Backward Induction - Backward Induction and Economic Entry

Backward Induction and Economic Entry

Consider a dynamic game in which the players are an incumbent firm in an industry and a potential entrant to that industry. As it stands, the incumbent has a monopoly over the industry and does not want to lose some of its market share to the entrant. If the entrant chooses not to enter, the payoff to the incumbent is high (it maintains its monopoly) and the entrant neither loses nor gains (its payoff is zero). If the entrant enters, the incumbent can "fight" or "accommodate" the entrant. It will fight by lowering its price, running the entrant out of business (and incurring exit costs — a negative payoff) and damaging its own profits. If it accommodates the entrant it will lose some of its sales, but a high price will be maintained and it will receive greater profits than by lowering its price (but lower than monopoly profits).

Say that, the best response of the incumbent is to accommodate if the entrant enters. If the incumbent accommodates, the best response of the entrant is to enter (and gain profit). Hence the strategy profile in which the entrant enters and the incumbent accommodates if the entrant enters is a Nash equilibrium consistent with backward induction. However, if the incumbent is going to fight, the best response of the entrant is to not enter, and if the entrant does not enter, it does not matter what the incumbent chooses to do in the hypothetical case that the incumbent does enter. Hence the strategy profile in which the incumbent fights if the entrant enters, but the entrant does not enter is also a Nash equilibrium. However, were the entrant to deviate and enter, the incumbent's best response is to accommodate---the threat of fighting is not credible. This second Nash equilibrium can therefore be eliminated by backward induction.