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We study equilibrium computation with extensive-form correlation in two-player turn-taking stochastic games. Our main results are two-fold: (1) We give an algorithm for computing a Stackelberg extensive-form correlated equilibrium (SEFCE), which runs in time polynomial in the size of the game, as well as the number of bits required to encode each input number. (2) We give an efficient algorithm for approximately computing an optimal extensive-form correlated equilibrium (EFCE) up to machine precision, i.e., the algorithm achieves approximation error ε in time polynomial in the size of the game, as well as log(1/ε). Our algorithm for SEFCE is the first polynomial-time algorithm for equilibrium computation with commitment in such a general class of stochastic games. Existing algorithms for SEFCE typically make stronger assumptions such as no chance moves, and are designed for extensive-form games in the less succinct tree form. Our algorithm for approximately optimal EFCE is, to our knowledge, the first algorithm that achieves 3 desiderata simultaneously: approximate optimality, polylogarithmic dependency on the approximation error and compatibility with stochastic games in the more succinct graph form. Existing algorithms achieve at most 2 of these desiderata, often also relying on additional technical assumptions. [ABSTRACT FROM AUTHOR]

We consider the problem of planning with participation constraints introduced in[24]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the agent. However, the agent can and will choose to end the process whenever his expected onward utility becomes negative. The principal seeks to compute and commit to a policy that maximizes her expected utility, under the constraint that the agent should always want to continue participating. We provide the first polynomial-time exact algorithm for this problem for finite-horizon settings, where previously only an additive ε-approximation algorithm was known. Our approach can also be extended to the (discounted) infinite-horizon case, for which we give an algorithm that runs in time polynomial in the size of the input and log(1/ε), and returns a policy that is optimal up to an additive error of ε. [ABSTRACT FROM AUTHOR]

We consider a combinatorial variant of the classical ski rental problem -- which we call combinatorial ski rental -- where multiple resources are available to purchase and to rent, and are demanded online. Moreover, the costs of purchasing and renting are potentially combinatorial. The dual problem of combinatorial ski rental, which we call combinatorial online bipartite matching, generalizes the classical online bipartite matching problem into a form where constraints, induced by both offline and online vertices, can be combinatorial. We give a 2-competitive (resp. e/(e - 1)-competitive) deterministic (resp. randomized) algorithm for combinatorial ski rental, and an e/(e - 1)-competitive algorithm for combinatorial online bipartite matching. All these ratios are optimal given simple lower bounds inherited from the respective well-studied special cases. We also prove information-theoretic impossibility of constant-factor algorithms when any part of our assumptions is considerably relaxed. [ABSTRACT FROM AUTHOR]

The revelation principle is a key tool in mechanism design. It allows the designer to restrict attention to the class of truthful mechanisms, greatly facilitating analysis. This is also borne out in an algorithmic sense, allowing certain computational problems in mechanism design to be solved in polynomial time. Unfortunately, when not every type can misreport every other type (the partial verification model), or--more generally-- misreporting can be costly, the revelation principle can fail to hold. This also leads to NP-hardness results. The primary contribution of this paper consists of characterizations of conditions under which the revelation principle still holds when misreporting can be costly. (These are generalizations of conditions given earlier for the partial verification case [Green and Laffont 1986; Yu 2011].) We also study associated computational problems. [ABSTRACT FROM AUTHOR]

In many settings, a group of voters must come to a joint decision on multiple issues. In practice, this is often done by voting on the issues in sequence. We model sequential voting in multi-issue domains as a complete-information extensive-form game, in which the voters are perfectly rational and their preferences are common knowledge. In each step, the voters simultaneously vote on one issue, and the order of the issues is given exogenously before the process. We call this model strategic sequential voting. We focus on domains characterized by multiple binary issues, so that strategic sequential voting leads to a unique outcome under a natural solution concept. We show that under some conditions on the preferences, this leads to the same outcome as truthful sequential voting, but in general it can result in very different outcomes. In particular, sometimes the order of the issues has a strong influence on the winner. We also analyze the communication complexity of the corresponding social choice rule. Most significantly, we illustrate several multiple-election paradoxes in strategic sequential voting: there exists a profile for which the winner under strategic sequential voting is ranked nearly at the bottom in all voters' true preferences, and the winner is Pareto-dominated by almost every other alternative. We show that changing the order of the issues cannot completely prevent such paradoxes. We also study the possibility of avoiding the paradoxes for strategic sequential voting by imposing some constraints on the profile, such as separability, lexicographicity or O-legality. [ABSTRACT FROM AUTHOR]

Computing optimal strategies to commit to in general normal-form or Bayesian games is a topic that has recently been gaining attention, in part due to the application of such algorithms in various security and law enforcement scenarios. In this paper, we extend this line of work to the more general case of commitment in extensiveform games. We show that in some cases, the optimal strategy can be computed in polynomial time; in others, computing it is NP-hard. [ABSTRACT FROM AUTHOR]

The coalitional manipulation problem is one of the central problems in computational social choice. In this paper, we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008, AIJ 2009]. Ourmain result is a polynomialtime algorithm with (roughly speaking) the following theoretical guarantee: given a manipulable instance with m alternatives, the algorithm finds a successful manipulation with at most m - 2 additional manipulators. Our technique is based on a reduction to the scheduling problem known as Q∣pmtn∣Cmax, along with a novel rounding procedure. We demonstrate that our analysis is tight by establishing a new type of integrality gap. We also resolve a known open question in computational social choice by showing that the coalitional manipulation problem remains (strongly) NP-complete for positional scoring rules even when votes are unweighted. Finally, we discuss the implications of our results with respect to the question: "Is there a prominent voting rule that is usually hard to manipulate?" [ABSTRACT FROM AUTHOR]