Perception-perfect strategies

To formalize our predictions about how the three types behave, we assume people follow "perception-perfect strategies," which in this environment implies that people choose to hit today if and only if hitting today is optimal given their current preferences and their current beliefs about how they will behave in the future. 1... 

TCs are time consistent, so for each k, t) their continuation strategy maximizes their continuation utility. The implication of time consistency in the framework discussed in the preceding paragraph is that TCs correctly perceive their future behavior and that they discount the future benefit from current restraint by 6. Hence, we define perception-perfect strategies for TCs as ... 

At any point in time, naifs believe they will behave like TCs beginning with the next period. Hence, in any period, naifs perceive that they will follow strategy a beginning with the next period. Since naifs discount the future benefit of current restraint by , we define perception-perfect strategies for naifs as ... 

We begin with a three-period example that provides some intuition and also illustrates how to solve for the perception-perfect strategies for TCs, naifs, and sophisticates. Suppose people live for three periods, which we interpret as youth, middle age, and old age. In any given period, people are currently hooked if = 1 (that is, because they hit last period) and unhooked if Jfc=0(that is, because they refrained last period). Finally, suppose that people s preferences in each of the three periods can be represented with the following instantaneous utilities ... 

For sophisticates, there can be multiple perception-perfect strategies when there is an infinite horizon. However, there is a unique perception-perfect strategy for sophisticates when there is a finite horizon (given the assumption of hitting when indifferent). Throughout this chapter, we focus on perception-perfect strategies for an infinite... 

For both TCs and naifs, the unique infinite-horizon perception-perfect strategy corresponds to the unique finite-horizon perception-perfect strategy as the horizon becomes long. 

This conclusion relies on our restricting our attention to infinite-horizon, perception-perfect strategies that correspond to a perception-perfect strategy for some long, finite horizon. 

Recall that we restrict attention to perception-perfect strategies corresponding to the unique perception-perfect strategy for a finite horizon as the horizon becomes long. For a finite horizon, we suppose the last period is a weekend, and of course people hit whether or not they are hooked on this weekend. 

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