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 ofabstract games 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 patternsculture-laden games 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.

○ ○ ○○ Example of an abstract game

Example of a culture-laden game ○○ ○○

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 ofcommon feature 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 style x”, which applies to all games in a block. In abstract games, no features are built into the design.no features

Image 1 Image 2 Image 3 Image 4 Game 1 Game 2 Game 3 Game 4 Game 5 Example of a culture-laden block

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.2 equal parts 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 ), and 2) “what do you think the other person likes most?” = “secondary salience hypothesis” (Mehta et al 1994, p ).

1 st part 8 Questionnaires 2 nd part 8 Questionnaires 1st Block of 5 tasks 8 Questionnaires 2nd Block of 5 tasks 3rd Block of 5 tasks 4th Block of 5 tasks 1st Block of 5 tasks 2nd Block of 5 tasks 3rd Block of 5 tasks 4th Block of 5 tasks 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.coordination problem feedback

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

Didn't match... try again! Other’s choice Your choice

Main result 1: Overall coordination > randomness a. Mean: 0392 a. Mean : 0369 b. Median: b. Median: c. Minimum: c. Minimum: d. Maximum: d. Maximum: e. Random: e. Random: Mean > Random Mean > Random (  2 test, p<0.01)(  2 test, p<0.01)

VariableDescriptionModel 1Model 2Model 3Model 4Model 5Model 6Model 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) (0.129) (0.222) (0.163) (0.163) (0.238) Block number of games of the same type within a block (1-5) (0.014) (0.011) (0.029) (0.029) (0.098) (0.191) (0.297) Secondroundsecond*round (0.040) (0.019) (0.103) (0.154) (0.172) (0.436) (0.457) Secondblocksecond*block (0.791) (0.829) Culturoundculture*round (0.240) (0.100) (0.440) (0.410) (0.412) (0.616) Culturblockculture*block (0.970) Cultursecondroundculture*second*round (0.646) (0.460) (0.548) (0.594) Cultursecondblockculture*second*block (0.471) (0.681) (0.755) Secondmatch-1second*match (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) (0.001) Culturmatch-1culture*match (0.031) (0.015) (0.016) (0.025) (0.023) (0.022) (0.023) Cultusecondmatch-1culture*second*match (0.010) (0.014) (0.028) (0.068) (0.055) (0.056) (0.057) Constant (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Log likelihood No. Observations2360 Main result 2: Evidence of learning within blocks, within types, within pairs Random effects probit regression results: a. p-values are shown in brackets

Main result 3: Coordination prior to repetition=randomness a.  (  )= b. se(  )= (Delta method) c. t  < t 0.05 =1.645 (1-tailed)

Main result 4: Evidence of differences between pairs a. Binomial distribution, with p=0.392 a. Binomial distribution, with p=0.369 Actual ≠ Binomial Actual = Binomial (  2 test, p 0.05)

Main result 5: Evidence that different pairs use different rules a. f 0.05  0.174<0.526 (actual) a. f 0.05  <0.498 (actual) a. f 0.05  <0.278 (actual) a. f 0.05  <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).