Laboratory studies of social stratification and “class”

Anna GunnthorsdottirAustralian School of Business and Vienna Univ. of Economics & Business

Kevin McCabe George Mason Univ. Stefan Seifert Technical Univ. Karlsruhe

Jianfei Shen, Univ. of New South Wales

Palmar Thorsteinsson, Univ. of Iceland

Roumen Vragov The Right Incentive, NY

J. Pub. Econ. 2010; Res. Exptal Econ. 2010

Three main findings from the program

1) We are responsive to social stratification (“class”)

2) We respond efficiently & precisely (eqm!) to social organization based on contribution (“merit”)

3) We can, in the aggregate, tacitly coordinate complex non-obvious asymmetric equilibria. It is however not quite clear how.

“…to a psychologist [the tacit coordination of an asymmetric equilibrium in a (simple) Market Entry game] looks like ‘Magic’.”

Kahneman, 1988, p.12

Kahneman, D. (1988). Experimental economics: a psychological perspective. In Tietz, R., Albers, W., Selten, R. (Eds.), Bounded Rational Behavior in Experimental Games and Markets. Berlin: Springer, pp. 11-18.

“Magic”

The Group-based Meritocracy Mechanism (GBM)

Competition for unit membership

Level 2

Level1

(VCM)

The Voluntary Contribution Mechanism (VCM)

Isaac, R.M., McCue, K. F., & Plott, C. R. (1984). Public goods provision in an experimental environment. Journal of Public Economics, 26, 51-74.

Divide endowment between two accounts

Private Account Group Account

ngs

n

i

i

1

For a social dilemma, set g > 1 and g < n

The 2nd GBM layer

Competition for team membership

Level 2

Level1

(VCM)

Basic requirements for a model of contribution-based grouping

1. Group membership is competitively and solely based on individual contributions

2. The equilibrium analysis extends across all players and all groups, since players compete for membership in groups that vary in their payoff

3. In the causal chain, the contribution decision precedes grouping and associated payoff

GBM equilibria (in pure strategies)

1) Free-riding equilibrium where nobody contributes

2) “Near-efficient” equilibrium (NEE)– z < n contribute 0, the rest contribute their entire endowment– Payoff dominant*

* Harsanyi, J. & R. Selten, 1988. A General Theory of Equilibrium Selection in Games.Cambridge, MA: MIT Press.

Theorem

For the near-efficient equilibrium, players must:

1. Coordinate which of the two equilibria to play

2. “Grasp” a non-obvious asymmetric equilibrium

3. Play only 2 out of their 101 strategies

4. Play only their corner strategies (0 or 100)

5. Play the two corner strategies in the right frequencies

6. Tacitly coordinate who plays which strategy

Experiment parameters

w(i=1,2,…N) = 100

N = total number of players = 12

Group size n = 4

g = 2

MPCR = 0.5

z = 2

# rounds = 80

Means per round

MPCR=0.5

0

20

40

60

80

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

Round #

Frequency of strategies observed/predicted

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100

0%

10%20%30%

40%50%

60%

70%

80%

90%

100%

Choice proportions Rounds 1-80

Public contribution

Perc

enta

ge

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 770

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

0

20

40

60

80

100

120

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77

Robust!

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0%10%20%30%40%50%60%70%80%90%

100%

Robots contribute 0 all 80 rounds

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0%10%20%30%40%50%60%70%80%90%

100%

Robots contribute 0 Rounds 21-80

A 2-type society where mingling cannot be avoided

One type more able to contribute than the other type

Type “Low”: wL = 80 Type “High”: wH = 120

N = 12 NH = 6NL = 6

n = 4g/n = MPCR = 0.5# rounds = 80

Equilibria in pure strategies:[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0][0, 0, 80, 80, 80, 80, 120, 120, 120, 120, 120, 120]

… mingling cannot be avoided

Low ability members try to sponge off high-ability members in the mixed group

High-ability members would like to escape this exploitation but can’t

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

110

115

120

0%10%20%30%40%50%60%70%80%90%

Choice proportions Rounds 1-80, four sessions

Public contribution

Perc

enta

ge

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 102

105

108

111

114

117

120

0%10%20%30%40%50%60%70%80%90%

Choice proportions Rounds 21-80, four sessions

Public contribution

Perc

enta

ge

A “segregated society” with “castes”

…“segregated with castes”

Assume NH mod n = 0 and NL ≥ 2n

For example: wL = 80 and wH = 120 NH = 4 and NL = 8

Is there an equilibrium w. positive contributions?

Payoff-dominant equilibrium prediction

(Non-contribution by all remains an alternative pure-strategy equilibrium)

s* = {0, 0, 80, 80, 80, 80, 80, 80, 81, 81, 81, 81, 81}

Lows: GBM (NEE)

Highs: VCM bounded from below by the

endowment of the Lows

Choice frequencies, w = 80 (“Lows”)

Mean contribution, w = 120 (“Highs’)

Choice frequencies, w = 120 (Highs)

A simple model of merit-based grouping

No lags, no reputation, no information asymmetry about contribution or the distribution of abilities to contribute

What you contribute determines where you find yourself (with an element of chance incorporated), with whom, and how much you earn.

A “perfect” world in that contribution, or a change in behavior for the better, is instantly recognized, and “transgressions” are immediately forgotten.

Class

E (1-12) = {80, 85, … 130, 135}

N = 12

n = 4g/n = 0.5T = 80

No NEE, not even considering that the strategy space is discrete Only a ZEE, a pure-mixed strategy eqm not yet fully excluded

Conclusions

Experimental subject respond in a natural, efficient and predictable way to contribution-based organization (policy?) – and they respond as “homini economici”

Subjects respond to differences based on ability (Rousseau: “products of nature”) and aim to maintain and exploit positions that stem from these differences

Aggregates of subjects are capable of tacit coordination to much larger extent than previously realized (How?)