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.

In game theory

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

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. 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.

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.

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. However, empirical research on hyperbolic discounting 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.

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".

Stylized examples

One famous example in literature of a mechanism for dealing with dynamic inconsistency is that of Odysseus and the Sirens. Curious to hear the Sirens' songs but mindful of the danger, Odysseus orders his men to stop their ears with beeswax and ties himself to the mast of the ship. Most importantly, he orders his men not to heed his cries while they pass the Sirens; recognizing that in the future he may behave irrationally, Odysseus limits his future agency and binds himself to a commitment mechanism (i.e. the mast) to survive this perilous example of dynamic inconsistency. While Homer likely did not have this in mind as a metaphor for the economic problem, this example has been used by economists to explain the benefits of commitment mechanisms in mitigating dynamic inconsistency.

See also

References

External links

Category:Game theory Category:Intertemporal economics