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A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that their favorite player wins?… (More)
Inspired by applications in parallel computing, we analyze the setting of work stealing in multithreaded computations. We obtain tight upper bounds on the number of steals when the computation can be modeled by rooted trees. In particular, we show that if the computation with n processors starts with one processor having a complete k-ary tree of height h… (More)
This paper investigates a variant of the work-stealing algorithm that we call the localized work-stealing algorithm. The intuition behind this variant is that because of locality, processors can benefit from working on their own work. Consequently, when a processor is free, it makes a steal attempt to get back its own work. We call this type of steal a… (More)
The problem of pricing the cloud has attracted much recent attention due to the widespread use of cloud computing and cloud services. From a theoretical perspective, several mechanisms that provide strong efficiency or fairness guarantees and desirable incentive properties have been designed. However, these mechanisms often rely on a rigid model, with… (More)
In this paper we explore some of the properties of the comb poset, whose notion was first introduced by J. M. Pallo. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees.… (More)
Random dictatorship has been characterized as the only social decision scheme that satisfies efficiency and strategyproofness when individual preferences are strict. We show that no extension of random dictatorship to weak preferences satisfies these properties, even when significantly weakening the required degree of strategyproofness.
NOTE: The content of these notes has not been formally reviewed by the lecturer. It is recommended that they are read critically. 1 Review We start with a review of some elements from last lecture. Let us consider a marketplace where the excess demand on goods is a well-defined vector-valued function f (p) of the prices p. This happens, e.g., when traders'… (More)
In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called weak saddle. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based value.
Fair division has long been an important problem in the economics literature. In this note, we consider the existence of proportionally fair allocations of indivisible goods, i.e., allocations of indivisible goods in which every agent gets at least her proportionally fair share according to her own utility function. We show that when utilities are additive… (More)