms that emerge in individual interactions as building blocks of more complex institutions also termed “packages of social norms” [Henrich, 2015b].

In Section 3, we analyze the behavior of norm-following (or moral) agents in the Public Goods game. This game serves as an abstract representation of a cooperative enterprise (a “firm”) that can emerge or not depending on whether agents decide to cooperate. We relate the parameters coming from the framework of KV to the intuitive notion of _trust_ that is considered by many authors to be the necessary ingredient of economic development [Keefer and Scartascini, 2022, Lederman et al., 2002]. We demonstrate that trust, operationalized by KV as having two dimensions, can account for a wide variety of

> 2The neoclassical approach remains silent about how firms and institutions emerge. A vigorous attempt to fix this came in the form of New Institutional Economics that proposed a set of models of firm formation based on various principles [e.g., Hart, 1989, Holmstr ̈om and Roberts, 1998].

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intuitive social constraints that prevent agents from successfully doing business with each other.

In Section 4, we define _institution for facilitation:_ the simplest form of institutional arrangement among three agents that allows two of them, who do not trust each other, to nevertheless cooperate with the facilitation from a common “acquaintance” whom both agents trust (the third agent called _facilitator_ ). We show how the norm with respect to the amount of _rent_ paid to the facilitator emerges endogenously from the parameters of the Public Goods game and trust weights. This in turn paves the way to natural definitions of _inclusive_ (or norm-abiding) and _extractive_ (or norm-breaking) institutions.

In Section 5, we consider how agents choose between institutions. We give definitions of _formal_ and _informal_ institutions, and model the choice of a norm-following agent between them. Given that the agent intrinsically cares about the normative arrangement in the two types of institutions, her choice will depend not only on the consumption utility expected from the two institutions, but also on how “fair” (inclusive or extractive) these institutions are. We finish this section with a stylized model of the dynamics of trust in government, the size of the informal sector, institutional policy, and growth. This model suggests that increasing the quality of public services leads to higher trust in government, which then leads to the increase in the relative size of the formal sector.

In Section 6 we consider arbitrary trust networks and discuss how and why some agents might prefer to work (participate in the Public Goods game) or facilitate (collect rent from facilitating cooperation of others). We show with an example that depending on the structure of the trust arrangements in the population, different forms of _clientelistic networks_ may emerge. Sometimes, one or two large informal institutions like that take hold over the whole network (similar to a monopoly or a duopoly), which leads to high barriers to enter and elitism. In other cases, many facilitators compete for clients (similar to perfect competition), which creates the opposite situation where clients are paid for their attention to facilitators.

In Section 7 we relate our framework to the theory of stages of development of historical and traditional societies [Acemoglu and Robinson, 2020]. We add a punishment mechanism for norm violations which in different settings generates the Hobbesian ”state of nature” (Warre), cage of norms, the Despotic Leviathan, and the Shackled Leviathan. We discuss examples of currently existing traditional societies and societies that existed in the past and show how institutional change in these societies can be viewed from the perspective of our model.

Finally, Sections 8 and 9 conclude with a discussion of further directions of research and the implications of our framework for economic and institutional policy.

# **2 Literature and Methodology**

It has been noted in the literature that institutions—both economic and political—can be a major obstacle to development [North, 2008]. The policy dilemma of the century that can be succinctly formulated as “How to change institutions?” has attracted a lot of attention in the literature, but still remains unsolved. According to the long tradition of institutional economics, institutions can be good or bad for economic 4
development, and Western-style institutions have been shown to correlate with economic growth. However, literature also documents many failed attempts at imposing them in developing countries [Putnam et al., 1992].<sup>3</sup> Empirical analysis of the importance of institutions for development has traditionally treated institutions as exogenous variables with evidence based on cross-country regressions that include proxies for “institutions” such as a democracy index, etc. The literature analyzing specific institutions, such as for example the legal regulations guiding financial market functioning, is not typically generalizable to other situations and takes the form of case studies. Other models do not take into account the context of economic interactions, rendering policy analysis impossible. It is no surprise that, similarly to Shirley [2005] and Knack and Keefer [1995], Rodrik et al. [2002] note that empirical studies show significant regularities in how institutional variables tend to dominate others in explaining growth and social progress, “but these studies lack a theory that would transform regularities into causal explanations.” Not many formal models of institutions—with the purpose to shed some light on their role in economic activity—have been proposed in the literature. For example, Ostrom [2000] uses social dilemmas to reason about the nature of collective action and social norms in Common Pool Resource problems [see also Kimbrough and Vostroknutov, 2015]. Some other approaches appear in the literature on the emergence of firms [e.g., Hart, 1989, Holmstr ̈om and Roberts, 1998]. Even though these models are capable of capturing certain elements of institutional influence on economic behavior, they cannot be used as the general models of institutional change or made more specific to arrive to more granular policy guidance.

What has been lacking is a workhorse model of institutional change. Such a model needs to be general enough to be able to account for a wide range of institutions, but at the same time it should allow for specific adaptations to accommodate the impacts of specific policies. More importantly, in such a model institutions would need to enter _endogenously_ [see also Engerman and Sokoloff, 2005], so that it is possible to consider the emergence and dynamic development of institutions depending on a set of parameters. This is needed for testing the model in practice as well as for policy implications and can only be achieved if institutions are introduced at the micro level, as social norms that aggregate into institutional packages [Henrich, 2015b]. This bottom-up approach would allow to organically incorporate both formal and informal institutions [Keefer and Knack, 2008]. Moreover, apart from straightforward variables describing “institutional quality” or specific institutions, the model should directly account for the structural distortions that accompany them. For example, inclusive institutions would correlate with lower informality as they reduce exclusion [Perry et al., 2007]. Clientelism can also emerge organically and coexist with the existing, extractive political system [Mu ̃noz, 2019].

> 3Acemoglu and Robinson [2020] provide many examples of “transplanted” formal institutions that have never taken root because they had been overwhelmed by pre-existing social norms and informal institutions. For example, the Peruvian pre-colonial _mita_ system is among the origins of extractive institutions in Latin America. The political economy literature documents many cases of the failure of transplanted democratic institutions, leading to corruption and clientelism [Acemoglu and Robinson, 2006]. Among many cases when formal institutions have been unsuccessfully over-imposed on existing informal institutions, the Latin American lettered city literature highlights the origins of modern widespread informality in the inconsistency of design of cities and reality of life for the poor, that has resulted in their continuous exclusion from the formal economy [Angel and Charles, 1996, Lazar, 2008].

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In this paper, we offer one such model. As was mentioned above, the main difference from the neoclassical approach is that agents are assumed to be moral (norm-following), or having an additional term in their norm-dependent utility that tracks social appropriateness of alternative outcomes they choose. This addition to selfish motivation makes agents want to cooperate and enter “business relationships” with each other.

It is worth mentioning that this idea is not new and that the connection between norm-abiding behavior and business activity has been pointed out in economics for a long time [e.g., Arrow, 1972]. However, the traditional definitions that simply suggest this connection are not enough for policy and understanding institutional change. To have a workable model of institutions, the moral agents’ utility-maximizing behavior should be pinned down exactly, which means that the normative values (social appropriateness) of all outcomes should be specified.

It may seem that in a given institution the values of social appropriateness of various actions and outcomes (what is considered appropriate to do within this institution) may heavily depend on the past history of the institution, local beliefs, and other specific cultural features. This is indeed true for many existing institutions. However, it is also true that people who consider entering a new business relationship face a new context (the set of feasible allocations) that depends on the specific business opportunities available to them at that time. So, it is plausible that there are no pre-specified norms from the past, customs, or traditions that prescribe what is moral in this new context. KV propose that for such cases people have evolved _moral psychology_ , or specific machinery in the brain that computes social appropriateness of outcomes solely from the information available in any current context (feasible allocations). Such computations, if done in the same way by all moral agents, should lead to formation of similar normative beliefs about social appropriateness and consequently to coordinated, cooperative behavior [see also Rusch and Vostroknutov, 2023].

KV describe a specific moral psychology of norm formation in any context that is based on the idea of aggregating _dissatisfaction_ . Specifically, it is assumed that the social appropriateness of each given allocation is inversely proportional to the summed dissatisfactions of all agents in that allocation. The dissatisfaction of each agent in a given allocation is high when there are many other counterfactual allocations in the context that give the agent more consumption utility and low otherwise. Thus, dissatisfactions express personal grievances of agents in a given allocation, and the normative value of the allocation is formed by aggregating all these dissatisfactions. In other words, the allocation is considered more socially appropriate, the less aggregated dissatisfaction it evokes.

This construction may seem overly complex and unnecessary. However, tests of existing experimental data have shown that the model of dissatisfaction-based norms can account for many puzzles in social behavior known to behavioral economists.<sup>4</sup> Specifically, it resolves many issues pertaining to the existing models of social preferences and reciprocal kindness [see Vostroknutov, 2020, for discussion] that are not context-dependent enough to accommodate certain stylized facts (e.g., radical context-dependence 4Experiments by Merguei et al. [2022] and Panizza et al. [2021] perform direct and rather stringent tests of KV’s model and find a very good fit with the data.

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of social behavior [List, 2007, Bardsley, 2008] or extreme switches of moral principles with small changes in payoffs [Galeotti et al., 2018]). Moreover, the model of KV allows to introduce social weights (aka trust weights) that measure the importance of dissatisfaction of each agent in the aggregation.<sup>5</sup> This is an important mechanism that accounts for various observations about social behavior within and without an in-group [Chen and Li, 2009], and that translates intuitively to one of the dimensions of trust.

We base our model on the framework of KV exactly because it seems to fit well the moral intuitions used by people in _new_ contexts and because it provides a way to determine what norms may emerge in these contexts without assuming some ad hoc social motives like, for example, inequality aversion [Fehr and Schmidt, 1999] or payoff efficiency maximization [Engelmann and Strobel, 2004] that may or may not play a role in a given institution. Most importantly though, the model of KV shows how norms—or rules of social conduct that define how to behave in certain situations—can emerge _endogenously_ and later become the accepted rules of an emerging institution. The fact that norms are context-dependent and change with the environment provides the way to conceptualize institutional change that we follow in this paper.

# **3 Model**

## **3.1 Public Goods Game Played by Moral Agents**

We start by describing the simplest possible incentive structure and the type of interaction among moral agents that will be used as a building block in applications presented later in the paper. Specifically, we assume that two moral (norm-following) agents desire to profit from mutual cooperation in the Public Goods game (PG), which is similar to game forms used by Ostrom [1990] to study common pool resource problems.<sup>6</sup> This interaction can be seen as representing various forms of “doing business,” which can produce surplus and consequently growth of wealth through cooperation (or not). This assumption can be seen as an embodiment of the various views in institutional economics, where institutions facilitate interactions of economic agents and impact transaction costs [North, 2016]. Similarly to Ostrom [1990], we focus on a specific form of such costs related to trust and problems with cooperation as any form of economic activity requires a certain degree of trust and cooperation/coordination among the people involved. Notice also that we consider PG as a versatile example of a social dilemma that embodies potentially variable levels of productivity (through the PG multiplier). In applications, any other game with social dilemma flavor can be utilized.

To describe how PG is played, suppose that before the game each player _i ∈{_ 1 _,_ 2 _}_ has some endowment _w ≥_ 0.<sup>7</sup> In the game, player _i_ chooses an amount to contribute to the public good with some PG

> 5In each allocation, the dissatisfaction is aggregated by summing up individual dissatisfactions of all agents. The weights multiplying these individual dissatisfactions act as measures of trust to individual agents. When an agent is not trusted (low weight), her dissatisfaction will count little in the aggregation, so that it may become socially appropriate to give her less than others (and vice versa for the agents with high trust weight).

> 6The argument easily generalizes to more than two players.

> 7A generalization to PG with unequal endowments is very interesting and easy to implement theoretically. However, for

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multiplier _p ∈_ [<sup><u>1</u></sup> 2<sup>_,_1). Suppose that player</sup><sup>_i_contributes</sup><sup>_xi∈_[0</sup><sup>_, w_], then her wealth after the game is</sup> In other words, player _i_ keeps the part of the endowment that was not contributed ( _w − xi_ ) and gains the return from the public good (the sum of contributions _xi_ + _x−i_ , where _x−i_ stands for the contribution of the other player, times _p_ ). Notice that the multiplier _p_ can be thought of as a measure of _productivity_ and defines how profitable the cooperation is. It can be influenced by various factors (e.g., it is high when good-quality public services are provided and low otherwise).

When agents are standard consumption utility maximizers, the unique Nash equilibrium of this game is to contribute nothing ( _x_<sup>_∗_</sup> _i_<sup>=0forall</sup><sup>_i_).Thisrepresentstheclassiccaseofunderprovisionofpublic</sup> goods. When player _i_ is assumed to be a moral agent, she chooses _xi_ to maximize her _norm-dependent utility_ [Kessler and Leider, 2012, Krupka and Weber, 2013] The utility function _Ui_ consists of two terms: the standard linear consumption utility _wi_ and the normative term _φiηi_ ( _wi, w−i_ ) representing the desire to follow norms. Here we implicitly see _wi_ as the function of _xi_ and _x−i_ as in (1); the coefficient _φi ≥_ 0 defines _i_ ’s propensity to follow norms; and _ηi_ : _C →_ R is the _norm function of player i_ that defines the _social appropriateness_ of each possible outcome ( _w_ 1 _, w_ 2) in the game and arises endogenously from the set of all achievable wealth allocations defined by _C_ = _{_ ( _w_ 1 _, w_ 2) _|_ ( _x_ 1 _, x_ 2) _∈_ [0 _, w_ ]<sup>2</sup> _}_ . Specifically, following KV we define _ηi_ as

Here, the notation _ηi_ ( _wi, w−i_ ; _τ_ ) emphasizes that the social appropriateness expressed by the norm function depends on _τ ≥_ 0, the _social weight_ that player _i_ attaches to the other player ( _−i_ ). _Di_ ( _wi_ ) stands for the _personal dissatisfaction_ that player _i_ feels should she receive wealth _wi_ after the game. This personal dissatisfaction, in its turn, is the sum of dissatisfactions due to all possible other allocations in _C_ where player _i_ receives more consumption utility than _wi_ (so, _i_ is dissatisfied because she could have had more consumption). This is expressed with the max operator in the second line of (3), that measures dissatisfaction at _wi_ due to some other possible consumption utility _ci_ (we notate _c_ = ( _ci, c−i_ ) since _C_ is a subset of R<sup>2</sup> ).

Thus, the social appropriateness _ηi_ ( _wi, w−i_ ) of outcome ( _wi, w−i_ ) from the perspective of player _i_ is the negative of the weighted sum of the personal dissatisfactions of the two players ( _Di_ ( _wi_ ) and _D−i_ ( _w−i_ )) with the latter weighted by the exogenously given social weight _τ_ . The idea here is that player _i_ feels that outcomes in _C_ are more socially appropriate when they evoke less dissatisfaction from both the sake of expositional simplicity we choose to not introduce it in this paper and leave it for future research.

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# **3.2 Norms and Trust**

As described in the previous section, agents cooperate or do business more willingly with people whom they trust, so the concept of trust is important to understanding the behavior and beliefs of moral agents. A widely used definition of trust states that it is the belief that someone will not behave opportunistically, as in Keefer and Scartascini [2022]. A more general definition is that trust is a situation-specific expectation about other agent’s behavior [Bauer and Freitag, 2018]. In other words, trust is context-dependent. In particular, trust can be linked to propensity to follow specific social norms. For example, agents exhibit higher trust towards people who belong to their social group [Chen and Li, 2009]. To reflect this, we add a second dimension to the commonly used definition of trust.

The first dimension of trust corresponds directly to the definition of Keefer and Scartascini [2022]. This kind of trust is defined by the individual propensities to follow norms _φi_ and _φ−i_ (and players’ beliefs about them). Indeed, if player _i_ believes, for example, that _φ−i_ = 0, then she is sure that the other player is selfish and only maximizes his consumption utility. She _does not trust him,_ because she believes that _−i_ will disregard the norms (whatever they may be) and contribute nothing in PG, which is _−i_ ’s strictly dominant strategy.

For the second dimension of trust (as we define it), notice that in our model _i_ ’s believing that _−i_ has high _φ−i_ is not enough for her to trust him. If _i_ believes that _φ−i_ is high but that _−i_ does not care about her (low _τ_ in _η−i_ ), then she also will not trust _−i_ . This happens not because _i_ thinks that _−i_ is selfish, but rather because _−i_ has _different norms_ that discount her, _i_ ’s, importance in the eyes of _−i_ . For example, the members of two warring tribes might be absolutely sure that the opponent is a highly moral norm-following individual. However, they will still not cooperate with each other (contribute in the PG) because they know that both of them do not care about the dissatisfaction of the other. They _do not trust each other due to different normative views_ [see e.g., Akerlof and Kranton, 2000, Chen and Li, 2009]. This is an important case of trust that we believe is the key to understanding the formation of institutions given that most human beings do follow norms of their—sometimes highly specific or imaginary—social groups most of the time.<sup>9</sup> In the rest of the paper, we will assume therefore that all players are moral agents who, by definition, have some propensity to follow norms ( _φ_ ’s are above zero), but that their normative views are different due to low social weights _τ_ put on other players. Thus, we describe the world where all agents want to

> 9 Our terminology with regard to _τ_ that we call the second dimension of trust might sound unfamiliar to some readers. The way _τ_ enters norm-dependent utility is technically similar to models of altruism where agents directly care about the utility of other players. However, the similarity is only technical. What is important is the interpretation. In case of norm-dependent utility, _τ_ is a parameter that determines _normative views_ . In other words, _τ_ determines whether an agent will consider some allocations involving other agents socially appropriate or not. Norms are social constructs that incentivize agents to act in the society, whereas altruism is a psychological construct that does not necessarily relate to social behavior. It can be easily imagined that there are agents who are not altruistic at all, but who follow norms nonetheless. Thus, if we consider utility representation (2) as just some utility function that involves utilities of other players, then _τ_ can be interpreted as altruism. But when we consider it as a _norm-dependent utility_ with norms that are supposed to be shared among many agents, then _τ_ obtains a different meaning, it becomes related to whom we should trust and whom we should not trust. In the example with warring tribes, _τ_ signifies how appropriate it is to be cooperative with the members of the other tribe and not how altruistic we should be towards them.

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cooperate by following _some_ norms (e.g., those of their social group), but might fail to cooperate with strangers because they think that they come from the out-group.<sup>10</sup>

# **4 Institutions for Facilitation**

Institutions are “humanly devised constraints that structure human interaction,” including formal constraints such as constitutions and laws and informal constraints, such as norms, conventions and selfimposed codes of conduct [North, 1990]. Describing the incentives for “doing business,” Coase argued that “if the costs of making an exchange are greater than the gains which that exchange would bring, that exchange would not take place.” Institutions thus emerge to reduce transaction costs associated with production [Coase, 1937].

To understand the functioning of endogenous institutions in our model, we must understand their emergence and trace their development. We start from the Hobbes’ primordial “state of nature,” devoid of any institutions or social norms and observe the emergence of institutions to support cooperation. We eventually arrive at a model with endogenous institutions, where institutional change is possible between inclusive and extractive institutions, depending on personal characteristics of agents involved ( _φ_ ) and their trust to each other ( _τ_ ).

## **4.1 The State of Nature**

To understand how and for what purpose institutions may emerge, we need to consider the motivation and incentives of agents in what moral philosophers call the _state of nature_ or _Warre_ [Hobbes, 1651, Acemoglu and Robinson, 2020]. This is a hypothetical world of unorganized individuals who do not hold any common views on how things should be done (social norms) and thus act mostly in their own self-interest in the absence of any shared norms, regulations, or laws. Translated to the language of our model in Section 3.1, this would correspond to the situation where moral agents, although willing to follow norms, are unable to cooperate because they do not trust anyone (high _φ_ , low _τ_ ; but see also Section 7). In this case, in equilibrium no two agents will contribute anything to the public good and thus there will be no growth of wealth. Such conditions are not inconceivable and existed for brief periods of time even in recent history [Leeson, 2007].<sup>11</sup> Even though the state of nature precludes wide-spread cooperation with strangers due to generally low trust, some episodic cooperation and growth of wealth might exist among moral agents who know each other well and have high social weights _τ_ attached to each other (e.g., family, friends). A pair of friends (or cousins) with high enough _τ_ will contribute fully to the public good, thus benefiting themselves. However, it is also reasonable to think that after some time they will exhaust all possibilities for

> 10The case with low _φ_ ’s is not interesting anyway, as it is approximated well by standard players with selfish preferences. In this case, we know already that no cooperation can happen at all in any social dilemma.

> 11Hobbes describes the state of nature as “war of all against all,” which can be likened to negative growth. In our model, such situation is also possible when social weights attached to other agents are negative ( _τ <_ 0). In this case, moral agents will find it socially appropriate to _increase_ dissatisfaction of others (e.g., by appropriating or destroying their wealth).

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profitable cooperation due to the fact that they most likely live in the same area and have access to the same resources. This will make the PG multiplier _p_ , applicable to their interaction, low and the resulting growth will be negligible.

From this we can argue that moral agents would strive to cooperate with others who have access to different resources and have potentially different skills and know-how (which makes the multiplier _p_ in the potential PG high). However, such others will typically be strangers that cannot be trusted in the state of nature (low _τ_ ). Thus, we have a situation where moral agents _want_ to cooperate because it is profitable, but are _unable to do so_ due to low trust. In this case, it is reasonable to believe that they will try to find _some arrangements_ that will make cooperation possible.

# **4.2 Facilitation**

The simplest possible arrangement that can expand cooperation beyond what is possible in the state of nature is _facilitation_ of cooperative relationship between two moral agents by a common friend, relative, or _facilitator_ . It is possible, as we discuss in more detail in Section 7, that first facilitators emerging from the state of nature were extended family members related to agents through family ties (e.g., cousins, inlaws, or clan members). In later times and in societies that started to interact with strangers, facilitators were traders or other individuals (e.g., priests) who managed to gain trust of separate groups of people with different norms or social identities. This allowed them to act as intermediaries between them also facilitating economic relationships.

Consider two moral agents in _{_ 1 _,_ 2 _}_ as in Section 3.1 with equal and low social weights _τ_ 2 _< τ_<sup>_∗_</sup> attached to each other, which is below the threshold _τ_<sup>_∗_</sup> above which the Nash equilibrium in the PG is to fully contribute (see Appendix A.1 for the values of _τ_<sup>_∗_</sup> as dependent on _p_ ).<sup>12</sup> Thus, in the PG the agents will optimally choose to contribute nothing when their mutual social weights are _τ_ 2 (the meaning of subindex 2 will become clear in Section 6). Now suppose that there is a facilitator agent _f_ with whom both agents maintain friendly relationships, so that the mutual social weights between any agent _i ∈{_ 1 _,_ 2 _}_ and _f_ are _τ_ 1 _> τ_<sup>_∗_</sup> . This means that agent _i_ would cooperate with _f_ if the opportunity arose. The left panel of Figure 2 illustrates: the dotted line emphasizes the impossibility of cooperation.

<!-- Start of picture text --> Without facilitation With facilitation<br>f f<br>τ1 τ1 τ1 τ1<br>1 τ2 2 1 τ1 2<br>payment payment<br><!-- End of picture text --> Figure 2: **Left.** Without facilitation players 1 and 2 cannot cooperate due to low social weights _τ_ 2. **Right.** Players 1 and 2 can pay _f_ for facilitation and cooperate with the same social weight _τ_ 1 that they have with the facilitator. 12 When _p_ = 0 _._ 8, we have _τ ∗_ = 0 _._ 25.

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Despite the possibility of cooperation with _f_ , the agents want to cooperate with each other as this brings more profit than cooperation with _f_ (see the argument above). Therefore, it is possible that the three agents agree on the following deal. Agent _f_ facilitates the relationship between agents 1 and 2 by “vouching” for each agent as a good cooperative partner (since both are his friends). In the presence of such facilitation, agents 1 and 2 can cooperate with each other _as if_ they share a friendly social weight _τ_ 1 that allows for an equilibrium with full contributions. Such deal is of course not free and agents also agree to pay the facilitator _f_ some amount _z_ for his services. Suppose that each agent pays _f_ the amount _z/_ 2. The right panel of Figure 2 illustrates that now players 1 and 2 can cooperate if they pay the facilitator.

It is clear that such deals can be profitable for all three agents as long as the payment _z_ to facilitator is “reasonable.” In this case, the profit from cooperation for agents 1 and 2 minus the payment _z/_ 2 can exceed the profit from all other available options, of which there are not so many, and the deal will be made. This form of interaction can be thought of as the simplest form of _institution for facilitation_ that allows for cooperation among strangers and that can emerge spontaneously due to its profitability to all parties involved. Of course, such an institution is not perfect as it cannot connect two agents who do not share a friend. However, with time more complex institutions can evolve from this simple interaction gradually involving more and more unrelated agents.

# **4.3 Norms in Institutions for Facilitation**

In Section 3.1 we analyzed how normativity and the notion of social appropriateness of outcomes emerges in a simple PG. The behavior of moral agents was consequently guided by these notions and allowed us to talk about morally “right” and “wrong” outcomes, or appropriate and inappropriate behavior (which leads to right or wrong outcomes). Using the same technique from KV, we can also analyze social appropriateness of outcomes in the institution for facilitation that includes an additional player, the facilitator. This analysis will allow us to understand the behavior of moral agents as well as define norms that become the inalienable part of this institutional arrangement. Thus, we can calculate, for example, what would be considered reasonable amount of payment _z_ to facilitator that agents 1 and 2 would find “fair.” This amount is the _norm_ associated with the institution for facilitation. This is an important notion that leads to the extended welfare analysis for moral agents (with norm-dependent utility) that includes standard consumption considerations as well as their utility losses or gains due to fairness or unfairness of the outcomes resulting from the institution for facilitation (see Section 5).

To do this, we consider the set of all allocations to three players (agents 1, 2, and _f_ ) that can be achieved in some (yet unspecified) non-cooperative game that represents how exactly agents interact in this institution.<sup>13</sup> As in Section 3.1, suppose that players 1 and 2 have endowments _w_ before the game 13An important feature of the framework of KV is that norm functions or measures of social appropriateness are defined on the sets of allocations that ignore the non-cooperative game structure (who moves when, which actions are available, etc.). It allows us to analyze games in the style of cooperative game theory without specifying ex ante how the game unfolds. This property can be very useful for applications where the exact game structure is often unknown or changes depending on 13
(facilitator does not have or need an endowment since he is not playing the PG). Suppose as well that if each player _i_ pays the amount _z/_ 2 to facilitator, then both of them have _w − z/_ 2 left to play the PG. Thus, we can say that the wealth of player _i_ after the game where _z_ was paid to the facilitator is given by where _x_<sup>_z_</sup> _i_<sup>_∈_[0</sup><sup>_, w −z/_2] for both</sup><sup>_i∈{_1</sup><sup>_,_2</sup><sup>_}_is the amount contributed.We define the set of achievable</sup> allocations as _CF_ = _{_ ( _w_ 1<sup>_z, w_</sup> 2<sup>_z, z_)</sup><sup>_|z∈_[0</sup><sup>_,_2</sup><sup>_w_]and(</sup><sup>_xz_</sup> 1<sup>_, xz_</sup> 2<sup>)</sup><sup>_∈_[0</sup><sup>_, w−z/_2]2</sup><sup>_}_.Hereweassumethat</sup> all payments _z_ are possible: from 0 (facilitator works for free) to full endowments of both players 2 _w_ (facilitator gets all the money and players 1 and 2 have nothing left). The set of allocations _CF_ is a pyramid in R<sup>3</sup> shown on the left panel of Figure 3.

The definition of _CF_ is all we need to specify the norm functions of the three players. For player _i ∈{_ 1 _,_ 2 _}_ , we have Here we notate _c_ = ( _ci, c−i, cf_ ) _∈ CF ⊆_ R<sup>3</sup> . In words, the social appropriateness of an outcome ( _wi_<sup>_z, w_</sup> _−_<sup>_z_</sup> _i_<sup>_, z_)</sup><sup>_∈CF_fromthe perspectiveof player</sup><sup>_i_is the weighted sum of personal dissatisfactions of</sup> the three players, with social weights _τ_ 1 for the other two players (as discussed in Section 4.2).

The norm function for the facilitator _f_ is This is just the reshuffling of the same personal dissatisfactions as above, only with social weights _τ_ 1 applied to the players 1 and 2.

We illustrate these functions in Figure 3. Specifically, the middle panel shows the unique norm function for all three players that arises when _τ_ 1 = 1, or when both players 1 and 2 trust the facilitator as they trust themselves (e.g., family). This case represents the most cooperative situation achievable within the institution where all players treat each other as they treat themselves (of course, players 1 and 2 do not trust each other much outside the institution for facilitation, they have weight _τ_ 2, see Section 4.2). Notice that in this case the norm (or the most appropriate allocation) obtained from maximization of (6) and marked on the graph in dark red gives 26% of 2 _w_ to the facilitator ( _z_ = 0 _._ 26 _·_ 2 _w_ ) and players 1 and 2 should choose to contribute the full amount of what is left after this payment. The right panel of Figure 3 shows the norm function of player 1 for the case when _τ_ 1 = 0 _._ 2. In this case, unsurprisingly, player 1 considers it socially appropriate to have more than both other players, which can be seen from the dark circumstances. See Kimbrough and Vostroknutov [2023a] for additional discussion.

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where all can participate (at an affordable cost), that leads to more cooperation and production; and exclusive nature of extractive institutions that allow for a group of agents to extract rents above the ”fair” cost, from the rest of the population.

Given that the state of nature does not provide players 1 and 2 with many outside options, it is not so hard to imagine that the facilitator can exercise power over them since without him players 1 and 2 cannot make any profits. Thus, we define the non-cooperative game as follows. First, the facilitator makes players 1 and 2 a take-it-or-leave-it offer of the payment _z ∈_ [0 _,_ 2 _w_ ] that he wants for his services. Then, players 1 and 2 pay the requested amount _z_ and play the PG with endowments _w − z/_ 2. As before, we assume that players 1 and 2 attach social weight _τ_ 1 _> τ_<sup>_∗_</sup> to the facilitator (and each other within the institution), so that they optimally cooperate in each subgame happening after any offer _z_ . Notice that in the non-cooperative game all that matters is that players 1 and 2 _believe_ that the social weight that they attach to the facilitator and guaranteed by him for their own relationship is _τ_ 1 (high enough for cooperation to be the Nash equilibrium in the subgames). This is important since, in principle, the facilitator does not have to respect or genuinely care about players 1 and 2 at all. All he needs to do for the institution to work (which leads to cooperation and payment of _z_ to himself) is to _convince_ the players that he can be trusted.<sup>15</sup> The last ingredient of the non-cooperative game are the utilities that the players eventually receive. This is straightforward: the norm-dependent utility of player _i ∈{_ 1 _,_ 2 _}_ is given by and the norm-dependent utility of the facilitator is The analysis of the equilibrium behavior proceeds by backward induction. Given that players 1 and 2 attach high social weight _τ_ 1 to each other within the institution and assuming that their propensities to follow norms _φ_ 1 and _φ_ 2 are high enough, they will choose full contributions _x_<sup>_∗_</sup> _i_<sup>(</sup><sup>_z_)=</sup><sup>_w −z/_2 given</sup> any offer _z_ (see Appendix A.2 for details).<sup>16</sup> In the next step of backward induction, the facilitator takes the equilibrium actions _x_<sup>_∗_</sup> _i_<sup>(</sup><sup>_z_) as given and solves the following maximization problem:</sup> Notice that here we use the wealth of player _i_ given equilibrium play _x_<sup>_∗_</sup> _i_<sup>(</sup><sup>_z_)and</sup><sup>_x∗_</sup> _−i_<sup>(</sup><sup>_z_)determinedas</sup> _wi_<sup>_z_=</sup><sup>_w −z/_2</sup><sup>_−x∗_</sup> _i_<sup>(</sup><sup>_z_) +</sup><sup>_p_(</sup><sup>_x∗_</sup> _i_<sup>(</sup><sup>_z_) +</sup><sup>_x_</sup> _−_<sup>_∗_</sup> _i_<sup>(</sup><sup>_z_)) =</sup><sup>_p_(2</sup><sup>_w −z_) for</sup><sup>_i ∈{_1</sup><sup>_,_2</sup><sup>_}_.</sup> What will determine optimal _z_<sup>_∗_</sup> that solves this maximization problem? As follows from the proof

> 15In Section 6 we will show how this can lead to the emergence of clientelistic networks.

> 16The case when _φ_ 1 and/or _φ_ 2 are low is uninteresting. Here players 1 and 2 will not contribute anything to the public good and cooperation will fail. Given that in our framework everyone strives to cooperate to make money, we assume that players 1 and 2 are norm-followers to a sufficient degree.

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of Compromise Theorem [see Proposition 5 in Kimbrough and Vostroknutov, 2022a], in the vicinity of the optimum the maximand function is a downward sloping parabola such that lim _φf →_ 0 _z_<sup>_∗_</sup> = 2 _w_ and lim _φf →∞ z_<sup>_∗_</sup> = _ηf_<sup>_∗_(</sup><sup>_w, p, τ_1),where</sup><sup>_η_</sup> _f_<sup>_∗_(</sup><sup>_w, p, τ_1)isthemaximumof</sup><sup>_ηf_givenparameters</sup><sup>_w, p_and</sup><sup>_τ_1.17</sup> This means that selfish facilitator with _φf_ = 0 will demand the highest possible payment of 2 _w_ thus leaving players 1 and 2 with nothing, and the most rule-following facilitator with _φf →∞_ will ask for the payment that is the most socially appropriate from his perspective (the maximum of _ηf_ ) given the optimal actions _x_<sup>_∗_</sup> _i_<sup>(</sup><sup>_z_) of players 1 and 2 in the subgames. This completely describes the Subgame-Perfect</sup> Nash equilibrium in this game.

From the analysis above, it is clear that the “kind” of institution we get in equilibrium depends solely on the payment _z_<sup>_∗_</sup> demanded by the facilitator (since players 1 and 2 fully cooperate in all subgames). Thus, we can classify institutions depending on the value of _z_<sup>_∗_</sup> that also determines the resulting welfare of players 1 and 2. When the facilitator is selfish ( _φf_ = 0), he extracts everything from the two players ( _z_<sup>_∗_</sup> = 2 _w_ ), which leads to the wealth allocation (0 _,_ 0 _,_ 2 _w_ ). This is the worst allocation from the perspective of the welfare of the two players not only because they are left with nothing, but also because this allocation is considered highly inappropriate by both of them. Players 1 and 2 get the lowest possible level of normative part of their norm-dependent utility at (0 _,_ 0 _,_ 2 _w_ ), see Figure 3. We formulate this as a definition.

**Definition 1.** _We call an institution for facilitation_ **fully extractive** _when players_ 1 _and_ 2 _pay their full endowments to the facilitator, which gives them the lowest possible level of both consumption and normative utility, and the facilitator gets the highest possible payment._

Fully extractive institutions can emerge for two different reasons that are related to the two dimensions of trust. The first possibility is when the facilitator is completely selfish ( _φf_ = 0) and thus disregards the norms: he will act as a standard consumption utility maximizer and extract all surplus from players 1 and 2. The second possibility, mentioned above, is that the facilitator is not selfish ( _φf >_ 0) but cares little for players 1 and 2 (e.g., his real trust weight towards them is very low). However, facilitator manages to convince players 1 and 2 that he can be trusted ( _τ_ 1 _> τ_<sup>_∗_</sup> ). Then, players 1 and 2 may agree to participate in the institution, only to learn later that they lose all their endowments.<sup>18</sup> Notice that fully extractive institutions can emerge for arbitrary levels of trust _τ_ 1 among agents in the institution. This is so because the other dimension of trust, namely the propensity to follow norms _φf_ , is responsible for creating such conditions, which eliminates the dependency of the equilibrium on trust all together. In order to define the other extreme where the propensity to follow norms is high, we need therefore to take into account both dimensions of trust ( _φ_ ’s and _τ_ ’s). We formulate it as follows.

**Definition 2.** _We call an institution for facilitation_ **fully inclusive** _when τ_ 1 = 1 _, or when all players in the institution care about each other as they care for themselves, and when the payment to the facilitator is consistent with the norm and is equal to ηf_<sup>_∗_(</sup><sup>_w, p,_1)</sup><sup>_, or the payment that all three players find most socially_</sup>

> 17By the symmetric nature of _ηf_ (with respect to players 1 and 2), its global maximum coincides with the maximum of _ηf_ ( _p_ (2 _w − z_ ) _, p_ (2 _w − z_ ) _, z_ ) as a function of _z_ .

> 18An example of a fully extractive institution is slavery.

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_appropriate._ These conditions are reached in equilibrium when _φf →∞_ , or when the facilitator only cares about social appropriateness and does not care about his own consumption (and when the trust in the institution is the highest, _τ_ 1 = 1).<sup>19</sup> In between fully extractive and fully inclusive institutions lies a continuum of possibilities that are characterized by non-extreme values of the two dimensions of trust: _φf_ and _τ_ 1. The problem with classifying this continuum into some flavors of “extractiveness” and “inclusiveness” lies in the fact that for _τ_ 1 _∈_ (0 _,_ 1) the norm functions _η_ 1, _η_ 2, and _ηf_ will in general be different and have three different maxima (all players 1, 2, and _f_ individually believe that they deserve more than the others). Thus, we need to pick a moral perspective from which to judge the welfare qualities of the institution. We propose to take the perspective of the players 1 and 2 since it is their welfare (and not that of the facilitator) that is important for economic policy. Moreover, the maxima of the norm functions _η_ 1 and _η_ 2 are reached at the same value _z_ ̄( _w, p, τ_ 1) of payment to the facilitator (the functions are symmetric). So, players 1 and 2, although disagreeing on how much they themselves should get in the most socially appropriate allocation, nonetheless agree on the most socially appropriate payment to the facilitator. We use this fact in the definition.

**Definition 3.** _Suppose that τ_ 1 _∈_ (0 _,_ 1) _. Then call an institution for facilitation_ **inclusive** _if the payment to the facilitator is consistent with the norms of players_ 1 _and_ 2 _and is equal to_  ̄ _z_ ( _w, p, τ_ 1) _. Such payment is considered fair by players_ 1 _and_ 2 _. Else, call the institution for facilitation_ **extractive** _._

Notice that in the last definition we do not specify what parameters of the norm-dependent utility of the facilitator lead in equilibrium to inclusive or extractive institutions. The reason is that, in general, when _τ_ 1 _∈_ (0 _,_ 1) the facilitator who maximizes his norm-dependent utility will always ask for strictly more payment than ̄ _z_ ( _w, p, τ_ 1). This is so simply because the facilitator cares more about his own dissatisfaction in the norm function _ηf_ than he cares about the dissatisfactions of players 1 and 2. Thus, any informal relationship with _τ_ 1 _∈_ (0 _,_ 1) will _always_ lead to extractive institutions. Only government that, in principle, does not have to follow its own norm-dependent utility since it is not a human being can set the payment to itself to be equal to _z_ ̄( _w, p, τ_ 1), thus creating an inclusive institution.

# **5 Choice of an Institution**

Today, most people live in developing countries, many of which have failed to create or sustain strong inclusive institutions [Acemoglu and Robinson, 2020]. As formal institutions are ineffective or not accessible, ”individuals enforce most bargains using informal institutions...and they have little trust in or trade with people not subject to these mechanisms” [Shirley, 2005]. We therefore assume that both formal and informal institutions exist, and that agents can choose between them.

In the previous section, we have provided the analysis of the behavior of moral agents in a single 19For example, family or a well-functioning democracy are inclusive institutions.

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institution for facilitation in which players 1 and 2 were forced to participate. We now assume that agents can try to cooperate with others through an informal institution (and pay some amount to the informal facilitator) or they can do business through government (and pay taxes). In other words, people have outside options, and in this section we consider the implications of the availability of such options; their influence on the optimal demand of payment by the informal facilitator; and the resulting choice of institution by players 1 and 2.

# **5.1 Formal and Informal Institutions**

In our model, both _informal institutions_ and _government_ (formal institution) work using the same facilitation mechanism described above. However, there are two tangible differences that we would like to emphasize. In the economy with players 1 and 2, an informal institution is an institution for facilitation where the facilitator is another player _f_ with his specific norm-dependent utility as in (8). This means that such _informal facilitator_ is a human being with some specific perspective on morality (as expressed by _ηf_ ) who maximizes his norm-dependent utility. Moreover, the informal facilitator collects the payment from the two players for himself and does not invest it in anything useful for them (e.g., public services). Thus, the informal institution is characterized by the norm-dependent utility of the informal facilitator _Uf_ (as in (8)) and the trust in informal facilitator _τ_ 1 that determines the fairness of different levels of payments to him from the perspective of players 1 and 2.

Government is a formal institution and another facilitator that also collects payment for its services, or taxes. But unlike the informal facilitator, government is not a human being, thus it does not have a specific morality described by the norm-dependent utility and consequently does not maximize it. Ideally, government’s job is to facilitate business transactions, collect taxes, and invest them into public services that enhance productivity _p_ in the future (see Section 5.3). Though in reality, governments are steered by people who bring to them ideologies and values that might not be in the best interest of people. For example, in Section 7 we discuss the case of medieval states in the Middle East who acted as governments but mostly in their own interest (see also Ekeh [1975] on the two publics in Africa).

Given this, an important parameter that defines government’s facilitation is the amount of trust in it determined by the social weight _τg_ that enters players’ norm-dependent utilities (with _τg_ instead of _τ_ 1 in (5)) and determines the fairness of tax payments from the perspective of players 1 and 2.

# **5.2 Model of Choice between Institutions**

To model the choice of institution by players 1 and 2, we consider the following parsimonious set-up that captures the main intuition of such choice. Suppose that the payment that government asks in taxes, in case players 1 and 2 use its facilitation services, is fixed before the game at _zg_ and known to all players. We assume that _zg_ is given and fixed since, realistically, government cannot adjust taxes quickly at any desired moment in time. Though, we can still work out the consequences of different choices of _zg_ by comparing the optimal responses of other players in the game (comparative statics). Suppose as well 19
that other parameters, namely, _w_ , _p_ , _τ_ 1, and _τg_ are known and fixed. The game proceeds as follows. First, the informal facilitator makes an offer for payment _z_ to him from players 1 and 2. Then players 1 and 2 compute the norm-dependent utilities they would get in both possible institutions (informal and formal) and choose an institution that brings them the highest utility. To avoid coordination problems (when the = two players want to choose different institutions), we assume for the sake of the argument that _φ_ 1 _φ_ 2, so that both players 1 and 2 will prefer the same institution. We also assume as above that _φ_ 1 and _φ_ 2 are high enough for players to be able to cooperate. These assumptions will be relaxed in the network economies with more than two players that we consider in later sections.

To analyze the game resulting from the above description, we again use backward induction and consider the choices of players 1 and 2 between institutions (the choices within institutions are already computed in Section 4). Player _i ∈{_ 1 _,_ 2 _}_ chooses formal institution when in the corresponding subgame her equilibrium norm-dependent utility in it is higher than that in the informal institution. This can be expressed using (7) as Plugging equilibrium choices corresponding to full cooperation _x_<sup>_z_</sup> _i_<sup>=</sup><sup>_w −z/_2 (and the same for</sup><sup>_zg_), we</sup> obtain _p_ (2 _w − zg_ ) + _φiηi_ ( _p_ (2 _w − zg_ ) _, p_ (2 _w − zg_ ) _, zg_ ; _τg_ ) _≥ p_ (2 _w − z_ ) + _φiηi_ ( _p_ (2 _w − z_ ) _, p_ (2 _w − z_ ) _, z_ ; _τ_ 1) or Notice that now _ηi_ is a function of _zg_ and _τg_ or _z_ and _τ_ 1, so we simplify the notation and rewrite the above as Inequality (9) is the condition under which player _i_ will choose the formal institution (government) for facilitation over the informal one (remember, player _−i_ has exactly the same condition, since by assumption _φ_ 1 = _φ_ 2). For player _i_ with high _φi_ , who cares about norms enough to be able to cooperate (an assumption made above that is also necessary for the full contributions in the subgames), this inequality represents a trade-off between the social appropriateness of participating in the two institutions (which is important for player _i_ ) and the payments that should be made in them.

Going up the game tree, we now consider the choice of offer _z_ by the informal facilitator _f_ , who understands that he can only make profit _z_ when (9) is _not_ satisfied (otherwise _f_ gets nothing).<sup>20</sup> In general, this choice of _z_ depends on _zg_ , _τg_ , _τ_ 1 in potentially non-trivial way. However, it is not hard to see what the choice of _z_ will be for the realistic case when 1) player _i_ considers the tax _zg_ too high and

> 20Technically, the informal facilitator compares his norm-dependent utility _Uf_ as in (8) in case _z_ is accepted to his _Uf_ when the players choose the formal institution, in which case we assume the informal facilitator’s normative part of the utility is the lowest: the deal that could have been made was not made, which creates dissatisfaction.

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inappropriate given the level of trust _τg_ that player _i_ has for the government; and 2) when _τg_ = _τ_ 1 = _τ_ . The latter condition is not too restrictive as the most socially appropriate level of taxes (or payments to informal facilitator) is not very sensitive to changes in _τ_ when it is higher than the minimum level of trust _τ_<sup>_∗_</sup> necessary for cooperation.

<!-- Start of picture text --> z' z z z<br>g g payment to<br>facilitator<br>social<br>approp.<br><!-- End of picture text --> Figure 4: The graph of _ηi_ ( _z_ ; _τ_ ). Amount _zg_ is the realistic, inappropriate level of taxation by the government and _zg_<sup>_′_istheappropriateleveloftaxation.Thechoicesof</sup><sup>_z_byinformalfacilitatoreithermakeplayer</sup><sup>_i_choosethe</sup> government ( _z_ to the right of _zg_ ) or the informal institution ( _z_ to the left of _zg_ ).

For this case, as Figure 4 illustrates, the choice of _z_ is straightforward. If the informal facilitator chooses _z > zg_ , the inequality (9) will be trivially satisfied as _zg − z <_ 0 and _ηi_ ( _zg_ ; _τ_ ) _− ηi_ ( _z_ ; _τ_ ) _>_ 0. In this case players 1 and 2 will prefer the government. Thus, the informal facilitator will choose some _z < zg_ to guarantee the opposite. The optimal value of _z_ will be just below _zg_ if the informal facilitator is selfish ( _φf_ = 0) and potentially something lower if he cares about norms ( _φf >_ 0). Either way, by choosing _z_ smaller than _zg_ the informal facilitator can always lure players 1 and 2 to use his institution instead of the government.

This situation is often observed in reality. For example, the informal sector in some developing countries employs more than 80% of the labor force and produces well over half of GDP. Following the seminal review in Perry et al. [2007], we can recognize two mechanisms that are at play. First, informal workers and firms are excluded from the formal economy in the sense that while they may not be paying taxes they also cannot enjoy the benefits provided by formality, such as contract enforcement or pensions. Second, economic agents and organizations (firms) in the informal sector have likely opted out of the formal sector based on a cost-benefit analysis weighing taxes and regulations against state’s enforcement effort and capability [following Hirschman, 1970].

How can the government avoid such an unappealing situation? The model suggests that the only way to do that is to make sure that _zg_ is as socially appropriate as possible from the perspective of player _i_ with trust _τg_ (e.g., _zg_<sup>_′_on Figure 4). In this case,</sup><sup>_ηi_(</sup><sup>_zg_;</sup><sup>_τg_) will be the highest and the undercutting by informal</sup> facilitator will be problematic, because now he will have to compromise the social appropriateness of his 21
institution.

This suggests that in order to make players prefer the government to informal institutions, the government should try to _align the level of taxes with their perceived social appropriateness_ . In the model, this can be achieved in two ways. First, the government can lower the taxes. This option is, however, very limited. Leaving aside the very inefficiency that prompts the use of informal institutions, the government (unlike the informal facilitator) is a complex institution that has costs and obligations to provide public services, so the taxes cannot be too low. The second way is to increase trust in government _τg_ that will then make the existing level of taxes seem more socially appropriate. This latter strategy would be consistent with reducing the main driver of informality: “a massive opting out of formal institutions by firms and individuals [...] implies a blunt societal indictment of the quality of the state’s service provision and its enforcement capability” [Perry et al., 2007, p. 2].

# **5.3 Dynamics of Trust in Government and Policy**

How can the trust in government _τg_ be increased? The classic view is based on its interconnection to the quality of institutions, where high quality of institutions can compensate for mistrust; for example Keefer and Scartascini [2022] emphasize prosecutors and audit agencies, dispute resolution systems, and electoral processes. Other approaches focus on the role of the social contract, citizenship, and collective action [Keefer et al., 2021]. In the latter vein, a policy that can increase collective action also increases trust in government. For example, Falconi and Robinson [2021] suggest promoting collective identities, ideas that have a unifying effect on the population (e.g., Peruvian cuisine). In theory, such a unifying national idea can spill over to the government and make people believe that it represents their national interests thus increasing _τg_ . In this section, we take a more traditional view and propose one intuition using a reduced-form dynamic model of public service provision. We link trust to the relative appropriateness of formal and informal institutions, and to quality of public services. In doing so, we also shed some light on the relationship between the size of formal and informal sectors and growth that is stimulated through the connection between the amount of public services and the quality of cooperation in PG or productivity (represented by the multiplier _p_ ).

For this exercise, we make several simplifying assumptions that do not compromise the main intuition, but make things more tractable. First, we assume that the informal facilitator is selfish ( _φf_ = 0). This assumption has one implication that will simplify the analysis. Selfish informal facilitator in the settings described above will always optimally choose _z_ = _zg − ε_ , where _ε_ is some small number, to barely undercut the government and attract players to his institution (the logic of this is similar to the standard Bertrand competition). This makes the right-hand side of inequality (9) equal to 0. Thus, the condition for the players to use the formal institution becomes Given this, we assume that there is a continuum of players on [0 _,_ 1], who in each discrete time period 22
_t_ = 1 _,_ 2 _, ..._ choose whether to join the formal or informal institution. We make a reduced-form assumption that, given the quantity _dt_ = _ηi_ ( _zg_ ; _τgt_ ) _− ηi_ ( _zg_ ; _τ_ 1), the measure _R_ ( _dt_ ) of players joins the formal institution. We assume that: _R_ (0) = 0 (when the appropriateness of formal and informal institutions is the same everyone joins the informal one) and _R_ () is an increasing function (the more appropriate the formal institution is, relatively to the informal one, the more players join it). The latter assumption is not that unrealistic, as heterogeneity in _φi_ in the population will generate optimal solutions of this sort anyway.

Next, we assume that the more players join the formal institution, the more taxes they pay, so the amount of total tax collected in period _t_ is equal to _Zt_ = _R_ ( _dt_ ) _zg_ . The quantity _Zt_ is spent by the government on public services that influence productivity, or multiplier _p_ in the PG. Suppose that in period _t_ we have productivity _pt_ = _pt−_ 1 + _π_ ( _Zt−_ 1), where _π_ () is an increasing function with _π_ (0) = _−π <_ 0. The idea here is that without constant provision of public services, the productivity can decrease due to depreciation of the existing ones.

Finally, assume that trust in government _τgt_ in period _t_ is related to the amount of public services that it provided in the previous period. When people see that the government is doing what it is supposed to do (provide public services), they start trusting it more. So, _τgt_ = _τgt−_ 1 + _g_ ( _Zt−_ 1), where _g_ ( _Zt−_ 1) = _g_ ̄ _>_ 0 ̄ when _Zt−_ 1 is higher than some fixed threshold _Z_<sup> ̄</sup> and _g_ ( _Zt−_ 1) = _−g <_ 0 otherwise (we proxy the amount of public services by the amount of taxes collected). The idea here is that people’s trust in government increases by a constant when they see that enough public services is provided and decreases otherwise. Thus, we have the system of equations The first two equations determine the joint dynamics of trust _τgt_ , the difference in the appropriateness of the two institutions _dt_ , and other related variables. Growth in represented by the third equation and expressed in terms of productivity of the PG. To understand how this system evolves, notice first that if the government does not pay specific attention to _dt_ , then the situation in the economy will deteriorate with time. Suppose that _d_ 1 = 0, which happens when _τg_ 1 = _τ_ 1, or the trust in the formal and informal institutions is the same. In this case, the informal sector constitutes 100% of the economy, trust in government decreases with time (because no new public services are provided), and productivity deteriorates due to depreciation for the same reason, which leads to negative growth. As time unfolds, the situation will get worse and worse and the economy will get to the state where no public services are provided at all.

If however, we start from a good initial conditions where _d_ 1 is positive enough so that enough people join the formal sector, pay taxes, and _R_ ( _dt_ ) _zg > Z_<sup> ̄</sup> , then the positive feedback loop in the first two equations will start. High tax revenues will generate a lot of public services that will increase trust.

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That in its turn will increase _dt_ even more. This will increase the proportion of the formal sector _R_ ( _dt_ ), which will consequently lead to more taxes and more public services. This in its turn will increase trust even further, etc. On this path, the informal sector will shrink with time and disappear, with all agents choosing the formal sector for their transactions. All this will be accompanied by increasing productivity _pt_ , which will lead to economic growth.

In this model, the opting out of the formal sector happens because taxes are considered too high for the public services that are provided, and trust in government is low. As a result, a vicious cycle of high informality and low trust ensues. According to our dynamic system, a way to start a virtuous cycle would be to create a positive shock to public services provision. If the government could improve public services consistently (for a number of periods), trust _τgt_ will gradually increase. As trust increases, a threshold will be reached at some point after which _dt_ will become positive. At this moment, some players will join the formal sector, which will then be able to increase taxes and provide more public services. This will feed back into growing trust and more people joining the formal sector until at some point we will have _R_ ( _dt_ ) _zg > Z_<sup> ̄</sup> . Once in this positive feedback loop, the economy will be growing, the formal sector will expand, and the informal sector will shrink.

# **6 General Trust Network**

Up to this point, our arguments were built on a micro-level interactions between four agents: players 1 and 2, the informal facilitator _f_ , and the government. The relationship between the two players and the informal facilitator was based on a small trust network (see Figure 2) where nodes represent people and the links are the social weights between them. Also, the roles of the players were fixed: players 1 and 2 were those who tried to cooperate and the informal facilitator always facilitated and did not participate in any cooperative activities. In this section, we expand this idea to a general trust network covering an arbitrary number of agents that can represent the whole economy. In such a general network, moral agents have a choice between cooperation (doing business with each other) or facilitation (collecting rent). We will provide some ideas about what determines the choice of becoming cooperator or facilitator, which will consequently shed some light on the emergence and evolution of informal institutions under various conditions. Then we apply these ideas to understanding the economics of clientelistic networks [Stokes, 2011, Mu ̃noz, 2019].

Suppose that there is a set of players _N_ with connections defined by _cij ∈{_ 0 _,_ 1 _}_ for _i, j ∈ N_ . If _i_ and _j_ “know each other” then _cij_ = _cji_ = 1, else _cij_ = _cji_ = 0. The weights _cij_ describe the “network of friends.” Let us define _nij ∈_ N as the _minimal_ number of links that connect players _i_ and _j_ . If they are direct friends with _cij_ = 1, or _1-friends_ , then _nij_ = 1. If _i_ and _j_ share a friend but themselves are not friends, then they are _2-friends_ with _nij_ = 2, etc.<sup>21</sup> The network described above not only defines the structure of friendship connections but also the levels of trust among them. If two players are 1-friends ( _nij_ = 1) then when they play some game with 21In the previous sections, players 1 and 2 are 2-friends.

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Government <!-- Start of picture text --> 6<br>7<br>τ1 5 9<br>τ1 τ1<br>τ1 τ1 τ1<br>11<br>8 τ1 1 τ1 10<br>4<br>τ1 τ1<br>2 3<br><!-- End of picture text --> Figure 5: An example of a trust network (informal, in black) and the government network (formal, in orange).

each other they use equal social weights _τ_ 1 in their norm-dependent utilities (as in (3)) and trust each other to the degree _τnij_ = _τ_ 1 _∈_ [0 _,_ 1]. In general, we assume that the level of trust is weakly decreasing in _nij_ , so the further away the players are on the network, the less they trust each other. In other words _τ_ 1 _≥ τ_ 2 _≥ τ_ 3 _≥ ..._ This definition takes into account possible “parochial tendencies” of the players [Kimbrough and Vostroknutov, 2022b] when the weights quickly decrease to 0 (e.g., if _τ_ 2 = 0, then players only trust their friends and no one else), but at the same time leaves room for some trust towards strangers _τ >_ 0 when lim _k→∞ τk_ = _τ_ . For convenience, let us define the level of trust between players _i_ and _j_ as _τij_ = _τnij_ and assume that _τii_ = _τ_ 0 _≡_ 1 for all _i ∈ N_ (any player trusts herself at least as much as her 1-friends, _τ_ 0 _≥ τ_ 1). Figure 5 shows an example of a trust network with links (in black) representing 1-friendships.

The trust network is the foundation on which informal institutions are built: as time unfolds, informal facilitation will generate some cooperation between 2-friends (and in more complex settings possibly between 3-friends, etc.). However, formal institutions, or government, are based on a slightly different idea. Government is modeled here as an agent to whom _all_ agents in the economy are connected by a direct link (in orange in Figure 5). This means that—through laws, regulations, and public services— government can act as a facilitator for any two agents, thus overcoming the parochial nature of informal facilitation. This makes formal institutions a potentially much more powerful mechanism for enhancing cooperation and eventually growth.

Given these definitions, we can now think about what makes agents want to cooperate or facilitate on the trust network. Simply from the structure of the network it is clear that some agents are better suited for cooperation and some for facilitation. Consider agent 1 on Figure 5. He is connected to many other agents, who in their turn are only connected to him. Thus, agent 1 is in perfect position for facilitation. He can make a lot of money by simply connecting his friends to each other, who might not be able to cooperate without him due to low trust. At the same time, agents with only one connection 25
cannot be facilitators, because they have only one friend, so they are best suited for cooperation. Thus, it is reasonable to expect that for agents with many friends facilitation will be more profitable than cooperation and vice versa. Well-connected agents will choose facilitation as their primary source of income, whereas agents with few friends will choose cooperation.

Another way to think about who should facilitate and who should cooperate is by imagining that new friendships can be forged at a cost. New friendships create opportunities for facilitation and thus profit, but constitute an investment. Thus, the question is Which agents would be willing to invest in finding new friends? To answer this, notice that in the previous sections we always assumed that players 1 and 2 have high propensities to follow norms _φ_ 1 and _φ_ 2, which made them able to cooperate with each other _in principle_ . Even if the agents do not originally trust each other, they can use facilitation to enter a successful cooperative relationship and make profit. However, experimental estimates of propensities to follow norms [e.g., Kimbrough and Vostroknutov, 2016, 2018] suggest that the distribution of _φ_ ’s is bimodal: around 20% of people have very high _φ_ ’s, around 20% very low _φ_ ’s, and the rest is spread somewhere in between, which is more or less the same across countries (see Figure 10 in Appendix B). This evidence suggests that around 20% of the population with high _φ_ ’s are able to cooperate, thus they might prefer that to investing into finding new friends. The other 20% with low _φ_ ’s are not able to cooperate at all, because in PG or any other social dilemma, they would always free ride. Given this, it is reasonable to think that selfish agents like that would invest in collecting new friends with the purpose of making money through facilitation. This argument suggests that the number of friendship links on a network might not be random, but rather modulated by agents’ propensity to follow norms: selfish agents in trust networks are motivated to invest into new connections with the purpose of facilitation, whereas norm-following agents might prefer to benefit from cooperation.

# **6.1 Clientelistic Networks**

In this section, we use the idea about the motivation of selfish and norm-following agents explained above to understand the nature and purpose of clientelistic networks. The literature on this topic [Stokes, 2011, Acemoglu, 2005] has catalogued many instances of this phenomenon that is reflected in the attempts of businessmen and politicians to “collect” clients through various forms of gifts, bribes, lobbying, public political events, etc. with the purpose of increasing their own power (through votes, increased political influence, rent, etc.). The literature has described the typologies and even network nature of clientelism [Mu ̃noz, 2019]. A new understanding of clientelism proposes that it arises organically to fill in the vacuum created by the weak state [Acemoglu, 2005, Lazar, 2008]. More specifically, Falconi and Robinson [2021] suggest that clientelism and state weakness in Latin America inhibit provision of basic public goods. Raiser [1997] highlights the role of informal institutions in fostering trust in third-party enforcement through the state during transition from a planned to a market economy in Eastern Europe; he describes how, if trust is eroded by persistent fiscal crises, the control over institutional change can be taken over by competing informal agents (”roving bandits”). But the literature stops short of an expla26
nation as to why this is happening, why this phenomenon takes so many different forms, and how to counteract it. The model of trust network and facilitation provides some new ideas in that regard.

One example of a clientelistic network is reported in Falconi and Robinson [2021], where the story of Jhon “Calzones,” a Colombian businessman turned politician, is analyzed. Calzones used his connections to provide public services to (illegal) plots of land, 10 _,_ 000 of which he then sold to the poorest people in the area with a subsidy for constructing a house, before he ran for mayor. Falconi and Robinson note that through his “philanthropic work [Calzones] formed a clientele, a political base, by using his wealth [and connections] to provide services that the Colombian government does not provide, and this allowed him to fill a niche intermediating between the people and the state.” To this day, the people of Yopal, or the ‘Ciudadela la Bendici ́on’ exist as a society independent of the state.

Dramatically, this is not a stand-alone case in Colombia (or several other countries in Latin America). In fact, these arrangements are viewed as a legitimate political process. When the state underprovides public goods, it often legalizes the local elites having emerged in similar way, and distributes resources and jobs through their networks. Other examples of structures parallel to the state exist and are sometimes described by the concept of the ”lettered city” [Lazar, 2008]. In this set-up, clientelism is no longer dismissed as undemocratic or inefficient. On the contrary, it provides a solid alternative to the weak formal political and economic institutions, and can even include competition between patrons for clients, who decide which network to support [Lazar, 2008, Falconi and Robinson, 2021].

The connection to the political system and parallel provision of public goods are important for understanding the nature of clientelistic networks and their impact on institutions. Fergusson et al. [2022] show that tax evasion, as a measure of state weakness, and vote buying, as a measure of clientelism, are highly correlated at individual level. Other studies have drawn parallels between the strength and degree of fragmentation of the political system and the level of clientelism [e.g., Levitsky and Zavaleta, 2016]. In another set of studies, Mu ̃noz [2019] analyzes the political system in Peru, where candidates employ clientelistic strategies in the absence of political machines or other means of bargain enforcement. She stresses that approaches focused on monitoring, reciprocity, and conditional loyalty cannot account for the widespread electoral clientelism. The absence of political machinery, Mun ̃oz claims, gives rise to clientelism as a means of determining candidates viability and election. Similar ideas have been expressed in the context of other countries with better organized political systems, which nevertheless are plagued with clientelism.

One puzzling feature of Peruvian clientelism is that many “facilitators” distribute gifts to populations in various ways seemingly without any means to guarantee that they get something in return (in form of votes or political influence), which puzzled many a political economist [Mu ̃noz, 2019]. Our network model provides an interesting account of this phenomenon. For clients living in remote areas or working in the informal sector, joining a patron network might be the only means to cooperate or “do business,” as they do not have access to formal networks. Figure 6 illustrates.

In such circumstances, selfish agents who are not constrained by the political system try to collect rent by enticing the unconnected individuals with promises of becoming connected to a trust network.

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<!-- Start of picture text --> Government<br>Agents not connected<br>to any trust network 6<br>7<br>8<br>2 τ1 5 9<br>τ1<br>3 4 τ1 τ1 τ1<br>11<br>1<br>10<br><!-- End of picture text --> Figure 6: An example of a network that has agents who are not connected to anything and do not have means to cooperate with others.

At the same time, such individuals desperately want to be connected to any trust network, since they realize that such connections can potentially bring them profitable opportunities for cooperation through facilitation. Thus, both sides of this “market” want something from the other. On the one side we have selfish agents who compete for the connections with poor people. On the other side of the market, we have poor people who want to be connected to some trust networks. As a result, we obtain a situation similar to _perfect competition_ among selfish facilitators, who are ready to do anything to obtain new connections. This competition decreases the price for facilitation services and also makes facilitators seek any new connections even if they cannot guarantee any tangible returns from the clients.

Clientelistic networks express themselves differently in countries where the political system is more established than in Peru (e.g., Brazil or the US). To continue the analogy with market organization, imagine that one clientelistic network manages to create a _monopoly_ in the form of an elite that facilitates cooperation of the whole country. Such a network will create the conditions where people who need to join the trust network have to pay high rents to enter, since there is only one network that they can use (the government is weak and does not provide good facilitation services). At the same time, the network will actively fight any attempts by outside facilitators to lure clients on their own, thus keeping the monopoly power and not allowing more “wild” forms of clientelism as in Peru. In this case, the network can spread to all strata of the society and become entrenched in the political system.

Yet other “market structures” for clientelistic networks are possible. The constant switch of governments from left to right in many Latin American countries can be accounted for as the system with two large clientelistic networks that constantly battle for political power and influence. Such _duopoly_ can have negative consequences for the economy and growth as the two networks have to reorient government organizations towards themselves after each election.

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# **7 Perspective on Historical and Traditional Societies**

The analysis of institutional change and the model presented in this paper have so far assumed that 1) agents have a possibility to walk away from a deal with a facilitator if they do not like it and 2) agents cannot impose _punishment_ for norm violation. These assumptions reflect modern conditions where there is considerable freedom of movement and many economic alternatives available in large, densely populated areas where multiple institutions exist and allow agents the choice between them.

However, in many traditional societies or societies that existed in the past these assumptions do not always hold.<sup>22</sup> Indeed, Acemoglu and Robinson [2020] describe many cases where lives of agents, to use Hobbes’ expression, are “poore, nasty, brutish, and short.” This can happen for many reasons. For example, some societies might be in the state of nature (or Warre) as was the case in the Democratic Republic of Congo in the 1990s or in the Dark Ages of Ancient Greece. Life in small, traditional societies like the Tiv of Nigeria might be very close to subsistence level and heavily depend on social security nets provided by extended kin or tribal affiliates. In such societies, agents cannot walk away from a deal because they have nowhere to go and will die without the support of their clan. The possibility of punishment and control by more powerful agents is very real and constitutes a large part of agents’ incentive structure.

This can also go the other way round. The Red Queen effect [Acemoglu and Robinson, 2020], or the constant state of bargaining between the people and their Leviathan that propels societies to liberty and economic prosperity by keeping them in the Narrow Corridor, critically depends on the ability of the people to impose punishment on their rulers. For example in Athens during Antiquity, people could ostracize their Archons by banishing them from the city for ten years. In reality, this did not actually happen too often. However, the _possibility_ of ostracism incentivized many a ruler to behave in the ways that allowed people more freedoms and thus stimulated the Red Queen effect. The Founding Fathers also (though grudgingly) admitted that the power of the people over government is crucial for maintaining liberty. Thomas Jefferson once asked: “What country can preserve its liberties if their rulers are not warned from time to time that their people preserve the spirit of resistance?” and answered: “Let them take arms.” To incorporate these considerations into our framework and thus to cover historical and traditional institutions in our analysis, we need to introduce one additional ingredient, namely, a _punishment technology_ . As noted by Henrich [2015a], punishment is a mechanism that is necessary to maintain the proper functioning of social norms. Without punishment (under a common assumption that people are selfish to some degree) norms disintegrate and cannot perform their primary function – that of maintaining cooperation and curbing violence. Mathematically, punishment technology can be introduced into our framework using, for example, the model proposed by Kimbrough and Vostroknutov [2023b]. This is straightforward, so we will not go into much detail and will propose only a brief sketch of what the model with punishment can tell us for different choices of other parameters like the propensity to

> 22Examples of such societies also exist today, for example in communities that are remote or in other ways cut off from alternative institutions, such as in gang-controlled neighborhoods, see for example Khanna et al. [2019].

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follow norms _φ_ and the social weights _τ_ .

To describe how punishment technology works, consider a network of agents with trust weights as discussed in Section 6. Suppose that each agent in the network can punish any other agent and that for each agent _i_ there is a cost of punishing any other agent _j_ , denoted by _cij_ . Also, let us assume that _i_ can punish _j_ by some maximal amount _kij_ . For example, some agents are _powerless_ and cannot exert much punishment over other agents (or only subset of other agents). This happens when agents have high _cij_ and/or low _kij_ . Agents can be _powerful_ , because they can punish others due to low _cij_ and/or high _kij_ .

With this simple setup, we can imagine how our framework can incorporate various institutional arrangements singled out by Acemoglu and Robinson [2020]. For example, Warre, the chaotic state of affairs with rampant violence, can be thought of as a network where all agents can be powerful with respect to all other agents and have _φ_ = 0 and _τ_ = 0 (in the most extreme case). In such a world, mostly selfish agents will take away from others what they want by force and without hesitation since norms are non-existent or weak. This is what happens in many African countries where various warring groups (e.g., RCD and Mai-Mai in Congo) attack villagers and fight with each other for resources. Notice that in the world of Warre, the institution for facilitation cannot take hold, because no one trusts anyone else (a prerequisite for facilitation is high trust in facilitator), so facilitation does not emerge spontaneously.

Another interesting case is the _cage of norms_ defined as a (seemingly) non-violent institution in which any attempt at grabbing power or control over others is quickly dealt with with severe punishments. Even though such institutions may sound like a great idea, in reality the extreme norms, traditions, and customs against anyone holding power or “unnecessary” wealth disincentivize independent thinking and make doing any business or accumulation of wealth practically impossible, thus leading to a meager existence of the population.

We can think of such institution as a collection of networks of agents divided by clan affiliation (high _τ_ for the agents in the own clan and low _τ_ for everyone else). Even though agents trust others in their clan, their _φ_ is low, so they are not very keen on following norms in general. However, the cost of punishment is also low for all agents with respect to all other agents, while the losses for those being punished can be very high (all agents are powerful). This leads to a seemingly contradictory situation where agents are mostly selfish (low _φ_ ), but are still willing to punish others for not sharing within a clan (low cost of punishment and high _τ_ for the clan members).

This is the case of the Tiv and their concept of _tsav_ (power). Among the Tiv, any activity that goes beyond growing food for the needs of own family (accumulation of wealth included) can be interpreted by others as witchcraft with the intention to obtain _tsav_ . Punishments can be easily meted upon others by spreading rumors that such and such is a witch (low cost) or secretly urinating on someone’s grain storage (evil spirits are accused of doing it). The losses from being punished can be high because people accused of witchcraft can be banished, suffer violence, or lose their food supplies. As a result, the Tiv always share food when asked by other clan members. But this is done not because they follow some strong norms of caring about others, but rather because they try to avoid punishment being overall selfish (low _φ_ ).

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It is interesting to notice that, within our framework, the cage of norms is almost identical to Warre in terms of parameters. Specifically, the only difference between Warre and the cage of norms is a barely positive _φ_ (so that people realize that norms exist) and high trust to the clan members _τ_ . Thus, our framework suggests how cage of norms could have evolved from Warre. This happens when clans take a more definite shape and promulgate some general idea of reciprocal duties towards other clan members. Notice as well that, similarly to Warre, the institution for facilitation cannot spontaneously emerge in this case either but for a different reason. Facilitation implies that agents who work together accumulate more wealth in the PG game than they would otherwise, which constitutes the violation of the norm against holding too much power (or wealth) and thus can be punished. Even though there is some trust in the system (towards other clan members), the low _φ_ and, more importantly, the norms against accumulation of power prevent facilitation from emerging and preclude the Tiv and other similar societies from increasing their production efficiency and developing markets and other institutions that promote economic growth.

The next example is the Despotic Leviathan. Medieval Arab writer Ibn Khaldun describes the rise and fall of Arab empires after conquest of the territories, roughly corresponding to what is now Middle East, by nomadic, desert tribes of the Bedouin. Khaldun proposed the general pattern of the evolution of these empires starting from the first generation rulers, who still retained cultural and economic connections to the Bedouin, and through second and third generations that lost these connections and turned to despotism passing the stage of some economic growth.

In our framework, the Despotic Leviathan in these stories can be seen as an extractive institution as defined above, where the population cannot escape and has to submit to the rule of the Caliph. However, what is interesting is the economic and institutional progression from the stateless Bedouin setup of tribal allegiance similar to the Tiv (all agents are powerful, low _φ_ , high _τ_ within each tribe) to the orderly imperial power asymmetry where the Caliph is the single supremely powerful agent among the powerless population.

When the Bedouin first created their empires through conquest, they needed to assert some rule over the culturally diverse populations of the conquered territories. This was done by the imposition of (some sort of) unified imperial law that applied on the whole territory together with a common language. The necessities of ruling the Caliphate, the need for taxation, and the laws that maintained this structure created a situation where the institutions for facilitation could and did emerge. Khaldun reports the development of trade within the Caliphates and consequent increase in productivity from the new types of crops brought from the tropics (like rice, sorghum, hard wheat, and coconut palms) together with better investment climate and rise in private enterprise. Despite the fact that culturally the first-generation Bedouin Caliphs remained the same barely norm-following individuals (low _φ_ ) who only answered to their tribe (high _τ_ ), as facilitators for the now vast territory, they did their job well in order to generate profits. They maintained the rule of law and reasonable taxes, which created a good environment for the development of institutions for facilitation. Common language gave people of the empire the ability to cooperate with each other on a broader scale and produce wealth by using the facilitation possibilities 31
for doing business within the new order, which generated economic growth.

However, their second- and third-generation descendants, who never changed their cultural attitudes (low _φ_ ) while losing their affinity with the tribes (now low _τ_ ) needed new alliances to maintain order. Given that they were selfish facilitators with a lot of power to punish, they used it profusely thus suppressing the environment where institutions for facilitation could thrive and destroying the achievements of the previous generation. This led to despotism, decrease in growth, and eventually fall of these empires as Khaldun colorfully depicts. All these observations can be reconciled theoretically within our framework that proposes a perspective on the institutional change that took place in this time period.

Finally, we turn to the Shackled Leviathan, the Red Queen effect, and the story of Solon, the Archon of Athens. When Solon came to power, he inherited the city state in economic crisis that was precipitated by the rich elites who consolidated a lot of power and enserfed many citizens of Athens with the help of then wide-spread _debt peonage_ norms among other standard economic means. These were extractive institutions at their extreme, where agents willing to do business used their own self as a collateral and lost their freedoms when their enterprise did not work out. Debt peonage was a big hurdle on the way of development of institutions for facilitation simply because more and more agents lost their freedom and were forced to do their owner’s bidding instead of exploring business opportunities. On top of that, Athenian society at the time had very little rule of law and economically deprived citizens had no way to protect themselves from the predatory practices of the wealthy elite. This was the hallmark of the Dark Ages of Ancient Greece, the Despotic Leviathan.

In only a single year while Solon was in power, he managed to change the path of Athens with his reforms towards the “shackling” of the Leviathan. He cancelled all peonage debts thus freeing all enserfed citizens, democratized Athenian institutions, which dramatically increased public participation in state affairs, and introduced the _Hubris Law_ that protected everyone including slaves from being assaulted by the wealthy. Anyone now could file a complaint to court that often led to punishments of the perpetrators of _hubris_ , the acts of intimidation.

These measures decreased the influence of the elites and gave citizens of Athens much more power over how to live their lives. In the terminology of our framework, Athens transited from the state with few powerful agents and powerless population to the state where the elites and the population had _power over each other_ (both had means to punish the other side). Moreover, the Hubris Law and the total ban on debt peonage have gradually changed the norms that now required Athenians to respect each other, which can be interpreted as an increase in both _φ_ and _τ_ (towards other Athenians).

As a result, the institutions for facilitation could take off and the economy of Athens started to grow. Solon’s reforms started the Red Queen effect: the new system, though not without troubles, managed to maintain the balance of power between elites and population and with time Athens became a wealthy city state. As we can see from this example, the balance of power and the adjusting norms created the environment where it was not worthwhile for either side to abuse the other. These conditions fit into our model without punishment described in the sections above. Moreover, such balance naturally promulgated the norms of mutual respect among the new citizens who were born into this new order, 32
which increased trust. Thus, the facilitation relationships similar to modern conditions have emerged and developed.

In this section, we connected some examples of institutions in traditional societies and institutional change in historical perspective to our formal framework. A defining feature of these examples (e.g., Arab empires and Athens) is that institutions change mostly without specifically engineered interference. Even though Solon’s reforms in Athens were deliberately directed at shackling the Leviathan, his example is rare in history, and it leaves us with no additional understanding of how to replicate his success in modern societies. However, relating these examples to the model presented in this paper does propose a path to systematic policy that can change this situation. One theory that encompasses both economic and social factors of institutional arrangements like the state of nature, cage of norms, the Despotic, and Shackled Leviathans allows to analyze existing institutions, to estimate model parameters for them (e.g., taxes and trust), and to provide quantitative instruments to guide institutional change into the Narrow Corridor.

# **8 Discussion**

In this paper, we show how introducing an additional motivation to the economic agent—namely, the motivation to cooperate with others that works through the innate desire to adhere to social norms— can give rise to a theory of institution formation and institutional change. Moral agents strive to follow norms and have good cooperative relationships with others, which incentivizes them to seek business opportunities in any economic environment. This implies that when the quality of the government is low and agents are not willing to use its services they will create informal institutions that allow them to cooperate outside the official channels. Various forms of informality ranging from elite capture to “wild” clientelistic networks can emerge depending on the political landscape and current economic situation.

It is important to note that the models presented above are just an illustration of this general approach and do not constitute some final word on how specifically institutions should be modeled. For example, we use the Public Goods game to represent a small business arrangement in which various agents may choose to cooperate with each other or not. However, given the specific context of some country or industry that needs to be modeled, other more tailored games might be used. Also, the way agents change their trust weights towards others in an institution for facilitation can be adapted to specific cases. What we try to present in this paper is the general style of modeling institutions that, similarly to game-theoretic Industrial Organization, can be flexible in treating specific details. Given all this, we believe that our approach contributes to the understanding of institutional change and can help develop new institutional policy.

Although the models of institutions with moral agents can get arbitrarily specific, we think that the value of our framework lies in its ability to model institutional change and to make general predictions about a variety of institutional arrangements. For example, the idea that moral agents choose whether to work in formal or informal sectors, and do so depending on the two institutions’ comparative economic 33
and normative characteristics, shows how easily standard economic policy can go awry. Imagine that the government decides to increase taxes expecting more tax revenue. However, in reality the revenues might fall because after the tax increase agents may leave the formal institution and join the informal one. This process will take place regardless of the specifics of the informal institutions. This example shows that taking institutions into account in a structural way within the model can have tangible and important policy implications.

Another important lesson to be learned from our framework is that moral agents, who have two motivations (selfish and moral), can be heterogeneous in how they mix them.<sup>23</sup> Some agents may be very selfish and disregard the norms, whereas others may be extremely norm-abiding. This fact implies that a policy may have differential effect on different agents and can fail because not all of them react to it in the desired way. For example, introducing a lower speed limit on a highway might make normabiding agents drive slower, which will decrease their utility. However, it may not decrease the number of accidents, because selfish agents who do not follow rules will keep driving very fast regardless of the change in the speed limit. This shows how a seemingly benign policy can have adverse effects in the world with moral agents. Our framework can be used to take situations like this into account.

The value of the model with endogenous institutions for applications, as well as empirical and policy work lies in the possibility to calibrate it to specific country or circumstances, existing interest groups, etc. For example, the version of the model as it is presented in this paper can be calibrated to a case of specific country where the estimates for trust weights ( _τ_ ), propensities to follow norms ( _φ_ ); choice context; and actual rents to facilitators can be obtained from surveys. Then, conclusions can be drawn regarding the “fairness” of the institutions, or how extractive they are, as well as on the effectiveness of specific policies. For example, having estimated the parameters pertaining to moral agents, it would be possible to say how effective a policy to increase tax rate would be in increasing revenue: it would be possible to estimate how many agents will leave for the informal sector, thus providing estimates for the revenue reduction through this channel.

On a final note, we would like to point out that our framework can be used not only for studying “current” institutional change in a given country, but also for understanding the broader historical processes of economic development that start with the emergence of informal institutions in the original state of nature, then proceed to more complex institutions like tribes, and finally lead to the formation of larger arrangements like kingdoms or states. Indeed, in the current version of the model we assume, for example, that government simply exists. However, we do not explicitly describe how it came to be. We believe that this is possible. The versatility of our framework that can be essentially seen as an upgrade of game theory with norms should in principle allow to model institutions of any complexity.

23Notice that this problem does not arise in the neoclassical world where agents have only one motivation.

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# **9 Conclusion**

In this paper, we propose a new framework to model institutions and institutional change based on Acemoglu and Robinson [2020] and the theory of norms by Kimbrough and Vostroknutov [2022a]. We show how moral agents, who care about following social norms and thus strive to cooperate with others, can form institutions that facilitate cooperation. Similarly to game-theoretic Industrial Organization, the framework allows to model informal as well as formal institutions as games played by moral agents. It is possible to conceptualize institutions as inclusive or extractive and model institutional change as a consequence of choice of moral agents among available institutions as time unfolds. We demonstrate how the framework can be used to understand the origins of informal institutions. With a series of examples of clientelistic networks, we show that our framework can be useful for understanding how and why such networks form and persist.

While in the paper we show how our framework is able to account for some interesting phenomena related to institutions in developing countries, these models are just mere illustrations of the full power of the framework that can be used to model any interactions among moral agents, thus giving rise to a wide variety of possible institutional settings. This opens new possibilities to model institutional change; devise new types of policies that take into account normative considerations of the agents; and understand informal and formal institutions in greater detail.

We use the example of clientelistic networks to show how the framework can be applied to specific types of institutions. In principle, one direction for future research could be to create more specific and applied models of clientelistic networks or other types of institutions. However, we believe that the power of the framework lies in its ability to produce general conclusions about broader classes of institutions. For that, more theoretical research is needed that could explore the general game-theoretic properties of institutions with moral agents.

Another important direction for future research is to make the framework more practical; to test it with real or experimental/survey data; and to see how to calibrate the model’s parameters from surveys or specifically designed tasks. In the next step, policy implications can be considered and estimated, and cost-benefit analysis of impact could be performed. We believe that with a developed applied methodology, our framework can become an indispensable tool for studying institutions, conducting economic policy, and suggesting paths to economic prosperity.

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