ON THE

EVOLU

TION O

F

DISCRIM

INAT

ION,

COOPERAT

ION, A

ND

PERCEP

TIONS

OF

ENTI

TLEM

ENT

YA N I S VA R O U FA K I SP H D C O L L O Q U I U M

L B J S C H O O L O F P U B L I C A F FA I S

S P R I N G 2 0 1 4

LESSONS FROM A LABORATORY EXPERIMENT

THE HAWK-DOVE GAME

H a w k – H a w k ( C o n fl i c t ) = l o s s o f $ 2 p e r s u b j e c t

D o v e – D o v e ( M u t u a l F l i g h t ) = g a i n o f $ 1 p e r s u b j e c t

H a w k – D o v e ( D i s t r i b u t i o n ) = g a i n o f $ 2 f o r t h e ‘ h a w k ’ a n d a z e r o p a y o ff f o r t h e ‘ d o v e ’

B h d A h -2,-2 2,0 d 0,2 1,1

THE ‘STANDARD’ ANALYSIS

Theorem: In equilibrium, subjects will play HAWK 1/3 of the time

Proof: Let p be the probability/frequency of HAWK play. Then the expected returns (ER) from HAWK and DOVE are, respectively:

ER(HAWK) = p(-2) + (1-p) (2) = 2 – 4p

ER(DOVE) = p0 + (1-p) 1 = 1 – p

In equilibrium, it is impossible to know!

Hence ER(HAWK) = ER(DOVE)

But then: p = 1/3

QED B h d A h -2,-2 2,0 d 0,2 1,1

ALFRED MARSHALL, PRINCIPLES OF ECONOMICS, 1890, XIV

“The Mecca of the economist lies in economic biology rather than mechanical economic dynamics…”

Rationality stumpedThe problem with indeterminacy (multiple equilibria)

A false dilemma: Rationality or evolving conventions?

B h d A h -2,-2 2,0 d 0,2 1,1

Enter Evolutionary Game Theory

d = Net Gains to Hawks = ER(HAWK) – ER(DOVE) =

= 2 – 4p – (1-p) = 1 – 3p

Adaptation Mechanism:d > 0 porp< 1/3 pp> 1/3 p

ONE DIMENSIONAL EVOLUTION

TWO DIMENSIONAL EVOLUTION

THEOREM: In equilibrium, all players of the same colour will either play HAWK or DOVE (while players of the other colour will play the opposite strategy)

PROOF: Let p = Pr(BLUE plays HAWK) and q = Pr(RED plays HAWK)

ERB(HAWK) = q(-2) + (1-q) (2) = 2 – 4q and ERB (DOVE) = q0 + (1-q) 1 = 1 – qÞ dB = -1 + 3q. So, dB >0 p or q< 1/3 p

Similarly, ERR(HAWK) = 2 – 4p, ERR (DOVE) = 1 – p dR = -1 + 3p dR = -1 + 3p. So, dR >0 q or p< 1/3 q

Two Dimensional Adaptation Mechanism:q< 1/3 p, q> 1/3 pp<1/3 q, p>1/3 q

TWO DIMENSIONAL EVOLUTION

JOHN MAYNARD SMITH, GEORGE PRICE, RICHARD DAWKINS

THEOREM: In equilibrium, all players of the same colour will either play HAWK or DOVE (while players of the other colour will play the opposite strategy)

q< 1/3 p, q> 1/3 pp<1/3 q, p>1/3 q

p=proportion of blue hawks

q = proportion of red hawks

0 1/3 1

1

1/3

Two evolutionary equilibria

THE PROMISE OF EVOLUTIONARY GAME THEORY

Escape from conventional theory’s ‘Abuse of Reason’

Evolutionary accounts of institutions, conventions and norms

Extraneous characteristics can ‘seed’ conventions which advantage one type of individual relative to another (even if the difference across individuals is arbitrary),

and

The resulting conventional discrimination is evolutionarily stable and, thus, tends to be institutionalised

AN EXPERIMENT (HARGREAVES-HEAP AND VAROUFAKIS, THE ECONOMIC JOURNAL, 2002)

6 4 5 E X P E R I M E N TA L S U B J E C T S

C O N T R O L L E D E N V I R O N M E N T

C O M P U T E R I S E D , A N O N Y M O U S ,

S I G H T L E S S P L AY

EXAMPLE OF THE SCREEN SUBJECTS FACED

The Game - Round 4 of 32 Information FOR THIS ROUND YOU HAVE BEEN Frequency of Strategies MATCHED (RANDOMLY) WITH A RED PLAYER previous choices 1 2 By the whole group 34% 66% (including yourself) in the LAST round By the whole group 39% 61% (including yourself) in ALL 3 previous rounds By the blue players 43% 57% (including yourself) in the LAST round By the blue players 40% 60% (including yourself) in ALL 3 previous rounds By the red players 25% 75% in the LAST round By the red players 38% 62% in ALL 3 previous rounds

THE OTHER PLAYER 1 2 1 -$2,-$2 $2,0 YOU 2 0,$2 $1,$1 Your payoffs so far: $3 Your average payoffs so far: $1

 

PLEASE: Predict the choice that the player you have just been randomly matched with will make in this round. [Recall that if you predict correctly, you will win, in addition to your money payoffs from this round, a lottery ticket. At the end of the session, $10 will be given to the player with the lucky ticket. The more lottery tickets you collect the greater the chances of winning the $10.]Punch in number 1 if you think that she/he will choose strategy 1, or 2 if you think that she will choose strategy 2.  

NOW CHOOSE YOUR OWN STRATEGY: Punch in number 1 if you wish to select strategy 1, or 2 if you prefer strategy 2.

THE DISCRIMINATION HYPOTHESIS

BLUE and RED labels will give rise to patterned, discriminatory outcomes

NULL HYPOTHESIS (supported by the standard analysis and one-dimensional evolution):

Colour labels will not influence behaviour

ALTERNATIVE HYPOTHESIS (supported by two-dimensional evolution):

Players will, eventually, make use of the extraneous information of colour labels to build a discriminatory convention

The Hawk-Dove-Cooperate GameNb. Co-operative outcome cc superior to any of the two equilibria but not

an equilibrium in its own right

A F T E R 3 2 R O U N D S O F T H I S G A M E A T H I R D S T R A T E G Y W A S M A D E A V A I L A B L E .

T H E N T H E G A M E W A S R E P E A T E D F O R A N O T H E R 3 2 R O U N D S .

B h d c h -2,-2 2,0 4,-1 A d 0,2 1,1 0,0 c -1,4 0,0 3,3

The Twist!

STANDARD AND EVOLUTIONARY THEORY’S PREDICTIONSStandard Analysis: The two games will elicit identical behaviour among rational players. ‘Learning’ will kill off the cooperative strategy, as players learn to play rationally.

Evolutionary Analysis:Cooperative behaviour will fade out independently of the availability or otherwise of colour labels.

My hypothesis: THE SEQUENCE HYPOTHESISThe availability of the cooperative option at the outset makes a difference to the evolution of discrimination. Order of play matters.

Null Hypothesis: It makes no difference whether HD is played first, followed by HDC, or vice versa.

COOPERATION DOOMED? IRRELEVANT?

THE 32 SESSIONS

Treatment

1st Game (32 rounds)

2nd Game (32 rounds)

Colour labels assigned?

HD-HDC-NClr HD HDC No HDC-HD-NClr HDC HD No HD-HDC-Clr HD HDC Yes HDC-HD-Clr HDC HD Yes

Abbreviations of the four treatments

Treatment N Treatment N Treatment N

1 HD-HDC-NClr 24 12 HD-HDC-Clr 18 23 HD-HDC-Clr 18 2 HDC-HD-NClr 16 13 HDC-HD-Clr 18 24 HD-HDC-Clr 16 3 HDC-HD-NClr 22 14 HDC-HD-Clr 20 25 HD-HDC-Clr 22 4 HDC-HD-NClr 22 15 HD-HDC-Clr 18 26 HDC-HD-Clr 18 5 HD-HDC-NClr 18 16 HD-HDC-Clr 16 27 HD-HDC-Clr 22 6 HD-HDC-NClr 24 17 HDC-HD-Clr 20 28 HD-HDC-Clr 16 7 HD-HDC-NClr 22 18 HDC-HD-Clr 24 29 HD-HDC-Clr 26 8 HDC-HD-NClr 16 19 HD-HDC-Clr 24 30 HD-HDC-Clr 18 9 HDC-HD-Clr 18 20 HD-HDC-Clr 16 31 HD-HDC-Clr 22

10 HD-HDC-Clr 16 21 HD-HDC-Clr 20 32 HD-HDC-Clr 26 11 HD-HDC-Clr 26 22 HD-HDC-Clr 16

Treatment No. of sessions No. of players Interactions per gameHD-HDC-NClr 4 88 1408HDC-HD-NClr 4 76 1216HD-HDC-Clr 16 330 5280HDC-HD-Clr 8 146 2336

Total 32 640 10240

AGGREGATE BEHAVIOURGame HD HDC

Outcomes (h,h)Conflict

(h,d)Asym.Distr.

(d,d)Flight

(h,h)Conflic

t

(h,d)Asym. Distr.

(d,d)

Flight

(c,c)

Coop

(h,c)

(d,c)

Treatment 11.11%  44.4% 

44.4%  11.11%  44.4%  44.4% 

0  0  0 

HD-HDC-NClr

29 39.8 31.2 36.7 9.8 3.7 6 30.2 13.6

HDC-HD-NClr

33 35.6 31.4 29.3 4.3 2 8.2 38.1 18.1

HD-HDC-Clr 21.4 51.8 26.8 19.2 38.7 2.2 9.3 20 10.6

HDC-HD-Clr 26.9 45.2 27.9 30.1 7.1 2.1 7.2 34.7 18.8

B h d c h -2,-2 2,0 4,-1 A d 0,2 1,1 0,0 c -1,4 0,0 3,3

1ST RESULT: DISCRIMINATION GALORE (IN THE COLOUR TREATMENTS)!

Session no. and colour treatment

 Game HD

 Game HDC

  

  

Convergence? Which Colour?

Which Round?

Convergence? Which colour?

Which Round?

9 HDC-HD Yes Red 26 No - -10 HD-HDC Yes Red 24 Yes Red 1211 HD-HDC Yes Blue 19 Yes Blue 812 HD-HDC Yes Blue 18 Yes Blue 513 HDC-HD Yes Blue 1 Yes Blue 2614 HDC-HD Yes Red 24 No - -15 HD-HDC Yes Red 21 Yes Red 1116 HD-HDC Yes Blue 20 Yes Blue 217 HDC-HD Yes Red 23 No - -18 HDC-HD No - - No - -19 HD-HDC Yes Blue 15 Yes Blue 820 HD-HDC Yes Blue 20 Yes Blue 621 HDC-HD No - - No - -22 HD-HDC Yes Red 14 Yes Red 1323 HD-HDC Yes Blue 16 Yes Blue 124 HD-HDC Yes Red   Yes Red 225 HD-HDC Yes Blue 10 Yes Blue 2026 HDC-HD No - - No - -27 HD-HDC Yes Red 20 Yes Red 2128 HD-HDC Yes Red 7 Yes Red 629 HDC-HD No - - No - -30 HD-HDC Yes Blue 18 Yes Blue 731 HD-HDC No - - No - -32 HD-HDC Yes Blue 16 Yes Blue 10

Outcomes

Pairs

conflict hh

asymmetrical distribution hd

mutual flight dd

A-D 9% 73% 18% A-A 40% 21% 19% D-D 17% 18% 73%

Stand. pred. (11.1%) (44.4%) (44.4%) No colours (29%) (40%) (31%) A = advantaged colour bearing players D = disadvantaged colour bearing players

GAME HD - TREATMENT HD-HDCDATA FROM AA, AD, DD PAIRINGS

LAST 11 ROUNDS OF 32DISTINCT PATTERNS OF DISCRIMINATION, AGGRESSION AND

ACQUIESCENCE

Remarkable acquiescence amongst the Disadvantaged

Exorbitant aggression amongst the Advantaged

Substantial coordination in cross colour meetings

The HDC GameLast 11 rounds in the HD-HDC Treatment

hh hd dd cc A-A 35% 34% 28% 2% D-D 1% 4% 1% 94% A-D 1% 92% 6% 1%

PREDICTIONS

A QUITE REMARKABLE RESULT

MOTIVATED COOPERATION AMONG THE DISADVANTAGED

SOCIALLY CONTINGENT TRUST

THE EMERGENCE OF CONVENTIONS OF FAIRNESS, INTERTWINED WITH EVOLVED DISCRIMINATION

hh hd dd cc A-A 51.2% 8.9% 1.81% 4% D-D 2.1% 3.5% 0.5% 89.9% A-D 8.2% 81% 0.4% 0.5%

OUTCOMES

BUT IS IT RATIONAL?

  Game HD Game HDC

A-players D-players A-players D-players

Meetings between an A and a D player

66.3 21.7 137.8 39.7

Meetings between two A

players

7.3 - 16.2 -

Meetings between two D

players

- 19.6 - 101.3

Average 36.8 20.7 77 70.5Average payoffs per round of A-players and D-players

in all 32 rounds of HD and HDC in treatment HD-HDC-Colour

WHY DID CO-OPERATION OCCUR AMONG THE ‘DISADVANTAGED’?

Nash Equilibrium: A set of strategies, one per player, that confirm the 1st order expectations of each.

2nd order expectations: That which Jill expects that Jack expects she will do.

Psychological Equilibrium : A set of strategies that confirm both 1st and 2nd order expectations of each player

Fairness Equilbrium: A psychological equilibrium consistent with particular perceptions of ‘entitlement’

MY HYPOTHESIS:

A-players develop higher normative expectations regarding what they are entitled too when pitted against D-players.

But D-players develop similarly heightened perceptions of entitlement when playing with other D-players

Thus, (c,c) is a ‘fairness’ equilibrium for D-players but not for A-players.

A-players with higher normative expectations may find themselves locked into a nasty (unkind) fairness equilibrium with players of the same colour.

THE GIST: EXPERIMENTAL FINDINGS SUMMARISED AND INTERPRETED MORE BROADLY

1. The observed distribution of social power, income, roles etc. may be predicated upon arbitrarydifferences (i.e. differences that have nothing to do with human capital, aptitude, application etc.)

2. Once a pattern of dominance is established in simple accumulative contests (HD), it colonises the ensuing, more complex social interactions (e.g. HDC).

3. Patterned discrimination (e.g. along the lines of class, gender, race) determines the likelihood of cooperation between and across different groups

4. Such power patterns are maintained through bonds of trust between the powerless. Moral legitimation ensues, as both the ‘advantaged’ and the ‘disadvantaged’, develop their separate, but intertwined, ideologies (e.g. the former focusing on ‘competition’ and ‘efficiency’, the latter on ‘justice’ and the virtues of co-operation)

5. Hierarchies are institutionalised in response to the structure of the interaction, rather than as a reflection of the distribution of the attributes, features and talents of the individuals.

EPILOGUE: NOTHING NEW, REALLY…

The weaker are always anxious for justice and equality. The strong pay heed to neither.

Nietzsche , Beyond Good and Evil

…there is master morality and slave morality…those qualities which serve to make easier the existence of the suffering will be brought into prominence and flooded with light… Slave morality is the morality of utility.

Aristotle, Politics, s1318b

Thucydides, History of the Peloponnesian War, Book 5, s90

Athenian General: “…on the one hand the principles of justice, as encompassed in human reason, hinge on the equal capacity to compel, yet on the other hand, the strong actually do what is possible and the weak suffer what they must.”

Melians: “…you should not destroy a principle that is in the general good – namely that those who find themselves in the clutches of misfortune should be justly and properly treated, and should be allowed to thrive beyond the limits set by the precise calculation of their power.”

If not, “your own fall will be visited by the most terrible vengeance, watched by the whole world.”

EPILOGUE: NOTHING NEW, REALLY…

Force cannot, like opinion, endure for long unless the tyrant extends his empire far enough afield to hide from the people, whom he divides and rules, the secret being that real power lies not with the oppressors but the oppressed.

Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743-1794),

THE END