# Mathematical network model for the ‘Battle of the Sexes’ experimentally tested

Why is it easier to bridge conflicting interests in one neighbourhood than in another? Social scientists think that the residents' social networks may play an important role in the answer to this question. In 2017, sociologists and theoretical physicists from Utrecht University presented the theoretical model for this complex problem. In a follow up study, the researchers tested the predictions made by the theoretical model in an experiment with 240 human subjects. The results of the experiment were recently published in Scientific Reports

## Battle of the Sexes

In game theory, the 'Battle of the Sexes' represents a situation in which people like to agree on options in the first place, but some people prefer one option more than the other. This situation is called 'Battle of the Sexes' based on a suggested story in which a man prefers to go to a sports game, while a woman prefers to go to the theatre. However, both would rather do something together than alone. The situation becomes of interest when people have to decide where to go independently from one another. The researchers have shown theoretically how different social network structures have different effects on overcoming conflicts of interest. Their results were published in Scientific Reports in 2017.

Computerized lab experiment
In the follow up study, the researchers tested predictions made by the theoretical model in a computerized lab experiment. During the experiment, groups of 20 people played the game Battle of the Sexes with other participants with whom they were connected through a network. The participants were asked to make a choice between the options 'blue' and 'yellow'. The participants could earn money if their choice corresponded with the choice of the participant they were connected to. However, some participants got more money if they coordinated their choice on 'blue', while others got more money when they coordinated on 'yellow'. Participants received nothing if one chose `blue’ and the other participant chose 'yellow'. So the game has both an element of coordination and an element of competition.

## Empirical validation

The theoretical study published before showed that what the group ends up choosing can be predicted by the properties of the network. The results of the experiment are very much in line with the predictions of the computational model. Some general results are, as expected, that the less 'random' the network structure, the more the experimental results are in line with the predictions of the computational models. The found correlation of behaviour between the computational model and the experimental results is low for a random network, intermediate for clustered 'small world' networks, and high for centralised 'preferential attachment' networks. Furthermore, clustering of the network leads to higher heterogeneity of choices. And some participants, mostly in the more centralised networks, clearly have more influence on the choices made in the network overall.