Two sellers offering the same homogeneous product compete against each other in a market with a certain number m of potential buyers. The two sellers decide at the beginning of each period a strategy that specifies the course of action to take at each of its rounds contingent on what happened in previous rounds of the same period. Thus, at the beginning of each round, each of the two sellers sets a price for his product according to their strategies for that period. Then, the market opens and the two prices become known to everybody. The m buyers walk in and each of them decides from which of the two sellers will buy based on the observation of this two prices.
Trade takes place and a new round begins.
The idea behind this sequence of events is that each seller uses the R rounds to learn about the behavior of its competitor. Thus, each period represents a step in a learning procedure. The model can also be thought as a evolutionary model where each period represents the end of an old generation of sellers and buyers and the birth of a new generation that inherits the characteristics of its parent generation with, hopefully, some improvements. We will refer to the two intuitions indistinctly. We will approach the resolution of the situation sketched above using two related but different tools.