The tendency to overestimate immediate utility is a common cognitive bias. As a result people behave inconsistently over time and fail to reach long-term goals. Behavioral economics tries to help affected individuals by implementing external incentives. However, designing robust incentives is often difficult due to imperfect knowledge of the parameter @math quantifying a person's present bias. Using the graphical model of Kleinberg and Oren, we approach this problem from an algorithmic perspective. Based on the assumption that the only information about @math is its membership in some set @math , we distinguish between two models of uncertainty: one in which @math is fixed and one in which it varies over time. As our main result we show that the conceptual loss of efficiency incurred by incentives in the form of penalty fees is at most @math in the former and @math in the latter model. We also give asymptotically matching lower bounds and approximation algorithms.
A significant amount of research in this field has been devoted to temporal discounting in general and quasi-hyperbolic discounting in particular, see @cite_5 for a survey. The quasi-hyperbolic discounting model proposed by Laibson @cite_12 is characterized by two parameters: the present bias @math and the exponential discount rate @math . People who plan according to this model have an accurate perception of the present, but scale down any costs and rewards realized @math time units in the future by a factor of @math . To keep our work clearly delineated in scope, we adopt Akerlof's model of quasi-hyperbolic discounting @cite_6 and make the following two assumptions: First, we focus on the present bias @math and set the exponential discount rate to @math . Secondly, we assume people to be naive in the sense that they are unaware of their present bias and only optimize their current perceived utility when making a decision. Note that Alice and Bob from the previous example behave like agents in Akerlof's model for a present bias of @math and @math respectively.
@cite_5 @cite_6 @cite_12
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Laboratory and field studies of time preference find that discount rates are much greater in the short run than in the long run. Hyperbolic discount functions capture this property. This paper presents simulations of the savings and asset allocation choices of households with hyperbolic preferences. The behavior of the hyperbolic households is compared to the behavior of exponential households. The hyperbolic households borrow much more frequently in the revolving credit market. The hyperbolic households exhibit greater consumption income comovement and experience a greater drop in consumption around retirement. The hyperbolic simulations match observed consumption and balance sheet data much better than the exponential simulations. We consider settings in which we wish to incentivize myopic agents (such as Airbnb landlords, who may emphasize short-term profits and property safety) to treat arriving clients fairly, in order to prevent overall discrimination against individuals or groups. We model such settings in both classical and contextual bandit models in which the myopic agents maximize rewards according to current empirical averages, but are also amenable to exogenous payments that may cause them to alter their choices. Our notion of fairness asks that more qualified individuals are never (probabilistically) preferred over less qualified ones []. We investigate whether it is possible to design inexpensive subsidy or payment schemes for a principal to motivate myopic agents to play fairly in all or almost all rounds. When the principal has full information about the state of the myopic agents, we show it is possible to induce fair play on every round with a subsidy scheme of total cost @math (for the classic setting with @math arms, @math , and for the @math -dimensional linear contextual setting @math ). If the principal has much more limited information (as might often be the case for an external regulator or watchdog), and only observes the number of rounds in which members from each of the @math groups were selected, but not the empirical estimates maintained by the myopic agent, the design of such a scheme becomes more complex. We show both positive and negative results in the classic and linear bandit settings by upper and lower bounding the cost of fair subsidy schemes. We present an algorithm for the statistical learning setting with a bounded exp-concave loss in @math dimensions that obtains excess risk @math with probability at least @math . The core technique is to boost the confidence of recent in-expectation @math excess risk bounds for empirical risk minimization (ERM), without sacrificing the rate, by leveraging a Bernstein condition which holds due to exp-concavity. We also show that with probability @math the standard ERM method obtains excess risk @math . We further show that a regret bound for any online learner in this setting translates to a high probability excess risk bound for the corresponding online-to-batch conversion of the online learner. Lastly, we present two high probability bounds for the exp-concave model selection aggregation problem that are quantile-adaptive in a certain sense. The first bound is a purely exponential weights type algorithm, obtains a nearly optimal rate, and has no explicit dependence on the Lipschitz continuity of the loss. The second bound requires Lipschitz continuity but obtains the optimal rate. We study the optimal pricing of a finite quantity of a fashion-like seasonal good in the presence of forward-looking (strategic) customers. We distinguish between two classes of pricing strategies: contingent and announced fixed-discount. In both cases, the seller acts as a Stackelberg leader announcing his pricing strategy, while consumers act as followers taking the seller's strategy as given and determining their purchasing behavior. In each case, we identify a subgame-perfect Nash equilibrium and show that given the seller's strategy, the equilibrium in the consumer subgame is unique and consists of symmetric threshold purchasing policies. For both cases, we develop a benchmark model in which customers are nonstrategic (myopic). We conduct a comprehensive numerical study to explore the impact of strategic consumer behavior on pricing policies and expected revenue performance. We show that strategic customer behavior suppresses the benefits of price segmentation, particularly under medium-to-high values of heterogeneity and modest rates of decline in valuations. However, when the level of consumer heterogeneity is small, the rate of decline is medium-to-high, and the seller can optimally choose the time of discount in advance, segmentation can be used quite effectively even with strategic consumers. We find that the seller cannot avoid the adverse impact of strategic consumer behavior even under low levels of initial inventory. We argue that while the seller expects customers to be more concerned about product availability at discount time, he cannot use high-price “betting” strategies as he would in the case of low inventory and myopic customers. Under certain qualifications, announced fixed-discount strategies perform essentially the same as contingent pricing policies in the case of myopic consumers. However, under strategic consumer behavior, announced pricing policies can be advantageous to the seller, compared to contingent pricing schemes. Interestingly, those cases that announced discount strategies offer a significant advantage compared to contingent pricing policies. They appear to offer only a minimal advantage in comparison to fixed-pricing policies. Finally, when the seller incorrectly assumes that strategic customers are myopic in their purchasing decisions, it can be quite costly, reaching potential revenue losses of about 20 .