相关论文: Complexity of Strong Implementability

Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…

We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides $m^{\frac 1 2 -\epsilon}$ approximation to the social welfare and uses value queries only must use…

We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the…

Discrete probabilistic programs (DPPs) provide a highly expressive formalism for compactly defining arbitrary finite probabilistic models. This expressivity comes at a price: DPP inference is PSPACE-hard. In this work, we show that DPP…

We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…

Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social…

We consider a notion of rationalizability, where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of…

A workflow specification defines a set of steps and the order in which those steps must be executed. Security requirements may impose constraints on which groups of users are permitted to perform subsets of those steps. A workflow…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…

Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every quasi-order must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of…

We introduce the study of sequential information elicitation in strategic multi-agent systems. In an information elicitation setup a center attempts to compute the value of a function based on private information (a-k-a secrets) accessible…

This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…

Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by…

Let $(f,P)$ be an incentive compatible mechanism where $f$ is the social choice function and $P$ is the payment function. In many important settings, $f$ uniquely determines $P$ (up to a constant) and therefore a common approach is to focus…

We study three axioms in the model of constrained social choice under uncertainty where (i) agents have subjective expected utility preferences over acts and (ii) different states of nature have (possibly) different sets of available…

We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…

In this paper, we consider the revealed preferences problem from a learning perspective. Every day, a price vector and a budget is drawn from an unknown distribution, and a rational agent buys his most preferred bundle according to some…

This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…

The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…

This paper investigates the computational complexity of reinforcement learning in a novel linear function approximation regime, termed partial $q^{\pi}$-realizability. In this framework, the objective is to learn an $\epsilon$-optimal…