**TITLE:** Pricing with markups in congested markets

**SPEAKER:** Dr. Jose Correa

**ABSTRACT:**

We study a game that models a market in which heterogeneous producers make pricing decisions in a first stage, followed by consumers that select a producer selling at lowest price. Producers submit a price function to the market, which maps a production level to a price. Solutions of this type of models are normally referred to as supply function equilibria, and the most common application is in electricity markets. In our model, producers have increasing marginal production costs equal to a linear function, and adopt price functions that are proportional to their production costs. Therefore, the decision in the first phase of the game is the markup producers apply to the production cost. In a second phase of the game, consumers learn the producers' price functions, which leads to an allocation of consumers to producers.

We prove that an equilibrium exists if and only if there are at least three producers, and if an equilibrium exists, it is unique. We also establish that for highly competitive markets, the equilibrium assignment is nearly efficient, where an efficient assignment is one that minimizes the total production cost. Furthermore, we establish an almost tight bound on the worstcase inefficiency of an equilibrium. In particular, the bound states that when there are two equally efficient producers and possibly other less efficient ones, the production cost under an equilibrium is at most 50% worse than the optimal one, and the worst-case gap between the two assignments decreases rapidly as competition increases. For instance, for three similarly-efficient producers plus perhaps other less efficient ones, the inefficiency is below 6.2%.

This is joint work with Nicolas Stier-Moses.