Experimental evidence of the emergence of aesthetic rules in pure coordination games Federica Alberti University of East Anglia ESA World Meeting 2007 Rome, June 30

Introduction and motivation The evidence of behaviour in Schelling’s pure coordination games (e.g. Schelling 1960, Mehta et al 1994) is that people use pre-existing concepts of salience, which have cultural content e.g. “Head” in “Head or tail?”, and which are general i.e. apply across a family of games. What hasn’t been investigated is how these concepts emerge.

Our experiment We investigate experimentally how concepts of salience emerge in repeated play. A new feature of our experiment is that two players play 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; but for control, there are also “culture-laden games”, in which images areculture-laden games fabrics 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.

Outline of the presentation Research questions Experimental design 1: Games Experimental design 2: Structure Experimental design 3: Procedures Experimental results Discussion and conclusion

Research questions 1)Are people able to coordinate (more than if they chose randomly)? a)Are they capable of coordinating prior to repetition? b)Can they learn to coordinate? i) … e.g. within “abstract games”? ii) … e.g. from “culture-laden games”? 2)Is learning pair-specific? 3)Do some players exhibit a better capacity? 4)Do players choose what they like?

Experimental design 1: Games There are two 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 feature x”) which applies to all games in a block. In abstract games, no features are built into the design.no features

Experimental design 2: Structure 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 tasks varies across pairs. In particular, the order of tasks 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 coordination2 equal parts tasks and 2 identical set of questionnaires. One questionnaire is presented at the outset of the sequence of coordination tasks and the other 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” (Mehta et al 1994, p ), and 2) “what do you think the other person likes most?” = “secondary salience” (Mehta et al 1994, p ).

Experimental design 3: 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. See a sample of a possible coordination problem and its feedback.coordination problem feedback

Main results 1)Overall coordination > randomness i.e Overall coordination  for “abstract games”, the rate of success is 0.392;  for “culture-laden games”, the rate of success is 0.369; 1a)There is evidence of learning (time series; probit; all; fitted)time seriesprobitallfitted i) within blocks of “abstract games” (and “culture-laden games”); ii) within the series of “abstract games” (and “culture-laden games”); iii) between the two types, especially in the “culture-first” treatment… 1b)Coordination prior to learning = randomnessCoordination prior  in “abstract games”, the probability of matching at the outset is 0.279;  in “culture-laden games”, the probability of matching at the outset is 0.279; 2)Evidence of pair-specific learning (bootstrap)  in “abstract games”, (=actual)>0.320 (=simulated)>0.250 (=random);abstract games  in “culture-laden games”, (=actual)>0.318 (=simulated)>0.250 (=random);culture-laden games 3)Some pairs perform better than others (binomial)binomial  in “abstract games” (see distribution);distribution  not in “culture-laden games” (see distribution);distribution 4)Predominant method of coordination is “primary salience”, although the frequency ofprimary salience “primary-salient” choices is declining (especially within blocks).

Additional results from the questionnaires  Best-performing pairs use “primary salience” more than others.  Best-performing pairs have more similar tastes compared with others.  Best-performing pairs 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 blue”) are developed in “abstract games”.

Conclusions Schelling’s earlier experiments are well known, and the conclusions following the results of those experiments have been widely accepted as models of coordination. However, the question of how concepts of salience emerge in Schelling games has not been explored. Our experiment investigates the emergence of the cultural rules of salience used in Schelling games. Our results show that people are capable of learning rules over a class of 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, like “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”. We find evidence that rules are learned by experience of pairs of subjects within blocks of related problems, and that experience of problems of one type i.e. “culture-laden” can significantly improve coordination in another type i.e. “abstract” by teaching generic coordination skills. The results also show the following: i) learning is pair-specific, 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” and/or better skills; iii) the rules learned are based on “personal favourites”, which may account for the individual basis of aesthetic concepts.