Experimental evidence of the emergence of aesthetic rules

in pure coordination games

Federica Alberti (Uea)Creed/Cedex/Uea Meeting

Experimental Economics 2008 Amsterdam, June 6

Introduction and motivation

• The evidence of behaviour in Schelling’s pure coordination experiments (see e.g. Schelling 1960, Mehta et al. 1994) is that people use pre-existing notions of salience, which have cultural content e.g. “Heads” in “Heads and Tails”, and which are general i.e. apply across a family of games.

• What hasn’t been investigated is how these notions of salience emerge.

The experiment

• I investigate experimentally how concepts of salience emerge in repeated play.

• A new feature of the experiment is that two players face a series of similar but not identical pure coordination games.

• In a game, each player faces the same set of 4 images and chooses one of them. Each is rewarded if and only if they both choose the same image.

• The main interest is in “abstract games”, in which images are chequered arrays of colours and the combinations of colours change from one game to another. But, for control, there are also “culture-laden games”, in which images are fabric patterns from the same set of 4 styles and paintings by the same 4 artists.

• In repeated “abstract games”, it may be possible for players to develop rules, applicable across games, for identifying salience.

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Example of an abstract game

Example of a culture-laden game

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Outline of the presentation

• Research questions• Experimental games• Structure of the experiment• Experimental procedures• Experimental results• Conclusions

Research questions

1) Do people coordinate more than randomly?2) Do they learn to coordinate more with experience…?

i) … e.g. within “abstract games”?ii) … e.g. from “culture-laden games”?

3) Do they coordinate prior to repetition? 4) Do some groups of players exhibit a better capacity?5) Do different groups of players learn different rules?6) Do players choose “what they like”?

Experimental games

• There are 2 types of games: “abstract”, with randomly-generated images, and “culture-laden”, with images of fabric patterns from a set of 4 styles and paintings from a set of 4 artists.

• There are 20 “abstract games” and 20 “culture-laden games”. Both these are

divided into blocks of 5 games.

• In a “culture-laden” block, images share a common feature. Each image has one of

four features (artist or style), and each game has one image with each feature. Thus,if players recognize these features, it is possible to use a rule, i.e. “Choose stylex”, which applies to all games in a block.

• In abstract games, no features are built into the design.

Image 1 Image 2 Image 3 Image 4

Game 1

Game 2

Game 3

Game 4

Game 5

Example of a culture-laden block

http://www.reproductionfabrics.com

Image 1 Image 2 Image 3 Image 4

Game 1

Game 2

Game 3

Game 4

Game 5

Example of an abstract block

Structure of the experiment

• Each subject plays the same 4 blocks of 5 “abstract games” + the same 4 blocks of 5 “culture-laden games” with the same (anonymous) co-player. Feedback is given at the end of each game.

• The order of playing games varies across pairs. In particular, the order of games varies at two levels: 1) treatment (therefore the two treatments: “abstract-first” and “culture-first”), and 2) block, where the order of blocks is randomised, as well as the order of tasks within a block.

• The experiment is divided into 2 equal parts. Each part includes 4 blocks of coordination tasks and 2 identical set of questionnaires. One questionnaire is presented at the outset of the sequence of coordination tasks and the other is presented at the end of the sequence of tasks.

• The questionnaires relate to the sets of images displayed in the coordination tasks, in particular the tasks presented in the first and last round of each block (the same for all players).

• Each questionnaire consists of 4 images and 2 questions. The questions are: 1) “what do you like most?” = “primary salience hypothesis” (Mehta et al 1994, p. 660-61), and 2) “what do you think the other person likes most?” = “secondary salience hypothesis” (Mehta et al 1994, p. 660-61).

1st part

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Layout of the experiment

Experimental procedures

• 118 subjects, both undergraduate and postgraduate students from the University of East Anglia, participated in 9 experimental sessions: 5 under the “abstract-first” treatment, and 4 under the “culture-first” treatment, with group size in a session ranging from 12 to 18 people. Random pairings…

“Welcome! With this experiment we are interested in how far people are able to coordinate their behaviour without communicating each other. This is how the experiment will work. You’ve been paired with another person in this room. These pairings have been made at random. You don’t know and will never know who you have been paired with. We will show you 4 pictures on this screen and ask you to choose one. The person you’ve been paired with will be shown the same 4 pictures but not necessarily in the same order. Your objective is to choose the same picture as the person you’ve been paired with. You will be asked to do this a total of 40 times, made up by 8 different blocks of 5 choice problems. You will score one point for every time you choose the same as the person you have been paired with.”

• The instructions also explained that a pool of £ [10 no. of participants] would be divided between the pairs in a session, each subject’s payment being proportional to the number of points scored by a subject’s pair relative to the number of points scored by all pairs.

• See a sample of a possible coordination problem and its feedback.

Choice Problem

Choose one picture by clicking the circle button below, then submit.

Submit

Didn't match... try again!

Other’s choice

Your choice

Proceed

Main result 1: Overall coordination > randomness

Distribution of outcomes (abstract games)

00,020,040,060,080,1

0,120,140,160,180,2

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a. Mean: 0392 a. Mean : 0369 b. Median: 0.350 b. Median: 0.350

c. Minimum: 0.150 c. Minimum: 0.050 d. Maximum: 0.800 d. Maximum: 0.950 e. Random: 0.250 e. Random: 0.250

Mean > Random Mean > Random (2 test, p<0.01) (2 test, p<0.01)

Distribution of outcomes (culture-laden games)

00,020,040,060,080,1

0,120,140,160,180,2

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Variable Description Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7

Match (Dependent)

1 if coordinate successfully;0 otherwise

Match-1 1 if coordinated successfully in the previous round; 0 otherwise

Second 1 if the game is in the second part; 0 otherwise

Culture 1 if the game is “culture-laden”; 0 otherwise

Round number of games of the same type (1-20)

0.0088378(0.129)

0.0077144(0.222)

0.0093822(0.163)

0.010072(0.163)

0.00991(0.238)

Block number of games of the same type within a block (1-5)

0.0468335(0.014)

0.048344(0.011)

0.0424828(0.029)

0.0424978(0.029)

0.0357165(0.098)

0.0324627(0.191)

0.0332161(0.297)

Secondround second*round 0.0093658(0.040)

0.0115288(0.019)

0.0086065 (0.103)

0.0113286(0.154)

0.0108874(0.172)

0.0087768(0.436)

0.0089346(0.457)

Secondblock second*block 0.0101172(0.791)

0.0093406(0.829)

Culturound culture*round -0.0057613 (0.240)

-0.0086272(0.100)

-0.0059958(0.440)

-0.0064269(0.410)

-0.0063907(0.412)

-0.0060441(0.616)

Culturblock culture*block -0.0016591(0.970)

Cultursecondround culture*second*round -0.0055931(0.646)

-0.0101645(0.460)

-0.008809(0.548)

-0.0091455(0.594)

Cultursecondblock culture*second*block 0.024904(0.471)

0.0178896(0.681)

0.0196016(0.755)

Secondmatch-1 second*match-1 0.4108559(0.000)

0.3676249(0.000)

0.3649547(0.000)

0.3517001(0.001)

0.3547181(0.001)

0.3506156(0.001)

0.3505908(0.001)

Culturmatch-1 culture*match-1 0.2294765(0.031)

0.2765204(0.015)

0.2738692(0.016)

0.2615261 (0.025)

.2654155(0.023)

0.2678935(0.022)

0.2685164(0.023)

Cultusecondmatch-1 culture*second*match-1 -0.4369601(0.010)

-0.4174866(0.014)

-0.3763963(0.028)

-0.3420521(0.068)

-0.3625353(0.055)

-0.3611437(0.056)

-0.3616929(0.057)

Constant -0.584125(0.000)

-0.5714474(0.000)

-0.6195799(0.000)

-0.618612(0.000)

-0.6177031(0.000)

-0.6173773(0.000)

-0.6174151(0.000)

Log likelihood -1532.1514 -1531.4605 -1530.3072 -1530.2018 -1529.9424 -1529.9073 -1529.9066

No. Observations 2360 2360 2360 2360 2360 2360 2360

Main result 2: Evidence of learning within blocks, within types, within pairsRandom effects probit regression results:

a. p-values are shown in brackets

Main result 3: Coordination prior to repetition=randomness

coordination in the 1st part

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coordination in the 2nd part

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a. (0.584125)=0.279568

b. se()=0.023882341 (Delta method) c. t 1.238 < t0.05=1.645 (1-tailed)

Main result 4: Evidence of differences between pairs

Binomial distribution and atual distribution of outcomes (abstract games)

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binomial actual

Binomial distribution and actual distribution of outcomes (culture-laden games)

00,020,040,060,080,1

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binomial actual

a. Binomial distribution, with p=0.392 a. Binomial distribution, with p=0.369

Actual ≠ Binomial Actual = Binomial (2 test, p<0.01) (2 test, p>0.05)

Main result 5: Evidence that different pairs use different rules

Distribution of average outcomes (bootstrap, abstract, best)

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Distribution of average outcomes (bootstrap, abstract, w orse)

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Distribution of average outcomes (bootstrap, culture, best)

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Distribution of average outcomes (boostrap, culture, w orse)

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a. f0.050.174<0.526 (actual) a. f0.050.1275<0.498 (actual)

a. f0.050.1665<0.278 (actual) a. f0.050.1665<0.278 (actual)

Main result 6: Players choose “what they like”

a. You like before: Average=0.519; St Dev=0.086 b. Other likes before: Average=0.440; St Dev=0.096 c. Random=0.250

a. You like before: Average=0.589; St Dev=0.100 b. Other likes before: Average=0.478; St Dev=0.099 c. Random=0.250

a. You like before: Average=0.410; St Dev=0.074 b. Other likes before: Average=0.357; St Dev=0.080 c. Random=0.250

a. You like before: Average=0.517; St Dev=0.074 b. Other likes before: Average=0.455; St Dev=0.072 c. Random=0.250

Additional results from the questionnaires

Better-performing players choose “what they like” more than others. Better-performing players have more similar tastes compared to others. Better-performing players are as “aesthetically attuned” as others.

Additional results about rules

“Styles” and “artists” are used as rules in culture-laden games. Colour-based rules, e.g. “Choose the bluish”, are developed in abstract

games.

Conclusions

• Schelling’s earlier experiments are well known, and the conclusions following the results of those experiments have been accepted as models of coordination. However, the question of such coordination is achieved in such one-shot coordination games has not been explored. This experiment investigates how people learn rules for identifying focal points solutions of pure coordination games.

• The results show that people are capable of learning rules over a class of different but related problems. A comparison between play in “abstract games” and “culture-laden games” shows that coordination is not only explained by the use of pre-existing rules, i.e. “common features” in culture-laden blocks, but also the learning of new associations of ideas connecting images in one game to another in “abstract games”. I find evidence that rules are learned by experience of pairs of subjects within blocks of different but related problems, and that experience of problems of one type i.e. “culture-laden” can help subjects to coordinate in another type i.e. “abstract”.

• The results also show the following: i) different pairs seem to learn different rules, which may explain why salience is culturally specific; ii) some pairs exhibit a better capacity of coordinating actions, which may be due to either “luck” (e.g. when the two players like the same objects) and/or better coordination skills (e.g. when the two players choose what they like); iii) the rules learned are related to “personal favourites”, especially “what players like” (although the frequency of choices of “what people like” is declining over time).