Today, I had the opportunity to meet with the professor guiding my research in economics. Our work integrates the interdisciplinary fields of game theory and elements of computer science. The current research problem that we’re focusing on, is outlined as follows:
Consider a market with two firms (denoted as $i = 1, 2$), each selling an identical product to unit-demand consumer. These firms set their respective prices, $p_1$ and $p_2$, which are transparent to the consumers.
We introduce a twist: the true value of the firms’ products is unknown to the consumers, who must incur an exogenous search cost $c$ to discover the product’s value, based on a prior independent and identically distributed (i.i.d.) probability distribution. Given the prices set by the firms, consumers make their purchasing decisions rationally.
The question then arises: What is the market’s equilibrium under these conditions?
Through rigorous analysis under a set of general formulations and straightforward assumptions, we have discovered that, surprisingly, an equilibrium does not exist in this scenario. This outcome contrasts sharply with similar market models without the search cost, where establishing an equilibrium is relatively straightforward. Our next step is to expand this research to more complex scenarios, such as relaxing the i.i.d. assumption or considering additional firms.
The professor has provided me with additional reading materials to deepen my understanding. Keep an eye out for updates in this research series!