In economics, dynamic inconsistency, or time inconsistency, describes a situation where a decision-maker's preferences change over time in such a way that what is preferred at one point in time is inconsistent with what is preferred at another point in time. It is often easiest to think about preferences over time in this context by thinking of decision-makers as being made up of many different "selves", with each self representing the decision-maker at a different point in time. So, for example, there is my today self, my tomorrow self, my next Tuesday self, my year from now self, etc. The inconsistency will occur when somehow the preferences of some of the selves are not aligned with each other.
One type of inconsistency is more closely affiliated with game theory, and "dynamic inconsistency" is the more commonly used terminology in this case. Another type of inconsistency is more closely affiliated with behavioral economics, and "time inconsistency" is the more commonly used terminology there.
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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.
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.
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 herself and not enough about her 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 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; this is generally what students are taught. Exponential discounting yields time-consistent preferences. Exponential discounting and, more generally, time-consistent preferences are often assumed in rational choice theory, since they imply that all of a decision-maker's selves will agree with the choices made by each self. Any decision that the individual makes for himself in advance will remain valid (i.e. an optimal choice) as time advances, unless utilities themselves change.
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.
For example, consider having the choice between getting the day off work tomorrow or getting a day and a half off work one month from now. Suppose you would choose one day off tomorrow. Now suppose that you were asked to make that same choice ten years ago. That is, you were asked then whether you would prefer getting one day off in ten years or getting one and a half days off in ten years and one month. Suppose that then you would have taken the day and a half off. This would be a case of time inconsistency because your relative preferences for tomorrow versus one month from now would be different at two different points in time — namely now versus ten years ago. The decision made ten years ago may have been rational, but the decision made just before the fact is biased towards immediate pleasure due to an exaggerated value of "now".
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 which were rationally made in advance.
One way that time-inconsistent preferences have been formally introduced into economic models is by first giving the decision-maker standard exponentially discounted preferences, and then adding an additional term that heavily discounts any time that is not now. Preferences of this sort have been called "present-biased preferences". The hyperbolic discounting model is another commonly used model that allows to obtain more realistic results with regard to human decision-making.
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. Individuals often become addicted to smoking or drugs because they underestimate future marginal utilities of these habits (such as craving for cigarettes) once they become addicted.[1]