Dynamic Duopolistic Competition with Market Capturing Opportunities

The model we use is a stochastic game, with transition probabilities between the states, depending on the actions performed in each state. The model's parameters can be chosen in such a way that a variety of economic situations can be analyzed. We derive results for the model with three states and five states. We are able to fully derive analytical results for the three states situation. If firms are very much focused on the short term, the only equilibrium is one in which both play the passive strategy (collusion). If the firms instead have high discount factors, the only remaining equilibrium is one in which they play aggressively. For average discount factors, a variety of (a)symmetric pure and mixed equilibria are found, in which monopolisation occurs with probability 1 in the long run. For the five states situation, we present numerical results using different parameter settings. We are able to provide equilibrium conditions for any kind of symmetric stationary strategy in these five states, including a collusive one in which firms always allow the market situation to go back to a symmetric state in which both firms play passively. As the model's parameters can be seen as indicators of market characteristics, predictions on the market circumstances under which firms will behave either collusively or competitively are made on the basis of our analytical and numerical results. Furthermore, we prove that if we extend the number of states to infinity, only the passive strategy equilibrium remains.