Exchange: Contracts, Power, and Norms
Goya, Riña a garrotazos
Background: limitations of the Walrasian paradigm
• Non contractual social interactions.
• Other-regarding preferences updated by adaptive
agents (hence endogenous)
• Generalized increasing returns.
In the remainder of these lectures these three aspects of
economic life will be taken as the rule rather the
exception.
Figure 14.1 summarizes the contrast between Walrasian
and post walrasian econ.
"[ Divine Providence] has not willed for everything that is
needed for life to be found in the same spot. Jacques
Savary : Le parfait négociant 1675
• Mechanisms of coordinating the division of labor:
Exchange, gift, theft, bargaining, fiat.
• Walrasian exchange may be contrasted with the views of
anthropologists, sociologists and others:
• Sahlins’ primative exchange: positive, balanced, and
negative reciprocity.
• Polanyi’s ficticious commodities.
• Peter Blau’s social exchange
• In no case are contracts complete, in all cases norms and
power are aspects of the exchange process
Market norms: the big idea
• Where contracts are incomplete, mutually beneficial
exchange may be sustained by social norms (trust, work
ethic, truth telling, etc) in the absence of which trade would
not be possible.(Arrow)
• These norms are cultural traits (learned behaviors) that are
updated occasionally in response to people's experiences,
information, etc. (Mill)
• The exchange process itself provides some of the salient
experiences relevant to this updating.
• Even if updating is payoff based, retaliation, segmentation
and reputation can support the evolution of exchange
supporting norms for some market structures.
• Conclusion: ideal Walrasian markets (anonymous and
ephemeral) would not favor the evolution of exchange
supporting norms.
• Kenneth Arrow: In the absence of trust
…opportunities for mutually beneficial
cooperation would have to be forgone…norms of
social behavior, including ethical and moral codes
(may be)…reactions of society to compensate for
market failures.
• Definition of norm?
• social norms are ethical prescriptions governing
actions towards others
Internalization of norms
• J.S. Mill: Nobody argues that the art of navigation is not
founded on astronomy because sailors cannot wait to
calculate the Nautical Almanac. Being rational creatures
they go to sea with it already calculated; and all rational
creatures go out upon the sea of life with their minds made
up on the common questions of right and wrong, as well as
on many of the far more difficult questions of wise and
foolish (Utilitarianism (1861):31).
• Internalization means that the norm becomes a preference
rather than a constraint. Internalized norms are sometimes
called values.
The evolution of exchange-supporting norms: model setup
C
D
• The one shot exchange game is a 2x2 with
mutual defect (steal) the DSE
C b,b d,a
• Traders in a large (infinite) population are D a,d c,c
paired.
• After playing, each updates by the rule: if your
partner in the last play did better than you,
switch with probability ().
• For the one shot game updating occurs only
when C meets D (in which case  = a-d)
• Replicator equation (ch 2) for p, the fraction
playing C: dp/dt = p(1-p)(d-a) < 0
• How can market structure sustain exchangesupporting norms?
Repetition and Retaliation
• The stage game is played
and with probability 
that period is the last; if
not terminated the stage
game is played again,
until it is terminated.
• In this setup if the C
strategy is ‘nice TfT,’ the
interaction may have an
Assurance Game
structure. Explain the
payoffs.
• How does this alter the
evolution of market
norms?
C
D
C b,b
d,a
D a,d
c,c
Payoffs for the Iterated Exchange Game
Tit for Tat
Defect
Tit for
tat
b/ρ
b/ρ
d + (1-ρ)c/ρ
a + (1-ρ)c/ρ
Defect
a + (1-ρ)c/ρ
d + (1-ρ)c/ρ
c/ρ
c/ρ
Payoffs for the Iterated Exchange Game
The evolution of Tit for Tat
What are the stationary values (in
the replicator equation) of ?
Which of these is stable?
Tit for Tat
Defect
Tit for
tat
b/ρ
b/ρ
d + (1-ρ)c/ρ
a + (1-ρ)c/ρ
Defect
a + (1-ρ)c/ρ
d + (1-ρ)c/ρ
c/ρ
c/ρ
Explain why increasing  makes the evolution of cooperation less likely.
Effect of
increased
probability of
termination
Basin of
attraction
of p=1
Segmentation
• How does it work?
• The degree of
segmentation?
P(C|C) = s + (1-s)
P(D|C) = (1-s)(1- )
P(C|D) = (1-s)
P(D|D) = s +(1-s)(1)
• What values of 
are stationary?
• Stable?
How would
you show that:
•  an s <1 s.t. * =1
•  an s* <1 s.t for
s>s* * > 0
• If *  (0,1) is
stable, d */ds > 0
• If *  (0,1) is not
stable, d */ds < 0
• Explain why the last
result increases the
likelihood of univeral
cooperation?
Table 7.1 How within-group payoff-based updating may support cooperation
Model
Effect favoring
cooperation
Necessary structure of
interaction
Examples
Retaliation
Withdrawal of later
co-operation
Frequent or long
lasting interactions (ρ
low)
Taylor (1987)
Fudenberg and
Maskin (1986)
Reputation
Cooperative
reputations are
rewarded
Low cost of information about others (δ
low)
Kreps (1990), Shapiro
(1983) Nowak and
Sigmund (1998)
Segmentation
Advantageous pairing for cooperators.
Non-random pairing
of agents (σ high)
Hamilton (1975),
Axelrod and Hamilton
(1981),Grafen (1979)
• Walrasian ideal markets as cultural environments.
– Ephemeral (low entry and exit costs)
– Anonymous (identity does not matter)
• Walrasian markets may be an impediment to exchange
unless contracts are complete.
In an economic theory which assumes that transaction costs
are non-existent, markets have no function to perform and it
seems perfectly reasonable to develop the theory of exchange
by an elaborate analysis of individuals exchanging nuts for
apples in the edge of the forest or some similar fanciful
example... Ronald Coase (1998): 7-8.
• So far we have addressed symmetric games of
incomplete contracts and the market structure in
evolution of norms allowing exchange in these settings
• We turn now to study another case of non Walrasian
markets: the asymmetric principal agent relationships that
arise when contracts are incomplete.
• We focus on ‘hidden actions’ (‘moral hazard’) rather than
hidden attributes (‘adverse selection’).
• Here power as well as norms will be aspects of exchange
Reasons why contracts are incomplete?
• Third-party enforcement of contracts requires
information which is available to both parties and is
recognized in courts of law (verifiable)
• Contracts are generally executed after a passage of time,
and a complete contract must thus specify outcomes for
every possible future state
• Many of the services or goods involved in the exchange
process are inherently difficult to measure
• Even if the nature of the goods or services to be
exchanged would permit a more complete contract, a less
complete contract may be favored for motivational
reasons (Brown et al and MBIE pp 261-264)
• NB: Asymmetric information is not necessary for
contracts to be incomplete.
Where contracts are incomplete, exchanges take may
be ‘hidden action’ principal agent relationships.
Necessary and sufficient conditions for this?
• The agent takes an action a which is not
subject to a complete enforceable contract.
• The agent’s utility u(.., a,..)
• The principal’s utility U(…,a,…)
• Ua and ua are of opposite sign over the
economically relevant ranges
Examples of Principal Agent Relationships
Good or service
Noncontractible:
Endogenous
enforcement
Principal/agent
labor services
effort, care
contingent renewal
employer/
employee
managerial services
effort, maximizing
owners profits
profit sharing,
contingent renewal
owner/manager
debt
level of risk taken
collateral, shared
control
lender/borrower
sovereign debt
probability of default
trade sanctions, other
interventions
lending gov/borrower/gov
goods
product quality
contingent renewal by buyer/seller
buyer
public policy
choice and
implementation
contingent renewal,
referendum
citizen/govt official
residential tenancy
care of residence,
local amenities
security deposit,
contingent renewal
landlord/tenant
agricultural tenancy
labor effort and
quality, care of land
shared residual
claimancy
landlord/sharecropper
equipment rental
care of the
equipment
deposit, ownership
share in equipment
owner/renter
Other examples?
Contingent renewal: an important class of P-A models.
• Supplier provides a single unit of an input to a Demander,
who then sells the good (D owns the trademark, eg, and
does nothing except market the good)
• Non verifiable quality of the input, q, is costly to provide
and is determined by S (one of n identical), whose per
period utility is u(p,q)
• Demander’s revenue is r(qn) with  = r(nq(p)) - pn
• Contingent renewal: D announces a price and a termination
schedule t(q) with t’<0. How to determine p*
• S’s present value of the transaction where z is the fallback
asset: v(q; p,z)
• Enforcement rent = v –z
Equilibrium price and quality
• S’s best response
function (brf): vq = 0
requires uq = t’(v-z)
(meaning?)
• NB (v-z) = 0 implies
uq = 0 (meaning?)
• D’s foc: p = n = 0
giving qr’= p and
q/p = q’ (meaning?)
Explain each of the following characteristic results of
a PA interaction with contingent renewal
• Pareto Inefficient Equilibrium
(also tech inefficient, ch 8))
• Equilibrium Rents
• Equilibrium Without Market
Clearing
• Price Making
• Durable Transactions
• The Exercise of Power
• Endogenous Preferences
• Thus the completeness (or not)
of the contract is likely to
influence market structure …
The co-evolution of contracts and norms
• We have learned that contracts influence norms because:
– different structures of social interactions support different
equilibrium preferences(repetition, reputation, segmentation)
– contractual structure (complete or not) alters the structure of
market interactions (durable vs one shot, network structure, etc
Brown et al 2004).
• It is also true that the distribution of norms influences the
distribution of contracts: if trustworthy people are common
in a population, it will be profitable to offer trusting
contracts (incomplete).
• And conversely, where trusting contracts are common,
trustworthy norms may proliferate (pp 261-264; discussed
previously)
• This is an example of the co-evolution of contracts and
norms (of institutions and preferences)
a mythical visitor from Mars… equipped with a telescope that
reveals social structures. The firms reveal themselves, say, as
solid green areas…market transactions show as red lines
connecting the firms forming a network in the spaces between
them. No matter whether our visitor approached the United
States or..urban China, or the European Community, the
greater part of the space below it would be within the green
areas, for almost all of the inhabitants would be employees,
hence inside the firm boundaries. Organizations would be the
dominant feature of the landscape. A message sent back
home, describing the scene would speak of “large green area
interconnected by red lines.” It would not speak of “a network
of red lines connecting green spots.” Herbert Simon (1991):27
Next time we study one of the most important of those ‘green spots’.
Read chapter 8 and decide which of the discussion questions you will
present
Additional reading
• Brown, Martin, Armin Falk, and Ernst Fehr. 2004. "Relational
Contracts and the Nature of Market Interactions." Econometrica.
• Polanyi, Karl. 1957. The Great Transformation: the Political and
Economic Origins of our Time. Beacon Hill: Beacon Press.
• Sahlins, Marshall. 1974. Stone Age Economics. Chicago: Aldine
Publishing Company. Chapter on ‘Primative Exchange’
• Bernstein, Lisa. 1992. "Opting Out of the Legal System: Extralegal
Contractual Relations in the Diamond Industry." Journal of Legal
Studies, 21:1, pp. 115-58.
• Weisbuch, Gerard, Alan Kirman, and Dorothea Herreiner. 2000.
"Market Organization and Trading Relationships." Economic Journal,
110:463, pp. 411 - 36.
Next time: labor markets, read MBIE ch 8, review discussion q’s
Discussion questions (with .ppt or handouts) on principal
agent models of employment (meetings with presenting
groups Tuesday afternoon)
• Apartheid as labor discipline (22.3)
• The distribution of gains from freer North South trade
(22.2)
• An employment subsidy with endogenous effort (23)
• An incentive compatible BIG (unconditional basic income
grant) (24)
• Husbands and wives/Principals and agents (29)
Presentation of Brown, Falk, and Fehr?
Structure of
interactions
Complete contracts
Incomplete contracts
Duration
one shot
contingent renewal
Offers
public
private
Price determination
Haggling offers rejected
Price setting by short sider
Traders’ relationship
anonymous
Trust, retaliation for
cheating
Market networks
Many thin connections
Bilateral trading islands
Source: Brown, Falk, and Fehr (2004)
Recall (pp 261-64)
Co-evolution of
contracts and
preferences (from
last year)
The vector field in figure 7.5 is given by
d/dt = (1-)(vI – vC) and
d/dt = (1-)(vR – vS)
At a, I-contracts are best responses though C are feasible
• Each traveler ...leaves the goods he has brought ...
and they retire to their camping ground. Next day
they go back to ...their goods and find opposite them
skins of sable, minever, and ermine. If the merchant
is satisfied with the exchange he takes them, but if
not he leaves them. The inhabitants then add more
skins, but sometimes they take away their goods and
leave the merchant’s. This is their method of
commerce. Those who go there do not know whom
they are trading with or whether they be jinn or men,
for they never see anyone. (1929:151) Ibn Battuta