Can Social Group-Formation Norms Influence Behavior?: An - - PowerPoint PPT Presentation

Can Social Group-Formation Norms Influence Behavior?: An Experimental Study

Alexandros Rigos

Lund University

Lund Brown Bag Seminar 2017-03-31

Alex Rigos (Lund) Social Group-Formation Norms Title

Motivation

Evolutionary Game Theory: More successful strategies evolve faster than less successful ones. (Maynard Smith and Price, 1973)

Alex Rigos (Lund) Social Group-Formation Norms 1 / 34

Motivation

Evolutionary Game Theory: More successful strategies evolve faster than less successful ones. (Maynard Smith and Price, 1973) Usual assumption: random matching.

Alex Rigos (Lund) Social Group-Formation Norms 1 / 34

Motivation

Evolutionary Game Theory: More successful strategies evolve faster than less successful ones. (Maynard Smith and Price, 1973) Usual assumption: random matching. But people do not meet at random.

Alex Rigos (Lund) Social Group-Formation Norms 1 / 34

Motivation

Evolutionary Game Theory: More successful strategies evolve faster than less successful ones. (Maynard Smith and Price, 1973) Usual assumption: random matching. But people do not meet at random. What if individuals meet similarly behaved ones more often?

Alex Rigos (Lund) Social Group-Formation Norms 1 / 34

Motivation

Evolutionary Game Theory: More successful strategies evolve faster than less successful ones. (Maynard Smith and Price, 1973) Usual assumption: random matching. But people do not meet at random. What if individuals meet similarly behaved ones more often? Such “assortative” group-formation norm would affect long-run

• utcomes (e.g. it can support cooperation in a PD).

Alex Rigos (Lund) Social Group-Formation Norms 1 / 34

Motivation

Evolutionary Game Theory: More successful strategies evolve faster than less successful ones. (Maynard Smith and Price, 1973) Usual assumption: random matching. But people do not meet at random. What if individuals meet similarly behaved ones more often? Such “assortative” group-formation norm would affect long-run

• utcomes (e.g. it can support cooperation in a PD).

We test the predictions of nonrandom matching models in a game of aggression (Hawk/Dove).

Alex Rigos (Lund) Social Group-Formation Norms 1 / 34

Motivation

Questions

If there was such assortative matching in place, would it actually change participants’ behaviour?

Alex Rigos (Lund) Social Group-Formation Norms 2 / 34

Motivation

Questions

If there was such assortative matching in place, would it actually change participants’ behaviour? How quickly do participants adapt under different matching regimes?

Alex Rigos (Lund) Social Group-Formation Norms 2 / 34

Motivation

Questions

If there was such assortative matching in place, would it actually change participants’ behaviour? How quickly do participants adapt under different matching regimes? How do they learn?

Alex Rigos (Lund) Social Group-Formation Norms 2 / 34

Motivation

Questions

If there was such assortative matching in place, would it actually change participants’ behaviour?

Answer: Yes!

How quickly do participants adapt under different matching regimes? How do they learn?

Alex Rigos (Lund) Social Group-Formation Norms 2 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Deviations from random matching

Kin selection (Hamilton, 1964).

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Deviations from random matching

Kin selection (Hamilton, 1964). Local interactions (Boyd and Richerson, 2002).

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Deviations from random matching

Kin selection (Hamilton, 1964). Local interactions (Boyd and Richerson, 2002). Homophily (Alger and Weibull, 2011).

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Deviations from random matching

Kin selection (Hamilton, 1964). Local interactions (Boyd and Richerson, 2002). Homophily (Alger and Weibull, 2011). Meritocracy (action assortativity) (Nax, Murphy, and Helbing, 2014).

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Deviations from random matching

Kin selection (Hamilton, 1964). Local interactions (Boyd and Richerson, 2002). Homophily (Alger and Weibull, 2011). Meritocracy (action assortativity) (Nax, Murphy, and Helbing, 2014).

Jensen and Rigos, (2014) generalize nonrandom matching rules.

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Evolutionary Game Theory (EGT)

Standard: Individuals meet at random. No support for pro-social behaviour.

Deviations from random matching

Kin selection (Hamilton, 1964). Local interactions (Boyd and Richerson, 2002). Homophily (Alger and Weibull, 2011). Meritocracy (action assortativity) (Nax, Murphy, and Helbing, 2014).

Jensen and Rigos, (2014) generalize nonrandom matching rules. Different matching rules lead to different evolutionary outcomes.

Alex Rigos (Lund) Social Group-Formation Norms 3 / 34

Background

Related Experiments Friedman and Oprea, (2011) and Oprea, Henwood, and Friedman, (2011) look at similar evolutionary setup in the lab in continuous time with random matching. They find fast convergence to theoretical predictions (Nash equilibrium). Yang, Yue, and Yu, (2007) show experimentally that assortative matching based on past actions increases cooperation in PD games. Nax et al., (2015) study public goods games under meritocratic matching. High levels of contributions are sustained.

Alex Rigos (Lund) Social Group-Formation Norms 4 / 34

Background

Related Experiments Friedman and Oprea, (2011) and Oprea, Henwood, and Friedman, (2011) look at similar evolutionary setup in the lab in continuous time with random matching. They find fast convergence to theoretical predictions (Nash equilibrium). Yang, Yue, and Yu, (2007) show experimentally that assortative matching based on past actions increases cooperation in PD games. Nax et al., (2015) study public goods games under meritocratic matching. High levels of contributions are sustained. What about other types of games?

Alex Rigos (Lund) Social Group-Formation Norms 4 / 34

Theoretical Concepts

The Game

There is a population of individuals.

Alex Rigos (Lund) Social Group-Formation Norms 5 / 34

Theoretical Concepts

The Game

There is a population of individuals. Each individual can follow one of two strategies: H or D.

Alex Rigos (Lund) Social Group-Formation Norms 5 / 34

Theoretical Concepts

The Game

There is a population of individuals. Each individual can follow one of two strategies: H or D. At each time t they are drawn to form pairs (1-population matching protocol).

Alex Rigos (Lund) Social Group-Formation Norms 5 / 34

Theoretical Concepts

The Game

There is a population of individuals. Each individual can follow one of two strategies: H or D. At each time t they are drawn to form pairs (1-population matching protocol). Each individual in each pair gets payoff according to HD game. Dove Hawk Dove 11,11 5,17 Hawk 17,5 2,2

Table: (Adapted from Oprea, Henwood, and Friedman, (2011))

Alex Rigos (Lund) Social Group-Formation Norms 5 / 34

Theoretical Concepts

The Game

There is a population of individuals. Each individual can follow one of two strategies: H or D. At each time t they are drawn to form pairs (1-population matching protocol). Each individual in each pair gets payoff according to HD game. Dove Hawk Dove 11,11 5,17 Hawk 17,5 2,2

Table: (Adapted from Oprea, Henwood, and Friedman, (2011))

Assumption: More successful strategies have more followers next round (because of imitation, replicator dynamics).

Alex Rigos (Lund) Social Group-Formation Norms 5 / 34

Theoretical Concepts

Matching Protocols

Say at time t there are (proportions of) xD Doves and xH Hawks in the population.

Alex Rigos (Lund) Social Group-Formation Norms 6 / 34

Theoretical Concepts

Matching Protocols

Say at time t there are (proportions of) xD Doves and xH Hawks in the population. Random matching: both Doves and Hawks have the same probability to get matched to a Dove (pDD = pHD = xD).

Alex Rigos (Lund) Social Group-Formation Norms 6 / 34

Theoretical Concepts

Matching Protocols

Say at time t there are (proportions of) xD Doves and xH Hawks in the population. Random matching: both Doves and Hawks have the same probability to get matched to a Dove (pDD = pHD = xD). Assortative matching: pDD −pHD = α (Index of Assortativity).

Alex Rigos (Lund) Social Group-Formation Norms 6 / 34

Theoretical Concepts

Matching Protocols

Say at time t there are (proportions of) xD Doves and xH Hawks in the population. Random matching: both Doves and Hawks have the same probability to get matched to a Dove (pDD = pHD = xD). Assortative matching: pDD −pHD = α (Index of Assortativity). Doves (Hawks) have a higher probability to meet a Dove (Hawk) than Hawks (Doves).

Alex Rigos (Lund) Social Group-Formation Norms 6 / 34

Theoretical Concepts

Matching Protocols

Say at time t there are (proportions of) xD Doves and xH Hawks in the population. Random matching: both Doves and Hawks have the same probability to get matched to a Dove (pDD = pHD = xD). Assortative matching: pDD −pHD = α (Index of Assortativity). Doves (Hawks) have a higher probability to meet a Dove (Hawk) than Hawks (Doves). For this experiment we use a matching rule with α = 0.3.

Alex Rigos (Lund) Social Group-Formation Norms 6 / 34

Theoretical Concepts

Theoretical Predictions

Continuum population

Random matching ⇒ Unique symmetric NE/ESS: x∗

D ≃ 0.33.

Nonrandom matching ⇒ Unique symmetric NE/ESS: x∗

D = 1+2α 3−3α.

We use an α = 0.3 ⇒ x∗

D ≃ 0.76.

Finite populations (size n): Unique symmetric equilibrium

x∗

D = n(1 +2α) +2(1 − α)

n(3 −4α) −3(1 − α) n = 12,α = 0 → xrand

D

= 14

33 ≃ 0.42

n = 12,α = 0.3 → xassort

D

= 206

231 ≃ 0.89

Alex Rigos (Lund) Social Group-Formation Norms 7 / 34

Experimental Design

Experimental Design

12 subjects in each session. They represent a population. They repeat the same task for 60 rounds. We use a method with two urns and colored balls for the implementation

• f the matching rule.

Alex Rigos (Lund) Social Group-Formation Norms 8 / 34

Experimental Design

Choice Screen

Alex Rigos (Lund) Social Group-Formation Norms 9 / 34

Experimental Design

The Matching Process

There are two urns as seen above: One which is blue and one which is red. After all participants have made a choice, for each participant 10 balls are going to be put into each of the two urns.

Alex Rigos (Lund) Social Group-Formation Norms 10 / 34

Experimental Design

Filling the Urns (1)

The following process takes place for each of the participants.

1

Firstly, 10 balls of the colour of the participant’s choice are put into the urn that has the same colour.

Alex Rigos (Lund) Social Group-Formation Norms 11 / 34

Experimental Design

Example

One participant chose Blue and 10 blue balls are put into the blue urn.

Alex Rigos (Lund) Social Group-Formation Norms 12 / 34

Experimental Design

Filling the Urns (2)

2

Then, 7 balls that have the same colour as the participant’s choice and 3 balls of the other colour are going to be put into the other urn (the one that has a colour different than the participant’s choice).

Alex Rigos (Lund) Social Group-Formation Norms 13 / 34

Experimental Design

Example

7 blue balls and 3 red balls are put into the red urn.

Alex Rigos (Lund) Social Group-Formation Norms 14 / 34

Experimental Design

Second participant

A different participant chose Red and so, 10 red balls are put into the red urn and 7 red balls and 3 blue balls are put into the blue urn.

Alex Rigos (Lund) Social Group-Formation Norms 15 / 34

Experimental Design

Third participant

A third participant chose Blue and so 10 blue balls are put into the blue urn whereas 7 blue balls and 3 red balls are put into the red urn.

Alex Rigos (Lund) Social Group-Formation Norms 16 / 34

Experimental Design

The process is being repeated for the rest of the participants until all 12 participants’ actions have been accounted for.

Alex Rigos (Lund) Social Group-Formation Norms 17 / 34

Experimental Design

56/120 64/120 92/120 28/120

Alex Rigos (Lund) Social Group-Formation Norms 18 / 34

Experimental Design

56/120 64/120 92/120 28/120

In the random matching treatment, 10 balls of the color of the participant’s choice are put into each of the two urns.

Alex Rigos (Lund) Social Group-Formation Norms 18 / 34

Experimental Design

Payoff Determination

Participants receive payoffs depending on their choice and the colour of the ball that is drawn for them according to the following table: Ball Drawn Red Blue Choice Red 11 5 Blue 17 2

Alex Rigos (Lund) Social Group-Formation Norms 19 / 34

Experimental Design

Feedback

Alex Rigos (Lund) Social Group-Formation Norms 20 / 34

Results

Experiment took place in BEEL (Birmingham) during 18-22/03/2013. 96 participants took part in 8 sessions (4 for each treatment). Participants were paid £19.74 on average including a show-up fee of £2.50.

Alex Rigos (Lund) Social Group-Formation Norms 21 / 34

Results

2 4 6 8 10 12 10 20 30 40 50 60 Doves t

(a) Random Treatment

2 4 6 8 10 12 10 20 30 40 50 60 Doves t

(b) Assortative Treatment

Alex Rigos (Lund) Social Group-Formation Norms 22 / 34

Results

0.2 0.4 0.6 0.8 1 10 20 30 40 50 60 Choice t Assortative Treatment Random Treatment 50/50 Assortative Equilibrium Random Equilibrium

Alex Rigos (Lund) Social Group-Formation Norms 23 / 34

Results

1st Period

As no feedback has been given yet, we can consider the first period to be a proxy of how people would play the game if it were one-off.

Alex Rigos (Lund) Social Group-Formation Norms 24 / 34

Results

1st Period

As no feedback has been given yet, we can consider the first period to be a proxy of how people would play the game if it were one-off. The choices of the subjects in the two treatments are compared with each

• ther. The null is that both samples are drawn from the same distribution.

Alex Rigos (Lund) Social Group-Formation Norms 24 / 34

Results

1st Period

As no feedback has been given yet, we can consider the first period to be a proxy of how people would play the game if it were one-off. The choices of the subjects in the two treatments are compared with each

• ther. The null is that both samples are drawn from the same distribution.

Mann-Whitney-Wilcoxon rank-sum test: p = 0.0255.

Alex Rigos (Lund) Social Group-Formation Norms 24 / 34

Results

1st Period

As no feedback has been given yet, we can consider the first period to be a proxy of how people would play the game if it were one-off. The choices of the subjects in the two treatments are compared with each

• ther. The null is that both samples are drawn from the same distribution.

Mann-Whitney-Wilcoxon rank-sum test: p = 0.0255. Robust Rank-order Test yields similar results: ` U = 2.2606 (significant at the 5% level).

Alex Rigos (Lund) Social Group-Formation Norms 24 / 34

Results

1st Period

As no feedback has been given yet, we can consider the first period to be a proxy of how people would play the game if it were one-off. The choices of the subjects in the two treatments are compared with each

• ther. The null is that both samples are drawn from the same distribution.

Mann-Whitney-Wilcoxon rank-sum test: p = 0.0255. Robust Rank-order Test yields similar results: ` U = 2.2606 (significant at the 5% level).

⇒ reject the null at the 5% significance level.

Alex Rigos (Lund) Social Group-Formation Norms 24 / 34

Results

All Periods

For each session k, we construct the variable:

αk = 60

t=1

12

i=1 CHOICEk it

60

Alex Rigos (Lund) Social Group-Formation Norms 25 / 34

Results

All Periods

For each session k, we construct the variable:

αk = 60

t=1

12

i=1 CHOICEk it

60 Mann-Whitney-Wilcoxon rank-sum test: p = 0.0209.

Alex Rigos (Lund) Social Group-Formation Norms 25 / 34

Results

All Periods

For each session k, we construct the variable:

αk = 60

t=1

12

i=1 CHOICEk it

60 Mann-Whitney-Wilcoxon rank-sum test: p = 0.0209. Robust Rank-order Test yields similar results: ` U = ∞ (significant at the 5% level).

Alex Rigos (Lund) Social Group-Formation Norms 25 / 34

Results

All Periods

For each session k, we construct the variable:

αk = 60

t=1

12

i=1 CHOICEk it

60 Mann-Whitney-Wilcoxon rank-sum test: p = 0.0209. Robust Rank-order Test yields similar results: ` U = ∞ (significant at the 5% level). Again, we can reject the null at the 5% significance level.

Alex Rigos (Lund) Social Group-Formation Norms 25 / 34

Results

Learning

We test whether the subjects act differently between the first 10 rounds and the final 10 rounds of the session. We do so by treatment.

Random Treatment: Mann-Whitney-Wilcoxon: p = 0.5006. Assortative Treatment: Mann-Whitney-Wilcoxon: p = 0.0012.

The subjects seem to change behaviour only in the assortative treatment. Random treatment close to equilibrium from the beginning.

Alex Rigos (Lund) Social Group-Formation Norms 26 / 34

Results

Learning Models

We want to evaluate 2 different learning models in our setting. Reinforcement learning à la Roth and Erev, (1995)

Probabilistic Payoff by an action increases the probability to follow that action.

SV payoff assessment learning (Sarin and Vahid, 1999, 2001)

Deterministic. Choose the action with the higher assessment, update with “strength” λ.

Alex Rigos (Lund) Social Group-Formation Norms 27 / 34

Results

Learning (Simulations)

We take averages over 800 simulations for each treatment. Then fit the results to the data so as to determine the parameters by minimizing Mean Squared Distance (MSD).

Alex Rigos (Lund) Social Group-Formation Norms 28 / 34

Results

Learning (Simulations)

We take averages over 800 simulations for each treatment. Then fit the results to the data so as to determine the parameters by minimizing Mean Squared Distance (MSD).

Random Assortative Model Param Value MSD (×100) Value MSD (×100) Random choice – – 0.2668 – 2.2851 Equilibrium – – 0.1253 – 6.1450 Reinforcement s(1) 15.891 0.1887 0.522 0.1006 SV

λ

0.007 0.2172 0.128 0.0475

Alex Rigos (Lund) Social Group-Formation Norms 28 / 34

Results

Reinforcement Learning, Random Treatment

10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Period Choice

Actual Choices Simulation Equilibrium Random Choice Alex Rigos (Lund) Social Group-Formation Norms 29 / 34

Results

Reinforcement Learning, Assort. Treatment

10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Period Choice

Actual Choices Simulation Equilibrium Random Choice Alex Rigos (Lund) Social Group-Formation Norms 30 / 34

Results

SV Learning, Random Treatment

10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Period Choice

Actual Choices Simulation Equilibrium Random Choice Alex Rigos (Lund) Social Group-Formation Norms 31 / 34

Results

SV Learning, Assort. Treatment

10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Period Choice

Actual Choices Simulation Equilibrium Random Choice Alex Rigos (Lund) Social Group-Formation Norms 32 / 34

Conclusion

Conclusion

Tested what effect different group-formation rules can have in behavior.

It is clear that different group-formation rules affect participants’ behavior. Increased assortativity induces lower aggression levels which is consistent with theoretical predictions.

Evidence for (slow) convergence towards equilibrium behavior. We evaluated the predictions of learning models.

Reinforcement Learning does better in the Random matching treatment. SV does better in the Assortative treatment.

Alex Rigos (Lund) Social Group-Formation Norms 33 / 34

Future Work

Theory: How can assortative matching norms come to existence? (Evolutionary axiomatisation – endogenisation)

Nax and Rigos (2016) is a start.

Experiments: Test the evolution of such (endogenous) matching norms-rules experimentally.

Alex Rigos (Lund) Social Group-Formation Norms 34 / 34