Bertrand Oligopoly with Boundedly Rational Consumers

Abstract

In this paper we consider a model of Bertrand oligopoly when consumers are boundedly rational and make their purchase decisions probabilistically, according to the Luce model. We consider three different cases: first, we characterize equilibrium when firms face boundedly rational consumers with the fixed irrationality parameter λ; second, we discuss the case of obfuscating oligopoly, when firms can invest in order to confuse consumers, i.e. to increase their λ; and third, we consider educating oligopoly, when firms can choose to invest to decrease λ. We show that while it is worthwhile for the firms to confuse the consumers, it is only optimal to educate them if they are sufficiently rational at default. We also analyze how the social welfare, consumer surplus and the firms' profits depend on the number of firms.

Degrees of Rationality in Agent-Based Retail Markets

“…They propose a model where sellers can choose to educate or confuse buyers, i.e., increase or decrease their degree of rationality respectively, and present the effects of these choices. Extending previous results (Basov and Danilkina 2015), Ait Omar et al (2017) show that within a Bertrand oligopoly, sellers can benefit if buyers have lower degree of rationality. Our model substantially differentiates from the aforementioned work in the following ways.…”

“…More specifically, we use the multinomial logit function to model the stochastic price selection of buyers (Anas 1983). Other works make use of the Luce choice axiom (Luce 1959), or the Softmax function (Sutton and Barto 1998) to model bounded rationality of buyers in markets (Basov and Danilkina 2015;Ait Omar et al 2017).…”

“…Previous work has also studied the effects of bounded rationality on Bertrand markets (Basov and Danilkina 2015;Ait Omar et al 2017;Zhang et al 2009). For instance, Zhang et al (2009) consider a Bertrand model with bounded rational sellers and study convergence properties of the competition.…”

“…For instance, Zhang et al (2009) consider a Bertrand model with bounded rational sellers and study convergence properties of the competition. In the closest to ours work, Basov and Danilkina (2015) study price equilibria with regards to the degree of buyers' rationality. They propose a model where sellers can choose to educate or confuse buyers, i.e., increase or decrease their degree of rationality respectively, and present the effects of these choices.…”

Price complexity and buyer confusion in markets

“…For exampleBasov and Danilkina (2015) present a model based on the probabilistic choice model ofLuce (1959), where the probability of choosing a good depends on the utilities offered by the goods in the market and the level of aggregate obfuscation. They show that equilibrium prices depend on the aggregate obfuscation level but not on a particular firm's obfuscation investment.…”