The Price of Uncertainty in Present-Biased Planning

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
β ∈ (0, 1] quantifying a person’s present bias. Using the graphical model
of Kleinberg and Oren [8], we approach this problem from an algorithmic
perspective. Based on the assumption that the only information about
β is its membership in some set B ⊂ (0, 1], we distinguish between two
models of uncertainty: one in which β is fixed and one in which it varies
over time. As our main result we show that the conceptual loss of effi-
ciency incurred by incentives in the form of penalty fees is at most 2
in the former and 1 + max B/ min B in the latter model. We also give
asymptotically matching lower bounds and approximation algorithms

Time-inconsistent Planning: Simple Motivation Is Hard to Find

With the introduction of the graph-theoretic time-inconsistent planning model due to Kleinberg and Oren, it has been possible to investigate the computational complexity of how a task designer best can support a present-biased agent in completing the task. In this paper, we study the complexity of finding a choice reduction for the agent; that is, how to remove edges and vertices from the task graph such that a present-biased agent will remain motivated to reach his target even for a limited reward. While this problem is NP-complete in general, this is not necessarily true for instances which occur in practice, or for solutions which are of interest to task designers. For instance, a task designer may desire to find the best task graph which is not too complicated. We therefore investigate the problem of finding simple motivating subgraphs. These are structures where the agent will modify his plan at most $k$ times along the way. We quantify this simplicity in the time-inconsistency model as a structural parameter: The number of branching vertices (vertices with out-degree at least $2$) in a minimal motivating subgraph. Our results are as follows: We give a linear algorithm for finding an optimal motivating path, i.e. when $k=0$. On the negative side, we show that finding a simple motivating subgraph is NP-complete even if we allow only a single branching vertex --- revealing that simple motivating subgraphs are indeed hard to find. However, we give a pseudo-polynomial algorithm for the case when $k$ is fixed and edge weights are rationals, which might be a reasonable assumption in practice.Comment: An extended abstract of this paper is accepted at AAAI 202

Collaborative Procrastination

The problem of inconsistent planning in decision making, which leads to undesirable effects such as procrastination, has been studied in the behavioral-economics literature, and more recently in the context of computational behavioral models. Individuals, however, do not function in isolation, and successful projects most often rely on team work. Team performance does not depend only on the skills of the individual team members, but also on other collective factors, such as team spirit and cohesion. It is not an uncommon situation (for instance, experienced by the authors while working on this paper) that a hard-working individual has the capacity to give a good example to her team-mates and motivate them to work harder. In this paper we adopt the model of Kleinberg and Oren (EC\u2714) on time-inconsistent planning, and extend it to account for the influence of procrastination within the members of a team. Our first contribution is to model collaborative work so that the relative progress of the team members, with respect to their respective subtasks, motivates (or discourages) them to work harder. We compare the total cost of completing a team project when the team members communicate with each other about their progress, with the corresponding cost when they work in isolation. Our main result is a tight bound on the ratio of these two costs, under mild assumptions. We also show that communication can either increase or decrease the total cost. We also consider the problem of assigning subtasks to team members, with the objective of minimizing the negative effects of collaborative procrastination. We show that whereas a simple problem of forming teams of two members can be solved in polynomial time, the problem of assigning n tasks to n agents is NP-hard

Exploiting graph structures for computational efficiency

Coping with NP-hard graph problems by doing better than simply brute force is a field of significant practical importance, and which have also sparked wide theoretical interest. One route to cope with such hard graph problems is to exploit structures which can possibly be found in the input data or in the witness for a solution. In the framework of parameterized complexity, we attempt to quantify such structures by defining numbers which describe "how structured" the graph is. We then do a fine-grained classification of its computational complexity, where not only the input size, but also the structural measure in question come in to play. There is a number of structural measures called width parameters, which includes treewidth, clique-width, and mim-width. These width parameters can be compared by how many classes of graphs that have bounded width. In general there is a tradeoff; if more graph classes have bounded width, then fewer problems can be efficiently solved with the aid of a small width; and if a width is bounded for only a few graph classes, then it is easier to design algorithms which exploit the structure described by the width parameter. For each of the mentioned width parameters, there are known meta-theorems describing algorithmic results for a wide array of graph problems. Hence, showing that decompositions with bounded width can be found for a certain graph class yields algorithmic results for the given class. In the current thesis, we show that several graph classes have bounded width measures, which thus gives algorithmic consequences. Algorithms which are FPT or XP parameterized by width parameters are exploiting structure of the input graph. However, it is also possible to exploit structures that are required of a witness to the solution. We use this perspective to give a handful of polynomial-time algorithms for NP-hard problems whenever the witness belongs to certain graph classes. It is also possible to combine structures of the input graph with structures of the solution witnesses in order to obtain parameterized algorithms, when each structure individually is provably insufficient to provide so under standard complexity assumptions. We give an example of this in the final chapter of the thesis

Chapter The Price of Uncertainty in Present-Biased Planning

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 β ∈ (0, 1] quantifying a person’s present bias. Using the graphical model of Kleinberg and Oren [8], we approach this problem from an algorithmic perspective. Based on the assumption that the only information about β is its membership in some set B ⊂ (0, 1], we distinguish between two models of uncertainty: one in which β is fixed and one in which it varies over time. As our main result we show that the conceptual loss of effi- ciency incurred by incentives in the form of penalty fees is at most 2 in the former and 1 + max B/ min B in the latter model. We also give asymptotically matching lower bounds and approximation algorithms

Chapter The Price of Uncertainty in Present-Biased Planning

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 β ∈ (0, 1] quantifying a person’s present bias. Using the graphical model of Kleinberg and Oren [8], we approach this problem from an algorithmic perspective. Based on the assumption that the only information about β is its membership in some set B ⊂ (0, 1], we distinguish between two models of uncertainty: one in which β is fixed and one in which it varies over time. As our main result we show that the conceptual loss of effi- ciency incurred by incentives in the form of penalty fees is at most 2 in the former and 1 + max B/ min B in the latter model. We also give asymptotically matching lower bounds and approximation algorithms