In economics, dynamic inconsistency or time inconsistency is a situation in which a decision-maker's preferences change over time in such a way that a preference can become inconsistent at another point in time. This can be thought of as there being many different "selves" within decision makers, with each "self" representing the decision-maker at a different point in time; the inconsistency occurs when not all preferences are aligned.
The term "dynamic inconsistency" is more closely affiliated with game theory, whereas "time inconsistency" is more closely affiliated with behavioral economics.
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 .
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.
In behavioral economics
In the context of behavioral economics, time inconsistency is related to how each different self of a decision-maker may have different preferences over current and future choices.
Consider, for example, the following question: (a) Which do you prefer, to be given 500 dollars today or 505 dollars tomorrow? (b) Which do you prefer, to be given 500 dollars 365 days from now or 505 dollars 366 days from now? When this question is asked, to be time-consistent, one must make the same choice for (b) as for (a). According to George Loewenstein and Drazen Prelec, however, people are not always consistent. People tend to choose "500 dollars today" and "505 dollars 366 days later", which is different from the time-consistent answer.
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. This is sometimes called the "immediacy effect" or "temporal discounting". As a result, the present self will care too much about itself and not enough about its future selves. 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. Formally, consider an economic model with different mathematical weightings placed on the utilities of each self. Consider the possibility that for any given self, the weightings that self places on all the utilities could differ from the weightings that another given self places on all the utilities. The important consideration now is the relative weighting between two particular utilities. Will this relative weighting be the same for one given self as it is for a different given self? If it is, then we have a case of time consistency. If the relative weightings of all pairs of utilities are all the same for all given selves, then the decision-maker has time-consistent preferences. If there exists a case of one relative weighting of utilities where one self has a different relative weighting of those utilities than another self has, then we have a case of time inconsistency and the decision-maker will be said to have time-inconsistent preferences.
It is common in economic models that involve decision-making over time to assume that decision-makers are exponential discounters. Exponential discounting posits that the decision maker assigns future utility of any good according to the formula