Duopolies happen when two players dominate the market. Many industries have a duopoly. Crest and Colgate. Airbus and Boeing. Uber and Lyft.
A Bertrand Duopoly is when two players offer a non-differentiated product consumers will buy the cheaper option.
In a bertrand duopoly, whatever cost cutting measure one player does, the other party has to react to those changes. Eventually both companies realize that neither party has anything to gain by changing strategies, hence we have a Nash Equillibrium.
How can we escape a bertrand duopoly?
This can be done by either offering a lower cost structure or a differentiated product. In the ride-sharing example, if Uber successfully develops an autonomous vehicle, it can offer a cheaper product to customers. Alternatively, if Lyft differentiates it’s offerings into scooters and e-bikes, then it can enter a brand new market.