Dynamic Inconsistency - in Game Theory

In Game Theory

In the context of game theory, dynamic inconsistency is a situation in a dynamic game where a player's best plan for some future period will not be optimal when that future period arrives. A dynamically inconsistent game is subgame imperfect. In this context, the inconsistency is primarily about commitment and credible threats. This manifests itself through a violation of Bellman's Principle of Optimality by the leader or dominant player, as shown in Simaan and Cruz (1973a, 1973b).

For example, a firm might want to commit itself to dramatically dropping the price of a product it sells if a rival firm enters its market. If this threat were credible, it would discourage the rival from entering. However, the firm might not be able to commit its future self to taking such an action because if the rival does in fact end up entering, the firm's future self might determine that, given the fact that the rival is now actually in the market and there is no point in trying to discourage entry, it is now not in its interest to dramatically drop the price. As such, the threat would not be credible. The present self of the firm has preferences that would have the future self be committed to the threat, but the future self has preferences that have it not carry out the threat. Hence, the dynamic inconsistency.