Mathematical models analyze competition among companies for consumers

Study applies game theory to understand market behavior in which companies try to attract consumers who are influenced by group decisions.

By Diego Freire

Agência FAPESP – On the basis of game theory and other mathematical models, researchers from the Riberão Preto Faculty of Philosophy, Science and Languages and Literature (FFCLRP) at the University of São Paulo (USP) and the Hebrew University of Jerusalem (HUJ), in Israel, have investigated market behaviors in which different companies compete for consumers subject to network effects – when the consumers are susceptible to decisions by their peers.

The study, “Externalities and economic behavior,” conducted with support from FAPESP and the HUJ, developed and tested theoretical models to understand the phenomenon.

“The models help to understand these markets, especially with regard to the product differentiation behavior that arises from the network externality,” said Fernando Pigeard de Almeida Prado of the FFCLRP-USP, principal investigator of the project.

In economics, an externality occurs when a decision influences those who take no part in making it, the researcher explained. Network externalities, in turn, occur when a consumer is influenced by the decisions of a group or by the number of consumers who have already purchased a particular good or service.

Network externalities are a deciding factor in several markets, and the models developed by the study may be applied to various segments. “It’s a very interesting relationship that opens the door to more efficient market mechanisms,” Prado said.

According to the researcher, the concept of externality is perhaps one of the most important concepts in the social sciences. “It refers to situations in which the actions of one person affect others, and it is hard to imagine a social environment that has no externalities. The focus of our work is in the externalities that emerge in economics,” Eyal Winter, principal investigator in Israel, told Agência FAPESP.

The researchers observed that, in the case of a duopoly under network effects, competitors tend not to accept any division of the market. “Using game theory, we can predict that the two companies will produce similar products and make rational decisions to compete for the larger share because even if one of them suffers from the other’s formation of a monopoly, what is in play are profits much larger than those generated by any possible shared market,” Prado explained.

The companies would then find themselves in what mathematicians call a Nash Equilibrium, a concept proposed by U.S. mathematician John Nash that demonstrates that no player can improve her outcome in relation to another by unilaterally modifying her decision.

“Whoever ends up with the largest share of consumers gains much more than if a ‘poorer’ market were divided, so both tend to go for broke,” Prado said. The research he conducted with Winter considered only competition between two players.

Coalitions

The researchers investigated the role of consumer choice in market behavior in the face of strong network effects – when decisions by the majority have a substantial influence – and little differentiation between product characteristics.

“We concluded that a company with the largest market share can increase its prices indiscriminately without any real consequences because the consumer – given strong network effects and low product differentiation – would have no better alternatives available. But this would not be the case if consumers were to act collectively and threaten to stop using the company’s products, forcing it to maintain its prices at acceptable levels,” Prado said.

To test the behavior of companies faced with the formation of consumer coalitions, the researchers conducted laboratory experiments with volunteers acting as business owners who needed to make decisions regarding their product prices.

A software tool was developed that simulates consumer behavior when faced with various price scenarios. Depending on the prices charged, the “players” won or lost market share.

“We observed that participants in the experiment behaved according to the mathematical models we developed, slashing prices to gain a larger share of the market and then increasing them as soon as market leadership was attained.”

According to Prado, future tests will include new elements such as the geographical location of the companies. “According to our theoretical findings, companies tend to opt for similarity in their products. We plan to test the behavior of company owners with regard to the level of product differentiation as well.”

The experiments carried out in Ribeirão Preto are the beginning of a project to build an experimental economics laboratory at USP, the researcher said. “These experiments will allow us to obtain new perspectives regarding the actual behavior of individuals faced with economic challenges, and they serve as an embryo of laboratory implementation.”

Segregation

The study by Prado and Winter is also investigating how the interaction between externalities and the market can lead to social segregation. The initiative emerged from the observation of neighborhoods in Jerusalem that have both orthodox and non-religious Jews.

“The way these neighborhoods are organized is related to the externalities of the decisions of certain populations over others. As soon as a group of non-religious Jews began to settle in a particular neighborhood, the orthodox group moved elsewhere. This is because the groups value certain networks over others due to their affinities. But what if the offer of basic services to these neighborhoods did not make this distinction between groups and did not affect how they behaved?” asked Winter, who lives in Jerusalem.

In the preliminary results of the mathematical models studied, the researchers observed that a monopoly situation would segregate less than a situation in which two similar companies were vying for the market.

“Our analysis shows that the spatial social structure is very much affected by the market. More specifically, it was determined that the oligopolistic market in which a small number of companies operate tends to segregate more than a monopolistic structure in which only one company operates,” Winter said.

According to the initial findings of the study, this situation results because in a monopoly, prices would be higher because there is no competition, and consumers who have purchasing power from the two cultural groups would divide the same region.

A duopoly, however, would lead to “excessively” low prices, as a way to rapidly select consumers from one group and thus exclude the rest who would migrate towards the other company and, as a result, to the other neighborhood because the first was dominated by the opposite company and group.

Winter warns that the outcome cannot be interpreted as a justification for monopolies. “Economists are typically opposed to monopolized markets, and for good reason. To a certain extent, a monopoly is the worst scenario in terms of the welfare of consumers, but what it shows us is that in a market with social externalities such as those we described, a duopoly could have worse social consequences,” he said.

According to Prado, the research showed that in a monopoly, all the neighborhoods would have fractional parts of the two groups. For the researcher, however, there are better alternatives.

“Instead of a monopoly that does not culturally segregate and an oligopoly that segregates, it would be more acceptable to have a competitive market in which several companies are authorized to operate and serve consumers in a regulated manner,” he suggested.