Generalized trust and wealth

International Review of Law and Economics 29 (2009) 46–56

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International Review of Law and Economics

Generalized trust and wealth Mehmet Bac Faculty of Arts and Social Sciences, Sabanci University, Orhanli, Tuzla, Istanbul 34956, Turkey

a r t i c l e

i n f o

JEL classification: Z13 D30 D82 Keywords: Trust Incomplete information Inequality Wealth Enforcement

a b s t r a c t The relation between economic inequality and trust is studied in a model where the ability to elicit trustworthiness from unrelated people depends on own wealth as well as the distribution and mean of population wealth. In equilibrium, the rich trust but betray while the poor do not trust but are trustworthy. Homogenizing wealth around its mean leads to a zero-trust outcome if mean wealth is sufficiently low, to full trust if mean wealth is large. More effective enforcement technologies increase, more effective counter-enforcement technologies decrease trust. Economic inequality reinforces itself through the trust and betray incentives it induces, suggesting a beneficial role for redistributive policies. © 2008 Elsevier Inc. All rights reserved.

1. Introduction The decision to trust people we do not know, though difficult and risky, is often necessary to generate value or initiate a transaction. We may lend money to a stranger in urgent need, not call the police in a minor traffic accident and rather exchange cards to fix the damages later, pay in the internet a seller we do not know much about for subsequent delivery, or trust a doctor we did not visit before. This trust in people we do not know, our expectation that they will behave honestly, responsibly and uphold their implicit or explicit promises is termed generalized trust.1 A recent, growing literature studies the determinants and consequences of generalized trust.2 Experimental and survey data show that trust has all the positive social and economic effects: Societies with higher levels of generalized trust are found to have higher civic engagement and participation rates, more effective government, less corruption and more redistributive policies.3 Trust significantly

E-mail address: [email protected]. Uslaner (2002) defines generalized trust as “a kind of trust that is not grounded in experience and links us to people we may not know.” Average societal trust and spontaneous sociability are sometimes used as alternative labels for generalized trust. Generalized trust is considered one of the most important determinants of social capital (e.g. Coleman, 1990; Putnam, 1993; Durlauf, 2002). A widely used measure for generalized trust is generated from the World Values Survey, as the percentage of subjects who answer “most people can be trusted” to the question “generally speaking, would you say that most people can be trusted or that you can’t be too careful?” 2 Ben-Ner and Putterman (2002) is an overview of the literature with special emphasis on trust in electronic commerce. 3 See La Porta, Lopez-de-Silane, Shleifer, and Vishny (1997) on the positive effect of trust on corruption and judicial efficiency. Uslaner (2002), Alesina and La Ferrara 1

0144-8188/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.irle.2008.07.008

affects economic growth.4 As for the determinants of generalized trust, the literature provides a long list of variables and identifies economic (income and/or wealth) inequality as most important and significant. Many authors, including Putnam (1993) and Fukuyama (1995), suggest that increasingly unequal income and wealth distributions are to blame for the fall in generalized trust and social capital; Uslaner (2002), for example, reports that trust in the US has dropped to 41 percent in 1999 from 47 percent in 1960 while the Gini index of economic inequality fell by 25 percent in the same period.5 A theory often expressed in academic and popular fora is that people trust if they have more in common or feel “less distant” from each other. According to this theory, economic inequality would erode trust by contributing to the distance between people, directly by inducing the feeling that they have less in common, or indirectly by promoting different cultures, attitudes, educational and social segregation. This paper develops a formal model of trust with the objective to unbox a different mechanism through which economic inequality and generalized trust affect each other. Motivations for trust include cultural factors, recurrence of interactions and reputation building, sex, ethnicity, past experience, religion, discrimination and may be shaped by the organization of economic and social activities. Recent experiments in neuroeconomics even establish a link between trusting behavior and oxytocin hormone, supporting the view that trust is not purely

(2002) and more recently Guiso, Sapienza, and Zingales (2005) identify and test for many correlates of trust. 4 See Fukuyama (1995), Putnam (1993), Knack and Keefer (1997), Zak and Knack (2001). 5 Fukuyama (1995) also reports a fall in generalized trust in the US, from 44.3 percent in 1980 to 38.4 percent in 1990, referring to General Social Survey data.

M. Bac / International Review of Law and Economics 29 (2009) 46–56

calculative.6 The calculative basis of trust comes from our trust in our ability to elicit performance, or our confidence in enforcing unkept promises. In the words of an organization scholar, Kieser (2001)), “calculative trust is based on one’s subjective estimates of the probability that others will reciprocate one’s own willingness to cooperate. [. . .] Trust is increased to the degree that deterrent and rewards are perceived as powerful, clear, and likely to occur if trust is violated.”7 Our confidence in eliciting performance or enforcing unkept promises is by and large determined by our relative economic power, wealth or income. The parties to a trust-based relation may eventually need resources, the beneficiary to elicit performance if trust is betrayed, the betraying trustee to countervail the beneficiary’s enforcement activities. These activities may range from litigation to private means of enforcement and, where the rule of law is rather weak, includes even extreme illegal methods such as paying gangsters to collect unpaid debt or exercise threats.8 I study a model of a large economy where agents are homogeneous in every respect but their wealth. In contrast with extant models of trust-based relations, there is no differential inherent proclivity for trust or trustworthiness, nor do preferences display any propensity to trust as a function of some measure of “distance” or observable difference from others. Wealth is private information. Pairs of agents are randomly matched, where one agent, called the beneficiary, decides on whether to trust his partner for future delivery of a surplus. The trustee then delivers the surplus, or betrays and initiates a sequential enforcement game. In this game the beneficiary first tries to enforce the promise by expending resources. If the beneficiary is successful, the trustee takes turn to devote resources to neutralize the outcome and keep witholding the promised surplus. If this counter-enforcement activity fails, the trustee incurs a loss and delivers the surplus. Otherwise the trustee reaps a fraction of the surplus and the game ends. The perfect Bayesian equilibrium of this game displays differential trust and trustworthiness as a function of own wealth and wealth distribution. In a world in which agents are all identical except for their wealth, under a sufficiently dispersed wealth distribution the set of trusting agents covers the upper tail, while the set of trustworthy agents covers the lower tail of the wealth distribution. Wealthy agents are able to devote large resources to enforce broken promises and therefore trust in equilibrium. They are likely to betray trust because they can stand strong against their partners’ enforcement efforts. The relatively poor are trustworthy because they lack the resources to countervail potential enforcement activities by their trusting partners. They do not trust for they lack the power to enforce promises. In this context, where wealth determines the ability to cheat or enforce promises, the impact of a wealth redistribution on equi-

6 See in particular Kosfeld, Heinrichs, Zak, Fischbacher, and Fehr (2005) and Zak, Kurzban, and Matzner (2005) for these experimental results, and Zak (2004) for a general overview of neuroeconomics. Noteboom (2002) and Williamson (1996) offer arguments in favor of non-calculative type of trust. Williamson notes that we may calculatively limit our calculativeness to “maintain atmosphere” or because we prefer to interact without a too detailed metering of profit and loss, whereas completely non-calculative trust is perhaps confined to our relationships with friends and family members. 7 It is this calculative behavior – a careful evaluation of the possibility that trust is abused – that leads 60 percent of adults with internet access in the United States not to do business online and 86 percent of those who do, to express concerns about providing personal information. (GartnerG2 survey, reported in Ben-Ner and Putterman (2002)). 8 News of mafia specialized in debt collection often appear in the media, especially in developing countries, involving the use of guns and threats. Enforcement of promises or contracts is a fundamental necessity. When the state fails to supply enforcement, private provision emerges as noted by Gambetta (1993) for the case of Sicily, Varese (1994) for the case of Russia.

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librium trust and trustworthiness depends on the enforcement technologies, the initial level of trust and trustworthiness in the economy and whom we take wealth from and whom we give. An agent who finds his wealth increased would become more trusting and less trustworthy, given trust and trustworthiness choices of all other agents. But redistribution of wealth will also affect others’ choices; if the enriched agents switch to betraying as trustees, others’ trust will be negatively affected and as a result overall trust may fall. A special, mean-preserving, type of redistribution provides a useful benchmark and yields clear results, depending critically on the level of mean wealth. I show that homogenizing wealth around its mean in an economy with sufficiently low per-capita wealth transforms it into a zero-trust economy. Low and equal wealth for all means none or negligible enforcement power, thus, high vulnerability from trusting others, which eliminates trust. Full wealth equality generates a full-trust equilibrium if mean wealth is large, unless counter-enforcement is much more effective than enforcement. But this qualification should not be overstressed because enforcement is in part publicly provided through the legal system, and international evidence suggests a strong correlation between effectiveness of law enforcement and per capita wealth. Thus, a fall in economic inequality should increase trust in wealthy Western economies with powerful public and private enforcement capabilities. Increased economic equality without growth can lead to opposite effects in poor countries. The model also shows that economic inequality and low trust feed each other. When the wealth distribution is dispersed and economic inequality is high, the poor do not trust, hence, stagnate or experience small increases in wealth whereas the rich trust and, despite the possibility of betray and waste of resources on unproductive enforcement activities, accumulate wealth. Wealth inequality is then aggravated by induced trust behavior. Redistributive policies have the potentially beneficial role of indirectly stimulating trust and economic activity by neutralizing the negative feedback from induced trust strategies to distribution of wealth. Formal models of trust are diverse and reflect the multitude of contexts and corresponding motivations behind trust, ranging from simple prisoner’s dilemma and stag hunt representations of trust-based bilateral relations to more elaborate dynamic models of preference formation or reputation building. A notable recent contribution is Bohnet, Frey, and Huck (2001) who use a similar stage game where the beneficiary tries enforcement by litigating in case of breach with exogeneously specified payoffs. They show that a more trustworthy preference structure may lead to larger individual payoffs for intermediate levels of law enforcement. Ullmann-Margalit (2002) views trust games people play with two possible structures as a prisoner’s dilemma or a stag hunt game. Berg, Dickhaut, and McCabe (1995) and Burnham, McCabe, and Smith (1999) provide analyses of several trust games. The payoff structure in this paper is determined by the parties’ enforcement strategies and privately known wealth. More to the point of this paper is Zak and Knack (2001), where beneficiaries devote time, called diligence, for inspecting betrayal through an external authority. In the present paper, individuals use their own resources to extract performance as well as countervailing enforcement. Though their general equilibrium setup incorporates a rich set of variables affecting trust, Zak and Knack do not allow trustees to countervail diligence. A reduction in income inequality implies a rise in trust because under their assumptions the trust response of the poor to a change in income is larger than the (opposite) trust response of the rich. More precisely, decreasing the wage of a high-wage person and increasing the wage of a low-wage person by the same amount decreases the latter’s diligence (increases trust) more than it increases the former’s diligence (decreases trust) so that overall, diligence falls and trust rises. Increases in income and wealth have

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opposite effects on diligence in their setup: while a large income implies a large opportunity cost of diligence in the form of foregone earnings, no such trade-off exists for wealth. Wealth affects trust not because it can “buy” the time spent on diligence, but indirectly, because wealth affects negatively the marginal utility of consumption, thereby the opportunity cost of foregone earnings through diligence. This is why an increase in wealth leads to a rise in diligence (fall in trust), whereas an increase in income leads to a fall in diligence (rise in trust) in their setup. Zak and Knack provide no proposition about the relation between wealth distribution and generalized trust.9 The next section presents a game of trust which pairs of agents play in a large economy. The equilibrium trust and betray strategies are characterized in Section 3. Sections 4 and 5 study the links between (level and distribution of) wealth and generalized trust. Section 6 summarizes the results and presents several lines along which the model can be extended. 2. A model of trust and enforcement Consider a large economy where possible wealth levels are W = {w1 , . . . , wz }, indexed in order of size, 0 < w1 < w2 < · · · < wz .10 The number of agents  holding wealth wk is mk ≥ 0 and the population size is M = mk . Wealth is private information. Agents match randomly and form pairs where one agent takes the position of “trustee” and the other takes the position of “beneficiary”. Positions are also randomly determined; each agent is equally likely to assume the role of trustee. A portion of the game played by a pair of agents is depicted in Fig. 1. The game begins with a binary choice by the beneficiary, denoted ti = 1 for trusting, ti = 0 for not trusting. A mixed strategy ti ∈ (0, 1) is also allowed. If the beneficiary does not trust, the pair is dissolved and the parties earn as payoff their respective wealth. If the beneficiary trusts, he incurs a cost x > 0. In the analysis I assume that x is a resource transfer to the trustee; note for now that this assumption can be dispensed with, depending on the context and interpretation, as I discuss below. Let i = prob(beneficiary has wealth wi |beneficiary trusts) denote the trustee’s beliefs about the trusting beneficiary’s wealth. The trustee makes a binary choice given her beliefs {i }, setting j = 1 if she betrays, j = 0 if she does not betray. Mixed betray strategy j ∈ (0, 1) is allowed. If the trustee does not betray trust and performs, the beneficiary gets a surplus of size S > 0 and the game ends.11 I assume that S > x. If the trustee betrays, the game extends to the enforcement phase. Given his revised beliefs j = prob(trustee has wealth wj |trustee betrays), the beneficiary moves to determine RE , the amount of resources he devotes to enforcement in the form of expenditures on threats, monitoring and investigating the most effective way of putting pressure on the trustee to perform. The beneficiary succeeds, meaning that he is in a position to secure performance, with probability p(RE ). This outcome is denoted pˆ = 1. With probability 1 − p(RE ) the enforcement activity definitely fails. This outcome is denoted pˆ = 0. The betraying trustee acts if pˆ = 1 to determine RC , the resources she devotes to countervail enforcement. With probability q(RC )

9 In fact, under their assumptions, the opposing effects of wealth and income on beneficiaries’ diligence suggests their model implies a positive correlation between wealth inequality and trust. 10 Alternatively wk could be labeled “endowment”, or “resource.” 11 A performing trustee could also get a share from the surplus S or a fixed positive payoff from performing. The results will all go through as long as this surplus share or payoff is not too large to make betraying a strictly dominated option.

she is able to neutralize the beneficiary’s enforcement activity and reaps an extra payoff consisting of a fraction ˛ ∈ (0, 1] of the net surplus S she owes the beneficiary. With probability 1 − q(RC ) the trustee fails. She is then forced to perform, yields the surplus S to the beneficiary and incurs a loss  > 0 herself. Thus, the enforcement game has two potential outcomes. The beneficiary secures performance with probability p(RE )(1 − q(RC )) and fails with probability 1 − p(RE )(1 − q(RC )). The probability functions p(.) and q(.) are strictly concave, increasing, with p (0) = q (0) = ∞. Agents are not allowed to spend beyond their net wealth in the enforcement game. Therefore RE and RC are bounded above by net holdings at the beginning of the enforcement game, implying wi − x − REi ≥ 0 and wj + x − RCj ≥ 0 for all i and j. The model thus aims to capture the essential features of an environment where individuals can potentially generate value by matching to trade with others. In the absence or impossibility of public enforcement delivery of the promised surplus can only be enforced by the beneficiary. The betraying trustee can respond to this activity by devoting resources of her own, called counterenforcement. If promises or the terms of trust are contractible and potentially enforceable by courts, in case of breach the parties need to spend resources and adjudicate conflicting claims. Under this interpretation of the enforcement game, given litigation expenditures RE , with probability 1 − p(RE ) the beneficiary fails to bring a successful charge and the case is dismissed. With probability p(RE ) the beneficiary succeeds to shift the burden of proof on the trustee, who as defendant now must raise sufficient doubts about the plaintiff’s claim or face punishment. The trustee succeeds with probability q(RC ) given the resources RC she devotes to this effect. If the trustee fails, she has to deliver performance and incurs a loss or penalty .12 Obviously private and public enforcement may be combined and used to complement each other. Broadly interpreted, the enforcement game can capture a wide range of enforcement mechanisms. Terminal payoffs are as follows. If the beneficiary trusts and the trustee performs, the trustee and the beneficiary respectively obtain uPj = wj + x,

vPi = wi − x + S.

When the beneficiary trusts, is betrayed, but the outcome of enforcement is failure, the parties’ payoffs are uNF = wj + x − pˆ RCj + ˛S, j

vNF = wi − x − REi . i

, that is, if the beneficiary’s enforcement is Note that if pˆ = 0 in uNF j observed to fail, the trustee does not have to expend RCj . Finally, if the beneficiary succeeds and secures the promised surplus, final payoffs are uNS = wj + x − RCj − , j

vNS = wi − x − REi + S. i

Clearly, the trustee will perform if she expects a high probability of successful enforcement and/or a low probability of counterenforcement. The parties’ resources in the enforcement game will affect these probabilities and thus, climbing up in the extensive form of the game, trustees’ decisions to betray and beneficiaries’ decisions to trust. The expected payoff from trust and betray will then depend directly on own wealth and, indirectly, on the mean and distribution of wealth. Modeling trust as the choice of one party, rather than both, simplifies the analysis. Allowing for bilateral trust decisions followed

12 The penalty  can be a damage that the trustee pays the beneficiary and the payoffs can be modified accordingly. The qualitative results will not be affected.

M. Bac / International Review of Law and Economics 29 (2009) 46–56

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Fig. 1. The trust game played by a pair of agents.

by an enforcement game if one or both agents betray should not modify the conclusions on the relation between trust and wealth. The amount x > 0 the trusting beneficiary transfers to the trustee has many interpretations. I exclude situations where the beneficiary can trust without “investing trust”; if x = 0, trusting is riskless, costless, and thus a weakly dominant strategy which all agents would adopt. A positive x could represent a minimum payment required to engage the trustee, possibly to cover a cost that the trustee will incur later in fulfilling the promise.13 The legal term for

13 One could endogenize x to arise from a bargaining outcome or make x and S depend on the wealth level of the trustees (low-wealth groups may have lowerpriced goods or services to offer). In Section 6 I discuss the impact of allowing for multiple surplus sizes among which the parties can choose for their relationship.

x is “consideration” for the promise. Another interpretation of x is the beneficiary’s (buyer) specific investment or reliance, without which performance (trade) yields no surplus. The only difference in payoffs under this interpretation is that x no longer accrues to the trustee (seller). Or, x could be the money the trustee borrows to invest in a project. Then S > x would be the amount, interest plus principal, that the trustee owes the beneficiary. While the model and the payoffs can easily be adapted to accommodate these modifications, it may not fit perfectly to other contexts in which trust is invested. One such context is trust in related people or in those revealed trustworthy from past experience. The model deliberately shies away from introducing connections and past trust experience to focus on generalized trust which, by a rough definition, is trust in people agents do not know. Also, the model is a one-shot matching game of a

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large economy and thus leaves no room for reputation building. The impact of a longer horizon for matched pairs of agents, however, is predictable: the possibility of learning about preferences and reciprocating trust can only enhance incentives to trust and perform. Beneficiaries’ trust and enforcement strategies, and trustees’ betray and counter-enforcement strategies, along with corresponding belief systems, must form a perfect Bayesian equilibrium. I focus on equilibria in which agents holding the same wealth adopt symmetric strategies and hitherto refer to an agent with wealth wi simply as agent i. 3. Equilibrium of the trust game Given a configuration of trust and betray strategies {s} = {{ti }, {j }}, let T{s} denote the set of agents who put positive probability on trusting and let B{s} denote the set of agents who put positive probability on betraying if trusted. There are two ways in which generalized trust can be defined in this model. The first is given by  ti mi /M, the proportion of trusting agents in the popT = i∈T {s}

ulation. The second is B = 1 −



j ∈ B{s}

j mj /M, the proportion of

performing agents as trustees. Though the first measure T seems a direct and obvious definition, the second measure B captures trustworthiness and offers a better fit to measures of generalized trust derived from survey data such as the World Values Survey. Agents who believe it very likely that they will be betrayed but trust because they have the power to extract the promised surplus would be included in T but not B . If such a person is asked the typical trust survey question, he or she would probably not give a positive answer, therefore, should not be counted as a trusting person. Though the expectation that a trustee will deliver the promise is better captured by the measure B of agents who do not betray trust, the two measures are highly correlated in equilibrium, as I show below. In particular, if in equilibrium every trustee performs (B = 1), then every beneficiary trusts (T = 1). Because trust is a decision based on rational expectations, the measure of trusting beneficiaries is proportional to the measure of performing trustees. The results presented below hold for both measures of trust. Consider the enforcement game where beneficiary i’s enforcement proves successful, i.e. pˆ = 1. Now trustee j moves to determine ∗ , maximizing RCj uN = wj + x − RC − (1 − q(RC )) + q(RC )˛S j

tion, to maximize

vNi = wi − x − REi + p(REi )(1 −



∗ j q(RCj ))S

j ∈ B{s} ∗ }) subject to the wealth constraint wi − x − REi ≥ 0. Define R¯ E ({RCj  ∗ ∗  ¯ j q(RCj ))S = 1 as the “interior through p (RE ({RCj }))(1 − j∈B {s}

optimum” enforcement level, ignoring the wealth constraint. ∗ }) is strictly decreasing in expected counterNote that R¯ E ({RCj enforcement probability



j ∈ B{s}

∗ ), which implies that the j q(RCj

beneficiary will reduce R¯ Ei (.) if the trustees more aggressively resist enforcement by devoting larger resources RCj . Therefore R¯ E is smallest possible when the beneficiary is sure that wj > wk , that is, when he believes he faces an unconstrained trustee with largest counterenforcement strategy R¯ C . If the wealth distribution is sufficiently dispersed, there will be beneficiaries of lowest wealth w1 who are ∗ while the beneficiary z with largest constrained in determining RE1 wealth is always unconstrained:14 w1 − x − R¯ E (R¯ C∗ ) < 0

and

wz − x − R¯ E (w1 − x) > 0.

Then, given a belief system {j } for the beneficiaries, a wealth level ∗ }) and w wn({j }) exists such that wn({j }) − x ≤ R¯ E ({RCj n+1({j }) − x > ¯RE ({R∗ }): Beneficiary i is constrained if wi ≤ wn({ }) , unconstrained Cj

j

otherwise. Therefore



∗ ∗ REi ({RCj }) =

∗ }) R¯ Ei ({RCj

wi + x

if

if

i > n({j }),

(2)

i ≤ n({j }).

The optimal enforcement strategies in (2) are unique by strict concavity of the success probability function p(.). Thus, given a belief system {j } for the beneficiaries, the enforcement game ∗ }, {R∗ }}. The sucadmits a unique continuation equilibrium {{REi Cj cessful enforcement probabilities generated by these strategies ∗ ({R∗ })) < · · · < p(R∗ ∗ })) < in order of wealth are p(RE1 ({RCj En({ }) Cj j

∗ ∗ })) = · · · = p(R∗ ({R∗ })): Beneficiaries with larger p(RE(n({ ({RCj Ez })+1) Cj j

wealth are more likely to succeed in enforcing promises. Going one step backward in the extensive form, given a belief system {i } about the trusting beneficiaries’ wealth levels and enforcement strategies {REi }, trustee j betrays if the corresponding expected payoff is larger than the sure payoff she gets from performing, wj + x. That is, the sequentially rational strategy of the trustee is to set j = 1 and betray if

subject to wj + x − RC ≥ 0. It is useful to define R¯ C through q (R¯ C )( + ˛S) = 1, the first-order condition for an interior optimum. In most of the analysis below I assume that the wealth distribution is sufficiently dispersed so that

∗ j ({i }, {REi }, RCj )

w1 + x < R¯ C

The function j (.,.,.) is decreasing, so that the trustee is less likely to betray, if REi are large given beliefs, or if the trustee believes it more likely that her beneficiary has large wealth and so will choose a large REi . Obviously a larger surplus ˛S or a smaller cost  from enforcement of betrayed promises enhances incentives to betray. Let prob( = 1) be i’s belief about how likely his trust will be betrayed. In equilibrium these beliefs must be consistent with the trustee’s incentives and future behavior in the potential enforcement game.15 Beneficiary i trusts if the corresponding net expected payoff is positive given {j } and thus a belief system {j } generated

and

wz + x > R¯ C .

That is, the most wealthy in this economy are not, whereas the ∗ . Then a wealth level most poor are, constrained in determining RCj ¯ wk must exist such that wk + x ≤ RC and wk+1 + x > R¯ C . The optimal strategy of trustee j is then



∗ RCj =

R¯ C if j > k, wj + x if j ≤ k.

(1)

∗ are unique. These counter-enforcement strategies Note that RCj ∗ ) < · · · < q(R∗ ) < q(R∗ generate success probabilities q(RC1 )= Ck C(k+1) ∗ ). · · · = q(RCz Consider now the betrayed beneficiary i with revised belief system {j } about the trustee’s type (wealth). This trustee will determine his enforcement strategy REi under incomplete informa-

= ˛S −



∗ ∗ i p(REi )[RCj + (1 − q(RCj ))( + ˛S)] ≥ 0.

(3)

i

∗ 14 More precisely, REz = R¯ E (.) and thus beneficiary z is unconstrained even when he is sure to face a betraying trustee with wealth w1 and thus with smallest counter∗ = w1 − x. enforcement resource RC1 15 The beneficiary computes the probability that his partner will betray, given a

M. Bac / International Review of Law and Economics 29 (2009) 46–56

by {j }: ∗ ∗ i ({j }, {j }, {REi }, {RCj }) = prob( = 0)S − x − prob( = 1)

⎡

× ⎣REi −p(REi )(1 −



⎤

∗ j q(RCj ))S ⎦ ≥ 0.

j ∈ B{s}

(4) The last term in squared brackets represents the loss the beneficiary expects to incur if trust is betrayed, given by the cost of enforcement resources minus the corresponding expected benefit. An equilibrium of the trust game can now be defined ∗ }, {R∗ }}, a collection of trust and as {{ti∗ }, {i∗ }, {i∗ }, {∗i }, {REi Cj

betray/perform strategies for each agent i = 1, 2, . . . , z, belief systems for beneficiaries and trustees, plus a collection of enforcement and counter-enforcement strategies in the enforcement game such that strategies in each matched pair are sequentially rational given beliefs and beliefs are derived from the strategies, whenever possible, using Bayes’ rule. An economy with sufficiently dispersed wealth distribution has an equilibrium in which only a subset of agents trust. I call “hybrid” equilibria those in which agents expect to be trusted with positive probability less than one and a trusting beneficiary expects to be betrayed with positive probability. Note that in hybrid equilibria beliefs {∗j } and {i∗ } can always be computed applying Bayes’ rule. The following proposition characterizes the sets T{s∗ } and B{s∗ } and highlights some properties of hybrid equilibria.16 Proposition 1. (a) In any equilibrium the set T{s∗ } of trusting agents is connected. That is, if agents i and j, where i < j, trust, an agent poorer than j and richer than i also trusts. B{s∗ } , the set of agents betraying trust, is also connected in the same sense. Moreover, j ∈ B{s∗ } ⇒ j + 1 ∈ B{s∗ } and i ∈ T{s∗ } ⇒ i + 1 ∈ T{s∗ } . (b) In a hybrid equilibrium where B{s∗ } a nd T{s∗ } include at least one constrained type of agent, (i) at most one beneficiary type randomizes between trusting and not trusting, and at most one trustee type randomizes between betraying and not betraying; (ii) all unconstrained beneficiaries i > n({j }) trust; (iii) all unconstrained trustees j > k betray. Proof. (a) Fix a set B of betraying agents and suppose ∗ }, {R∗ }) ≥ 0, so that agent i sets t ∗ > 0 as benei ({j }, {j }, {REi Cj i

strategy profile for the trustees, as prob( = 1) =

1 m1 + · · · + i (mi − 1) + · · ·z mz , m1 + · · · + (mi − 1) + · · · + mz

which incorporates the fact that there is one less agent of wealth wi to match with a trustee of wealth wi . 16 As in Huang and Wu (1994), the trust game considered here may have sunspot equilibria in which no agent trusts, based on the belief that all trusted agents will betray. Such equilibria can be ruled out if the wealth distribution is sufficiently dispersed, where agents with sufficiently large wealth and enforcement power will deviate to trusting even if they believe their trust will be betrayed with probability one. The conditions ruling out full-trust and zero-trust equilibria can be derived, using (4). A strategy configuration where all agents set t = 1 does not form an equilibrium if the agents with wealth w1 would deviate to t1 = 0, that is, if (4) fails for i = 1 given a positive probability of betray. On the other hand, the best candidates for a deviation from a zero-trust outcome are the unconstrained agents with wealth wj > wn ; if these agents do not deviate, no other agent will. Thus, a configuration of trust and betray strategies where all agents trust is not an equilibrium if (4) holds for agents with wealth wj > wn .

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∗ ∗ , ficiary. For a beneficiary with wealth wi+1 , we have RE(i+1) ≥ REi ∗ ∗ ∗ ∗ hence i+1 ({j }, {j }, {RE(i+1) }, {RCj }) ≥ i ({j }, {j }, {REi }, {RCj }), with strict inequality holding if beneficiary i is constrained, ∗ 0 if j∗ > 0 is established similarly, using ∗ ∗ implies  ∗ the fact that RC(j+1) ≥ RCj j+1 ({i }, {REi }, RC(j+1) ) ≥

∗ ). Therefore the sets T ∗ and B ∗ must each j ({i }, {REi }, RCj {s } {s } be connected in the sense stated in the proposition. (b) Parts (ii) and (iii) follow from the definition of a hybrid equilibrium and the fact that the net surplus j from betraying ∗ while the net surplus  from trusting is is increasing in RCj i ∗ increasing in REi . For part (i), note that a mixed betray strategy  ∈ (0, 1) can be optimal only if j = 0. If B{s∗ } includes two or more constrained types of agent, j = 0 can hold for only one of these types, which is the type with smallest wealth. Similarly, because i is increasing in REi , there can be at most one constrained beneficiary type i with i = 0. 

The sizes of T{s∗ } and B{s∗ } depend on the model parameters and functional forms of p(.) and q(.). In a hybrid equilibrium there will be agents who neither trust nor betray people they do not know; these agents are relatively poor. In contrast, the wealthy agents will both trust and betray people they do not know. There may also be agents of a third type who either trust and does not betray (the case T{s∗ } larger than B{s∗ } ) or do not trust and betray (the opposite case). Such agents belong to the middle wealth class. Trusting and betraying agents belong to the most wealthy group because they can devote relatively large resources on enforcement and counterenforcement. The presence of trusting, relatively low-wealth agents with constrained enforcement strategies makes wealthy agents more inclined to betray. Moderately low wealth agents may also trust in equilibrium if they expect a sufficiently large mass of trustworthy agents. Equilibrium trust and betray decisions thus depend, through the outcome of the enforcement game if trust is betrayed, on own wealth and the distribution of wealth in the economy. 4. From wealth to trust World Values Survey data (or the discussion in Zak, 2003, for instance) shows that trust and per capita wealth are correlated. Norway, Sweden, Canada and Germany display larger trust levels than Argentina, Brazil, Philippines and Turkey, whereas a country like France, where per capita wealth is relatively high, has lower trust than South Korea and Mexico. Dominican Republic displays more trust than the wealthier Chile. Of course, these variations in trust can in part be explained by factors unrelated to wealth, such as cultural variables, population heterogeneity, or enforcement of promises and contracts, but one of the points raised in this section is that the relation between trust and wealth may not be monotonic: Though larger per capita wealth is likely to lead to higher trust, one cannot rule out the opposite possibility. Because an increase in wealth can modify its distribution, it is possible to observe a higher average wealth associated with a lower trust level, at least locally. Two sets of theoretical questions come to mind, the first of which relates to increases in wealth: Would the number of trusting agents grow if some agents move to higher wealth brackets while all others’ wealth remain unchanged? What impact does a uniform increase in wealth have on trust? The second set of questions bear on the impact of wealth distribution: Does an economy with more equal wealth distribution display higher trust? What is the level of trust in a fully egalitarian economy, where all agents are assigned the same, average wealth of the population?

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4.1. Impact of increases in wealth

4.2. Impact of wealth redistributions

An increase in the wealth of a subset of agents provides these agents with better protection against trustee opportunism, hence, incentives to trust others. On the other hand, agents with larger wealth also have larger counter-enforcement power and thus weaker incentives to perform, which decreases other agents’ trust. If this negative effect dominates, the number of trusting agents falls. In the following case, the possibility that trust falls is evident. Consider mi agents who neither trust nor betray in the initial hybrid equilibrium where, suppose, the set of trusting agents is smaller than the set of betraying agents. By Proposition 1 these mi agents must initially be wealth-constrained. Increase their wealth from wi to wi + ı, choosing ı so that they move into the set of betraying agents but continue not to trust and remain wealth-constrained, that is, RE = wi + ı − x and RC = wi + ı + x. Given the strategies of other agents, the number of betraying trustees will increase, which may negatively affect other agents’ trust; the first agents to see their trust decisions be affected are those with the smallest wealth among the set of trusting agents.17 Then the number of trusting agents in the new equilibrium can only fall, or remain constant at best. Those who see their wealth grow gain more enforcement and counter-enforcement power, hence stronger incentives to both trust and betray, which generates an ambiguous trust response from the rest of the population.18 This ambiguity extends to the case of uniform wealth growth as long as counter-enforcement activities are effective. However, if the possibility of counter-enforcement is eliminated, an increase in the wealth of some, or all, agents can only increase trust because larger wealth then only means larger resources available for enforcement, thus smaller expected payoff from betraying trust and larger expected payoff from trusting. This conclusion continues to hold if the counter-enforcement technology is sufficiently ineffective, that is, if individually optimal counter-enforcement resources are low and sufficiently unproductive. Proposition 2 summarizes the discussion above.

If one dollar is transferred from Agent A to Agent B, the additional dollar in the enforcement game can only increase B’s trust, but B also has stronger incentives to betray. A’s trust can only fall, but A may now become more trustworthy. These potential changes in A’s and B’s strategies can produce external effects on the trust and betray strategies of other agents. Since lack of trust in this model stems from lack of relative enforcement power and wealth, intuition may suggest that any mean-preserving redistribution that reduces wealth inequality would increase trust and decrease the number of betraying trustees. This intuition is wrong. For instance, in an economy with low mean wealth and much heterogeneous wealth distribution trust will be positive thanks to the presence of the few trusting agents with sufficiently large wealth and enforcement power. Trustworthiness will also be positive, because there will be relatively poor trustees who know they will likely fail to get away with the surplus they owe. If wealth is redistributed and homogenized around its low mean, the number of beneficiaries with resources to effectively enforce promises, hence also the number of trusting beneficiaries, will most likely fall. The opposite effects should be expected if wealth is homogenized in an economy with large mean wealth. The impact of a meanpreserving wealth redistribution should therefore depend on the level of the mean. The analysis of the extreme case of full wealth equality is relatively transparent and suggestive about the direction of trust and trustworthiness following a reduction in wealth inequality. When all M agents have the same wealth wH , the only source of heterogeneity is removed and the economy admits two candidates for symmetric pure strategy equilibrium outcomes: one in which all agents trust and one in which no agent trusts. Beneficiaries will trust if the analogue of (4) below holds:

Proposition 2. An increase in the wealth of some, or all, agents can generate a fall in generalized trust (a decrease in T and B ). If counter-enforcement is sufficiently ineffective, i.e. if q(R) and q (R) are uniformly low enough, trust cannot fall given any increase in wealth. q (R)

Uniformly low q(R) and imply small equilibrium counter∗ and q(R∗ ) for all j. Then, when the enforcement expenditures RCj Cj enforcement game is a sequential litigation game and promises or contracts are enforced by courts, the above condition implies a large probability of enforcement. In other words, the legal system is more likely to punish the breaching trustee, hence, less likely to generate judicial errors. Then an alternative statement of Proposition 2 is, “in economies with sufficiently effective legal systems, growth in the wealth of some, or all, agents cannot produce a fall in generalized trust,” because enforcement power will increase for some, or all, agents. In such economies, as long as a nonnegligible fraction of the population does not experience a sharp fall in wealth, a relatively balanced or uniform wealth growth should enhance generalized trust.19

17 This so because for these agents, the net surplus from betraying is smallest among all agents with (.) ≥ 0. 18 The only exception is an increase in the wealth of a group of unconstrained, highwealth agents. This will leave generalized trust unchanged because it will produce no change in the interior-optimal enforcement strategies of these agents, hence no external effects on other agents. 19 In the limit, of course, if the legal system is fully effective so that contracts or promises are perfectly enforced, the economy displays full trust no matter the mean

 ≡ prob( = 0)S − x − prob( = 1)[RE∗ − p(RE∗ )(1 − q(RC∗ ))S] ≥ 0,(5) ∗ } and { } is suppressed. The analogue of (3), where RC∗ replaces {RCj j the condition under which trustees betray, now becomes

 ≡ ˛S − p(RE∗ )(1 − q(RC∗ ))[˛S + ] − p(RE∗ )RC∗ ≥ 0.

(6)

The equilibrium enforcement strategy of a beneficiary is RE∗ = wH − x if wH < R¯ E (R¯ C ) and RE∗ = R¯ E (R¯ C ) otherwise, whereas the counterenforcement strategy of a trustee is RC∗ = wH + x if wH < R¯ C and RC∗ = R¯ C otherwise. Note that for wH not too large, all agents will be wealth-constrained, implying RE∗ = wH − x and RC∗ = wH + x. A sufficient condition for a full-trust equilibrium is that no agent betrays if trusted: prob( = 0) = 1 implies  = S − x > 0, a positive net surplus from trusting. In terms of the two measures, B = 1 implies T = 1. Consider then the behavior of the net surplus  from betraying for wH in the range (x, R¯ C ]. Changes in the common wealth level wH will now be fully reflected in RE∗ and RC∗ . Note that the net surplus  from betraying is maximal, positive and equal to ˛S as wH → x from above. Thus, under full wealth equality at such low levels of wH , trustees foresee the lack of enforcement and will betray, which implies that beneficiaries will not trust. The zero-trust equilibrium prevails at low common wealth levels close enough to x. The policy implication is that wealth or income distribution should not be a prime concern in economies struggling with extreme poverty. One cannot hope to lubricate exchange and foster

and distribution of wealth. This corresponds to the case q(R) = 0 for all R ≥ 0: no resource the betraying trustee devotes can ever disable enforcement of the promised surplus.

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(iii) The more effective the enforcement technology relative to the counter-enforcement technology, the more likely is full wealth equality to produce a full-trust equilibrium (the larger is the set of mean wealth levels leading to full trust under full wealth equality).

Fig. 2. Possible shapes for the net betray surplus ˚ under homogenous wealth wH .

societal trust and trustworthiness by means of equalizing wealth and enforcement power. As the common wealth wH is increased at the right neighborhood of x, the net surplus  from betraying decreases, for betrayed beneficiaries are now able to devote larger resources on enforcement. This is clear from the derivative of  below:

Carrying out the redistribution until full wealth equality leads to a clear picture. Economic inequality and trust need not always, everywhere, be negatively correlated. The level of per capita wealth or income is an important qualification. Controlling for other factors, full economic equality should reduce trust and trustworthiness under conditions of extreme poverty, increase trust and trustworthiness in an industrialized, wealthy economy.21 While small changes in wealth can generate nonnegligible effects on trust in a hybrid equilibrium (under sufficiently dispersed wealth distribution), almost all limit equilibria (under full wealth equality) are robust to perturbations in the wealth of some, or all, agents. A zero or very low trust equilibrium will persist and the majority will continue not trusting if a very small minority becomes very rich; similarly, subjecting a very small minority to a negative wealth shock will not upset a full-trust equilibrium and the large majority will keep trusting. 4.3. Legal policy implications

(i) Full wealth equality definitely leads to a zero trust equilibrium if mean wealth is small and close enough to x. (ii) Full wealth equality is likely to induce a full trust equilibrium if mean wealth is large enough, where the beneficiaries are unconstrained in determining their optimal enforcement response to betraying trustees.

Consider the interpretation of the enforcement game as a litigation process, and the promise as a formal contract. More effective contract enforcement reduces the likelihood of unwarranted breach, thereby affects trust in the economy given the distribution of wealth. It also affects the limit trust level to which the economy converges as wealth inequality is gradually eliminated: The net betray payoff  in Fig. 2 shifts down and therefore full wealth equality is more likely to lead to full trustworthiness outcome, hence full trust outcome, if contracts are more effectively enforced. We know from survey data that per capita wealth and degree of law enforcement are positively correlated. On the other hand, the empirical studies cited in the Introduction suggest that economic equality and trust are positively correlated. Proposition 3 brings a qualification to these empirical findings, based on effectiveness of contract enforcement. An increase in wealth equality may reduce trust in low-wealth countries, increase trust in highwealth countries. However, investments on the legal system for a more effective contract enforcement will, by reducing the productivity of counter-enforcement, strengthen the positive impact of redistributive policies on trust. Even an economy with moderately low per capita wealth can converge to the full trust outcome by progressively reducing wealth inequality provided its legal system enforces contracts sufficiently effectively. In other words, effectiveness of contract enforcement can be a key intermediate variable for the relation between trust and wealth inequality. Any legal policy that affects the contracting parties’ payoffs from breach has potential implications on trust. Consider, for example, a change in the legal rule for allocation of trial costs, borne individually and denoted RE and RC in this model. Modifying the allocation of trial costs from “each-pays-his-own” (US rule) towards the polar opposite “loser-pays-all” system (English rule) will change the parties’ expected payoffs in the trust-enforcement game. If

20 This is verified by using in (7) the fact that R¯ C satisfies q (R¯ C )(˛S + ) = 1. That is, (7) is unambiguously negative at RC = R¯ C . The expression in (7) applies to the case of R¯ E (R¯ C ) + x ≥ R¯ C − x where, as the common wealth wH is increased, the trustees become unconstrained in their counter-enforcement strategy before the beneficiaries become unconstrained in their enforcement strategy. In this case, RE = wH − x as long as wH ≤ R¯ C − x. In the other case, which is omitted here for space considerations, beneficiaries become unconstrained before the trustees, but the same conclusions are reached.

21 If a person’s success probability depends solely on her (expected) relative wealth, an increase in mean wealth across all individuals in a fully equal society would not alter relative wealth and would not change success probabilities, hence, trust and trustworthiness. In the present model both relative and absolute wealth matter. Absolute wealth is also important because enforcement and counter-enforcement cannot succeed if the resources devoted to these effects are too small. This is why even under full wealth information two sufficiently poor parties to a relationship will not trust and therefore fail to realize the surplus.

∂ = −[p (wH − x)(1 − q(wH + x)) − p(wH − x)q (wH + x)] ∂wH × [˛S + ] − p (wH − x)(wH + x) − p(wH − x).

(7)

The first term in (7) is negative for small values of wH and positive for large values of wH whereas the second and the third terms are always negative.  may or not reach a local minimum inside the range (x, R¯ C ], but it is decreasing at the left neighborhood of R¯ C .20 Fig. 2 depicts these possibilities. Trust in an economy under full wealth equality depends on the technologies used in enforcement and counter-enforcement. A more effective enforcement technology, as represented by a firstorder stochastically dominated success probability function p(.), generates a larger probability of success given the same enforcement resource RE and decreases the net betray surplus  in (4). A less effective counter-enforcement technology with first-order stochastically dominating success probability function q(RC ) and a uniformly lower marginal success probability q (RC ) also make (4) less likely to hold. The following proposition obtains: Proposition 3.

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the assumption that individuals are constrained in borrowing to finance legal expenses-not unreasonable, given the fact that the ability to borrow is strongly correlated with wealth-is maintained, litigation expenditures are bounded above by personal wealth. If, in addition, the probability of winning in trial is a function of relative legal expenses, relatively wealthy individuals will be optimistic about the trial outcome as plaintiffs (beneficiary) and as defendants (trustee). Now, a change in the allocation rule towards the “loser-pays-all” system will affect incentives and prompt the unconstrained and optimistic wealthy litigants to increase their spending (RE or RC ). They will devote even larger resources to litigation because a greater chance of winning implies a greater chance of at least partially recovering these resources. Such a change in the trial cost allocation rule makes the resources of the wealthy even more productive, therefore, works in this model just as an increase in wealth inequality. The wealthy will become even more trusting and less trustworthy in their contractual relations whereas the poor, less trusting and more trustworthy.22 5. From trust to wealth Does the wealth distribution become more or less unequal through the trust and betray incentives it induces? Agents can increase their wealth by trusting as beneficiaries, which in equilibrium they do if the corresponding net surplus  is positive, or by betraying as trustees, provided the corresponding net payoff  is positive. Clearly, agents in a no-trust economy stagnate at the same wealth. A full-trust, no-betray economy finds its per capita wealth grow by a uniform expected amount S/2.23 A full-trust economy with a positive measure of betraying trustees generates a smaller increase in per capita wealth, but because the betraying trustees belong to the upper tail of the distribution, the most wealthy must, on average, experience relatively large increases in their wealth. Per capita wealth is expected to increase whenever the equilibrium displays positive trust because an agent’s individual choice to trust can only be justified in this model by expectation of a net positive surplus. Proposition 4. The trust and betray strategies in a hybrid equilibrium of an economy with sufficiently dispersed initial wealth distribution reinforce wealth inequality by generating relatively large wealth increases for the rich. Proof. In a hybrid equilibrium (see Proposition 1) there are three categories of agents. (a) Those who do not trust (i ∈ / T ). These agents belong to the lower tail of the wealth distribution and do not trust as trustees, thus remain at wealth wi . As trustees (a position each agent takes with probability 0.5), they may perform and earn x > 0. Since the probability of matching with a trusting agent is given by the measure of trust T , the expected increase in their wealth is T x/2 if they perform, T (iL + x)/2 if they find it optimal to betray as trustees. (b) Those who trust and betray (i ∈ T, ∈ B). These are the most wealthy agents who trust as beneficiaries and expect a posi-

22 The trust impacts of the “looser-pays-all” rule and the “each-pays-his-own” rule are not to date subjected to a formal analysis. Comparative analyses of the two rules hinge on their pre-trial screening effects; for instance, the number of cases that go to trial is believed to be relatively small under the “looser-pays-all” rule (Cooter & Ulen, 2000, p. 408). 23 If the equilibrium involves full trust and no betray, every pair of agents will generate performance and reap the corresponding surplus S, shifting half of the agents to upper wealth brackets. Since the position of an agent as beneficiary or trustee is random and equally likely, each agent expects his wealth to grow by S/2.

tive return i . As trustees they betray if trusted, thus expect an increase in their wealth by iH + x. The expected increase in their wealth is then i /2 + (x + iH )T /2. (c) Those who trust but do not betray, or those who do not trust but betray.24 These middle-wealth agents will see an intermediate effect on their wealth, falling somewhere in between those in category (a) and (b). Since iH ≥ iL (net betray surplus is larger for a wealthier agent), i /2 + (x + iH )T /2 > max{T x, T iL }/2, and thus the wealthy agents expect a larger increase in their wealth than the poor agents.  The trust games that agents play transform the wealth distribution in favor of the rich. Absent corrective redistributive policies, Proposition 4 states that wealth inequality will grow in time through the trust and betray strategies it induces. In a high per capita wealth economy the result is likely to be a fall in trust, to extend the insight gained from Proposition 4, especially if the economy initially is in a high-trust state and wealth is quite equally distributed. This is consistent with the empirical finding that high-trust societies are characterized by more distributive policies and less economic inequality (e.g. Uslaner, 2002). The exception the model provides to this statement is the case of extreme poverty conditions where people are deprived of enforcement power and therefore where, as mentioned in Proposition 3, increased wealth inequality can lead to an increase (though limited) in generalized trust. Leaving this exception aside, downsizing redistributive policies should, by promoting wealth inequality, lead to a fall in generalized trust, thereby a further rise in wealth inequality, a fall in trust and so on, generating a cycle of feedbacks. The basic tool for redistributive policies is taxation. Then another testable implication of Proposition 4 is that controlling for other factors, countries with more progressive taxation should display higher levels of generalized trust because progressive taxation can offset the impact of induced trust on wealth distribution. This prediction, too, seems to hold for at least a group of Western countries. Tax schedules in high-trust Scandinavian countries, for example, are much more progressive than those in the UK or US where generalized trust is relatively low. 6. Summary and concluding remarks The present paper presents a theoretical analysis of the link between generalized trust and wealth based on the fact that wealth is both a source of enforcement power and a shield from enforcement. In the equilibrium of an economy with dispersed wealth distribution wealthy agents trust but are not trustworthy while relatively poor agents are trustworthy but do not trust. Both absolute and expected relative wealth matter for an individual’s trust and trustworthiness decisions. An exogenous increase in the wealth of some, or all, agents makes these agents more trusting and less trustworthy, producing also external effects on others’ trusting incentives. In general, trust and trustworthiness in an economy is not necessarily in any sense monotonic in wealth. A wealth redistribution induces opposing effects on equilibrium trust for the same reasons. If redistribution is carried out

24 One of the two cases may arise, depending on model parameters and functional forms. For instance if in equilibrium the set of trusting agents turns out to be larger than the set of betraying agents, then there will be some who trust and do not betray, but no agent who betrays and does not trust.

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until the extreme of full wealth equality, the level of trust depends on mean wealth. A low mean wealth leads to zero trust. A large mean wealth is likely to generate a full-trust equilibrium. Enforcement and counter-enforcement capabilities play an important role here: Where enforcement capabilities are strong and counter-enforcement is rather ineffective, equilibrium trust can only increase and wealth equality leads to a full trust outcome even if mean wealth is relatively low. Culture could be incorporated into the model as an attribute of individuals, along wealth. Individuals sharing a common culture benefit from lower costs of enforcing promises and contracts.25 If culture and wealth are correlated, that is, if culture group A is formed of low-wealth agents while culture B agents are mostly from the wealthy bracket of the population, in equilibrium culture A would display low trust while culture B would display high trust. Suppose cultures are common knowledge among pairs of matched agents (which may be revealed through ways, language, race, and many other observable attributes) so that the decision to trust can be based on the opponent’s culture as well as expected wealth and enforcement power. Then, keeping the assumption that culture A is mostly formed of poor agents, this extended model would predict that low-wealth agents prefer trusting and exchanging only with Culture A agents and never trusting agents with other cultures, simply because enforcement is relatively easy and trusting safe. Note that an outside observer may mistakenly take introversion of Culture A agents as an inherent trait of that culture. On the other hand, agents with large wealth would be more trusting and open to exchange with other cultures. Trust and betray decisions are informative signals and lead to updating of beliefs about the partner’s wealth along the equilibrium path. The costs and benefits of being privately informed about one’s own wealth depend not only on own wealth but also on one’s position, beneficiary or trustee. Low-wealth agents would prefer their wealth be known as trustees to increase the probability that they are trusted, but as beneficiaries they would conceal their wealth. The wealthy experience the opposite effects. They would prefer their wealth and enforcement capabilities be commonly known as beneficiaries but would prefer concealing their wealth and incentives to betray as trustees.26 These preferences about the information structure may not automatically lead to an equilibrium in which agents accordingly signal or conceal their wealth. Take, for example, a seemingly straightforward extension of the model to allow matched beneficiary-trustee pairs to choose among several surpluses S1 < S2 < · · · , each corresponding to a different kind of promise, contract or performance. Then, if, as assumed in this paper, the payoff from betraying trust is increasing in the size of the promised surplus, poor beneficiaries will have a preference for smaller surplus sizes. Rich beneficiaries with enforcement power will prefer large surpluses. This extension would bring in additional complications because the choice of the surplus size can signal wealth, an activity that poor beneficiaries would prefer avoiding and rich beneficiaries would volunteer. But signaling a low wealth is risky and trusting beneficiaries may all choose the same surplus in a pooling equilibrium. In such an equilibrium, interestingly, poor

25 Based on this fact, Lazear (1999) builds a theory of culture acquisition and assimilation. 26 Mansbridge (1999) makes a similar point on incentives to signal type, noting that the trustworthy members of a society have a benefit from developing signals to distinguish themselves from others. In this model, equilibrium trustworthiness and enforcement power are inversely related. Thus, ex-ante, before matching with their partners, agents have no basis for a preference to signal or conceal their wealth as they are equally likely to assume the roles of trustee and beneficiary. Since all agents are alike except for their wealth, revealing a low wealth signals trustworthiness as well as a weak enforcement capability and invites betray from the trustee.

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beneficiaries’ imitation of the rich would arise not from the need to signal status but from the desire to avoid conveying weak enforcement capabilities so that they can elicit performance or prevent breach of contract. The conditions under which agents would adopt a pooling strategy and choose the same surplus size for their trust relations remains to be identified in a formal model. An important extension is to introduce dynamics to analyze evolution of wealth distribution in time through the temporal, induced trust equilibria. What kind of initial wealth distributions (and does one exist) progressively lead to a more trusting economy? Proposition 4 leads to the conjecture that low-trust economies with unequal wealth distributions would become even less trusting and increasingly unequal while high-trust economies with relatively homogenous wealth distribution would maintain these properties for a long period of time in the absence of shocks or corrective redistributions. Existence and levels of long run trust to which an economy would converge in time is an interesting research question. The present model can also endogenously generate intermediation of trust based on wealth distribution. Suppose wealth is common knowledge. If agent A cannot trust agent C because C has considerably larger wealth and counter-enforcement capability, A can trust C through another agent, B, who as the catalyst has an intermediate level of wealth and enforcement power. B would be A’s trustee and C would be B’s trustee. The intermediaries would be most needed in an economy with dispersed wealth distribution. They would serve as a safe bridge and restore a poor beneficiary’s trust to a rich agent. The wealth of these intermediaries would be neither too large to lose the trust of the poor, nor too small to produce betray from rich trustees. Erosion of the middle class can make a society less trusting to the extent that the middle class performs the role of intermediating trust-based exchange between lower and upper wealth classes. References Alesina, A., & La Ferrara, E. (2002). Who trusts others? Journal of Public Economics, 85, 207–234. Ben-Ner, A., & Putterman, L. (2002). Trust in the new economy. HHRI Working Paper 11-02 University of Minnesota. Berg, J., Dickhaut, J., & McCabe, K. A. (1995). Trust, reciprocity, and social history. Games and Economic Behavior, 10, 122–142. Burnham, T, McCabe, A. K., & Smith, V. (1999). Friend-or-foe intentionality priming in an extensive form trust game, mimeo, Harvard University and University of Arizona. Bohnet, I., Frey, B. S., & Huck, S. (2001). More order with less law: On contract enforcement, trust, and crowding. American Political Science Review, 95, 131–144. Coleman, J. (1990). Foundations of social theory. Cambridge, MA: Harvard University Press. Cooter, R., & Ulen, T. (2000). Law and economics. Addison-Wesley. Fukuyama, F. (1995). Trust: Social virtues and the creation of prosperity. New York: The Free Press. Gambetta, D. (Ed.). (1993). The Sicilian Mafia: The Business of Private Protection. Cambridge, MA: Harvard University Press. Guiso, L., Sapienza P., & Zingales, L. (2005). Cultural biases in economic exchange, University of Chicago GSB Working paper. Huang, P. H., & Wu, H.-M. (1994). More order without more law: A theory of social norms and organizational cultures. Journal of Law, Economics and Organization, 10, 390–406. Kieser, A. (2001). Trust as a Change Agent for Capitalism or as Ideology? A Commentary. Organization Science, 12, 241–246. Knack, S., & Keefer, P. (1997). Does social capital have an economic payoff? A crosscountry investigation. Quarterly Journal of Economics, 112, 1251–1288. Kosfeld, M., Heinrichs, M., Zak, P. J., Fischbacher, U., & Fehr, E. (2005). Oxytocin—A biological basis for trust. Nature, 435, 673–676. La Porta, R., Lopez-de-Silane, F., Shleifer, A., & Vishny, R. W. (1997). Trust in large organizations. American Economic Review, 87, 333–338. Lazear, E. P. (1999). Culture and language. Journal of Political Economy, 107, 95–126. Mansbridge, J. (1999). Altruistic trust. In M. E. Warren (Ed.), Democracy and trust (pp. 290–309). Cambridge: Cambridge University Press. Noteboom, B. (2002). Trust: Forms, foundations, functions, failures and figures. Cheltenham, Northampton: Edward Elgar Publishing. Putnam, R. (1993). Making democracy work: Civic traditions in modern Italy. Princeton, NJ: Princeton University Press.

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Ullmann-Margalit, E. (2002). Trust out of distrust. Center for rationality and Interactive Decision Theory, The Hebrew University, Mimeo. Uslaner, E. (2002). The moral foundations of trust. New York: Cambridge University Press. Varese, F. (1994). Is Sicily the future of Russia? Private protection and the rise of Russian Mafia. Archives Europennes de Sociologie, 35, 224–238. Williamson, O. F. (1996). Calculativeness, trust and economic organization. In O. F. Williamson (Ed.), The mechanisms of Governance (pp. 250–275). New York: Oxford University Press.

Zak, P. J. (2003). Trust. Capco Institute Journal of Financial Transformation, 7, 13–21. Zak, P. J. (2004). Neuroeconomics. Philosophical Transactions of the Royal Society B, 359, 1737–1748. Zak, P. J., & Knack, S. (2001). Trust and economic growth. Economic Journal, 111, 295–321. Zak, P. J., Kurzban, R., & Matzner, W. T. (2005). Oxytocin is associated with human trustworthiness. Hormones and Behavior, 48, 522–527, 295–321.