In many settings, people exhibit behavior that is inconsistent across time --- we allocate a block of time to get work done and then procrastinate, or put effort into a project and then later fail to complete it. An active line of research in behavio
ral economics and related fields has developed and analyzed models for this type of time-inconsistent behavior. Here we propose a graph-theoretic model of tasks and goals, in which dependencies among actions are represented by a directed graph, and a time-inconsistent agent constructs a path through this graph. We first show how instances of this path-finding problem on different input graphs can reconstruct a wide range of qualitative phenomena observed in the literature on time-inconsistency, including procrastination, abandonment of long-range tasks, and the benefits of reduced sets of choices. We then explore a set of analyses that quantify over the set of all graphs; among other results, we find that in any graph, there can be only polynomially many distinct forms of time-inconsistent behavior; and any graph in which a time-inconsistent agent incurs significantly more cost than an optimal agent must contain a large procrastination structure as a minor. Finally, we use this graph-theoretic model to explore ways in which tasks can be designed to help motivate agents to reach designated goals.
We study the necessity of interaction between individuals for obtaining approximately efficient allocations. The role of interaction in markets has received significant attention in economic thinking, e.g. in Hayeks 1945 classic paper. We consider
this problem in the framework of simultaneous communication complexity. We analyze the amount of simultaneous communication required for achieving an approximately efficient allocation. In particular, we consider two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders. For both settings we first show that non-interactive systems have enormous communication costs relative to interactive ones. On the other hand, we show that limited interaction enables us to find approximately efficient allocations.
We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others selected actions. This is, arguably
, the simplest setting that models selection among certain and uncertain outcomes in a multi-agent system. We study the properties of equilibria in such games from both a game-theoretic perspective and a computational perspective. Our main positive result establishes the existence of a semi-strong equilibrium in every such game. We show that although simple, pay of play games contain a large variety of well-studied environments, e.g., vaccination games. We discuss the interesting implications of our results for these environments.
