Transcript Document

Evolution of Institutions
Samuel Bowles
Santa Fe Institute and
University of Siena
Avercamp, On the Ice
Institutional evolution: two approaches
• Constitutional design (political philosophy
(Hobbes, Locke et seq.), optimal contract theory,
implementation theory). Ch 1
• Evolutionary (Hume, Marx, Hayek) Ch 2
Social engineering and spontaneous order
The man of systems . . . imagines that he can arrange the different
members of a great society with as much ease as the hand arranges
the different pieces upon a chess-board; he does not consider . . . that
in the great chess- board of human society, every single piece has a
principle of motion of its own.
Adam Smith, Theory of Moral Sentiments (1759)
I observe, that it will be for my interest to leave another in the possession
of his goods, provided he act in the sam manner with regard to me. ...
And this may properly be call'd a convention... ..[T]he stability of
possession... arises gradually, and acquires force by a slow
progression, and by our repeated experience of the inconveniences of
transgressing it. ... In like manner are languages gradually establish'd
by human conventions without any promise. In like manner do gold
and silver become the common measures of exchange...
David Hume, A Treatise of Human Nature, Volume II (1739)
Spontaneous order: what is it?
• Sugden (1989) rules regulating human action can evolve
without conscious human design, and can maintain
themselves without there being any formal machinery for
enforcing them. (86) ...conventions are not the product of
our reason.... Nor are these patters of behavior necessarily
efficient. They have evolved because they are more
successful at replicating themselves than other patterns: If
they can be said to have any purpose or function, it is
simply replication. (97).
• Classic contributions: Mandeville, Scottish historical school
(Ferguson, Smith, Hume), Rousseau, Hayek, Maynard
Smith
Questions
• How can evolutionary game theory illuminate the
process by which institutions evolve (emerge, persist,
pass out of existence)?
• What can we say about the nature of institutions that
emerge often, persist for long periods, rarely go
extinct?
• In particular, are these ‘evolutionarily successful’
institutions efficient?
The blind watchmaker and the social engineer. Do invisible
hand arguments apply to institutional evolution?
• Fisher’s Fundamental Theorem and the Fundamental
Theorem of Welfare Economics (the axioms exclude
epistatic (i.e non additive) and non contractual interactions).
• But economists, according to Douglass North think that
"competition in the face of ubiquitous scarcity dictates that
the more efficient institutions will survive and the
inefficient ones perish.“
• Many economists advising the ex-Communist countries
thought that if private property was introduced the other
institutions of a well functioning capitalist economy would
emerge endogenously (a misapplication of the Coase
theorem).
state of nature and co-evolutionary models
• …to study the rise and evolution of social institutions.. we
should start our analysis [with] only agents, their
preferences, and the technology they have …to transform
inputs into outputs.. [and to then study] when during the
evolution of this economy such institutions as money, banks,
property rights, competitive markets, insurance contracts
and the state would evolve.” Schotter (1980.)
• Is this history or a thought experiment?“The philosophers
who have examined the foundations of society have all felt it
necessary to go back to the state of nature, but none of them
has succeeded in getting there.” J.-J.Rousseau (1775)
• Co-evolutionary models study the joint dynamics of
preferences and institutions, with no presumed “initial
condition” no tabla rasa.
Payoffs in the Hawk dove game?
In a large population
individuals are
randomly paired for
an interaction with
the payoffs given in
the table to the
right. C is the cost
of a fight; V is the
prize and C>V>0
Hawk
Dove
Hawk
(V-C)/2
(V-C)/2
O
V
Dove
V
0
V/2
V/2
Expected payoffs where p is the fraction of the population who are
hawks (I, J) is the expected payoff to playing I against a J-player
bh(p) = p(H,H) + (1-p)(H,D)
bd (p) = p(D,H) + (1-p)(D,D)
Frequency dependent expected payoffs in the HD game
Which stationary points in the
replicator dynamic are stable?
v
b(H,p)
.5v
b(D,p)
0
0
.5(v-c)
p*
0
1
p
NB: the fraction of the population that are hawks =p
The replicator dynamics of the hawk dove game
• The trait H or D is genetically inherited and b(p) + f is the
number of replicas made (ie, fitness, so f is “benchmark
fitness”), and population size is normalized to unity, so
next year’s population frequency of hawks, p’ is
p' = p (bh + f) '{p(bh + f) + (1-p)(bd + f)}
The numerator is the number of hawks, next period The
denominator gives us the number of hawks and doves
combined, next year.
• Suppose population is constant, so average fitness, b = 1 =
{p(bh + f) + (1-p)(bd + f)}. Subtracting p from both sides
b)p / p’-p = p(bh + f) - p{p(bh + f) + (1-p)(bd) +
f)}
which gives the replicator equation
repeating the replicator eq:
)p = p(1-p)(bh - bd)
• NB: identical to the equation describing the dynamics of
the housing market.
• Using pbh + (1-p) bd = b , it can also be expressed in a way
that permits any number of strategies:
)p = p(1-p)(bh - bd) = p{bh - b}
• Stationarity: dp/dt = 0 requires p = 0, p = 1 or bh(p) =
bd(p), so the stationary interior value of p,
p* = {(H,D) - (D,D)}/{(H,D) -(H,H) -(D,D)} = V/C
Asymptotic and neutral (Lyapunov) stability?
• Is p* asymptotically stable?
• This requires d(bh- bd)/dp = d{(V-pC)/2}/dp = -c/2 < 0
an increase in the % H will disadvantage H relative to D:
this negative feedback makes p* stable.
• Recall that in addition to p*=V/C, p=0 and p=1 are also
stationary, but they are not asympotically stable (or even
neutrally – Lyapunov – stable): an all hawk or all dove
population can be invaded but mutants of the other type
• The replicator dynamic is not illuminating about stability
in the presence of innovation (mutation).
• The concept of ESS addresses this shortcoming (also,
stochastic evolutionary game theory)
ESS?
• ESS= resistance to invasion by mutant strategies
• x is an evolutionarily stable strategy with respect to
some other strategy y iff (x,x) > (y,x) or
(x,x) = (y,x) and (x,y) > (y,y)
• ..thus an ESS is a best response to itself (at least weakly,
and if it is a weak best response to itself then the other
strategy is not a best response to itself.)
ESSs continued.
• Equivalently: x is evolutionarily stable against y iff there
exists a fraction of the population, p~ > 0 (call this the
invasion barrier) such that if the fraction of the population
playing y is less than p~, then the incumbent strategy will
produce more replicas than y and hence will eliminate the
entrant (if p~ is interior, is an unstable equilibrium defining
the boundary of the basin of attraction of p=0 and p=1)
4
3
l
2
e
0
0
p*
1.0
How can the ESS be used as the basis of predictions?
Y is an ESS
Y is not an ESS
X is an ESS
p*(0,1) unstable
p* = 1 stable
X is not and ESS
p* = 0 stable
p* (0,1) stable
Assurance Game
Figure 5. ESS and the existence and
stability of interior equilibrium. Note p* is a
fraction of x-types in the population which is
stationary in the replicator dynamic.
HD game
4
3
l
2
e
0
0
p*
1.0
The evolution of private property rights: the Hawk–DoveBourgeois (or GSB) Game. What is the B-strategy?
• Bourgeois: if owner play a Hawk, if intruder play Dove.
• Explain the expanded payoff matrix
Hawk
Dove
Bourgeois
Hawk
½(V-C)
V
½V +¼(V-C)
Dove
0
½V
¼V
Bourgeois ¼(V-C)
½V + ¼V ½V
• Is B an ESS? Why or Why not?
• B is an ESS because it exploits the asymmetry of
possession to avert fighting
• NB: as a mutual best response, for an ESS the diagonal
element in the payoff column must exceed other payoffs;
in the HD game this is not true of either strategy, in the
HDB game it is true for B (check the matrix above).
Contested bourgeois: ill defined property rights
• Suppose that with probability , the intruding Bourgeois
believes (or acts as if ) he is the possessor. Thus  =1,
Bourgeois acts like or Hawk.
• Note:  may be interpreted as a measure of the noisiness
of the information about possession, or about the degree
of contestability of possession (my shirt vs Bill Gates’
programs)
• (B(), B()) = ½(v- c) < 0 < (D, B()))
• Thus, for large  < 1, (B(), B()) < 0 < (D,
B()), so B is not an ESS can invade).
• Why is it that if property rights are ill defined it is D, not
H that can invade?
• If possession is unclear, sharing rules unrelated to
possession may proliferate.
Summing up: Are Nash equilibria relevant to the real
world?
• Stationarity, even when coupled with stability, does not
ensure that an equilibrium will be observed in the real world
– Some equilibria are inaccessible (if a population got there it might
stay, but getting there is very improbable)
– Even accessible stable equilibria may be easily displaced by
stochastic events (their basin of attraction is small).
• Even a payoff dominant stable Nash equilibrium may be
historically irrelevant if it is not also risk dominant (because
it has a small basin of attraction)
• There may exist no stationary state in the relevant dynamic
(in this case it may be possible to study long term average
behavior)
How good is the blind watchmaker? Reasons to doubt the
applicability of invisible hand arguments to institutions?
• efficiency and success in replication are rarely identical, and
may be quite different (risk dominant equilibrium may
persist even when payoff dominant eq are possible; success
in replication may require military prowess or a large
population not closely related to efficiency)
• generalized increasing returns may induce populations to
spend much of their time at or near Pareto inferior (possibly
risk dominant) equilibria
• restricted variance: institutional speciation (Pagano) is
difficult
• the rates of change induced by real world selection
processes may be slow relative to the pace of changes
induced by other sources.
The invisible hand and the blind watchmaker..
The take home message: selection processes implement a kind
of hill climbing, but the hilltop need not bear any close
relationship to normative criteria such as efficiency, there
may be many hilltops, and rate of ascent may be
overwhelmed by shifts in the underlying topography.
Hayek (1988:27): I do not claim that the results [of
evolutionary processes] are “good” any more than I claim
that other things that have long survived such as
cockroaches (scarafaggii) have moral value.
3
2
Caution:
danger of
earthquakes
1
1
0
The end
Wrong hill
0.5
Wrong
direction
0
-0.5
-1
0
1
Perils of the invisible hand..
Next time?
2
• For next week: read ch 3.
Review: Risk dominance
• Risk dominant strategy: in a
2x2 game the best response
when one believes that the
other is equally likely to
play his two strategies is the
risk dominant strategy.
Planting late is risk
dominant (p = fraction
planting early).
• Risk dominant equilibrium:
both players play their risk
dominant strategies.
4
3
l
2
e
0
p*
0
Risk dominant
equilibriium
Basin of attraction
of the risk dominant
equilibrium
1.0
Payoff dominant
equilibrium