Mathematical Approach of an Oligopol Model

Modern analysis of strategic interactions through game theory has allowed to make some concepts clear. The equillibrium cannot be explained by the process of behaviour study. Each firm should guess the choice of the other firm, just like in a game of type "scissors-leaves-stone". The game theory eliminates this arbitrage showing that people act rationally, making decisions strictly individually. Three elements are taken into account:players, strategies and results. The two firms are the two players, the gains are the profits of the two firms and the strategies are represented by the product amount the two firms can produce. Within the present paper, an algebric model will be developed which is in condition to offer to the interested ones a new perspective on (1) how the interaction between firms in a Stackelberg model can be studied and, (2) the way this framework can be extended to a talking about getting into an industry.