[vague][citation needed] 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.
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).
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.
One common way in which selves may differ in their preferences is they may be modeled as all holding the view that "now" has especially high value compared to any future time.
The self control literature relies heavily on this type of time inconsistency, and it relates to a variety of topics including procrastination, addiction, efforts at weight loss, and saving for retirement.
Time inconsistency basically means that there is disagreement between a decision-maker's different selves about what actions should be taken.
Exponential discounting posits that the decision maker assigns future utility of any good according to the formula where
However, empirical research makes a strong case that time inconsistency is, in fact, standard in human preferences.
This would imply disagreement by people's different selves on decisions made and a rejection of the time consistency aspect of rational choice theory.
More generally, humans have a systematic tendency to switch towards "vices" (products or activities which are pleasant in the short term) from "virtues" (products or activities which are seen as valuable in the long term) as the moment of consumption approaches, even if this involves changing decisions made in advance.
A different form of dynamic inconsistency arises as a consequence of "projection bias" (not to be confused with a defense mechanism of the same name).
Humans have a tendency to mispredict their future marginal utilities by assuming that they will remain at present levels.
This leads to inconsistency as marginal utilities (for example, tastes) change over time in a way that the individual did not expect.
For example, when individuals are asked to choose between a piece of fruit and an unhealthy snack (such as a candy bar) for a future meal, the choice is strongly affected by their "current" level of hunger.
It also highlights that inconsistent choice is even more frequent and relevant in the digital environment, as higher stimulation and multitasking makes it easier to opt for immediate gratification even in the presence of different long-term preferences.