Structured preference domains, such as, for example, the domains of single-peaked and single-crossing preferences, are known to admit efficient algorithms for many problems in computational social choice. Some of these algorithms extend to preferences that are close to having the respective structural property, i.e., can be made to enjoy this property by performing minor changes to voters' preferences, such as deleting a small number of voters or candidates. However, it has recently been shown that finding the optimal number of voters or candidates to delete in order to achieve the desired structural property is NP-hard for many such domains. In this paper, we show that these problems admit efficient approximation algorithms. Our results apply to all domains that can be characterized in terms of forbidden configurations; this includes, in particular, single-peaked and single-crossing elections. For a large range of scenarios, our approximation results are optimal under a plausible complexity-theoretic assumption. We also provide parameterized complexity results for this class of problems.

Individual rationality, Pareto efficiency, and strategy- proofness are crucial properties of decision making functions, or mechanisms, in social choice literatures. In this paper we investigate mechanisms for exchange models where each agent is initially endowed with a set of goods and may have indifferences on distinct bundles of goods, and monetary transfers are not allowed. Sonmez (1999) showed that in such models, those three properties are not compatible in general. The impossibility, however, only holds under an assumption on preference domains. The main purpose of this paper is to discuss the compatibility of those three properties when the assumption does not hold. We first establish a preference domain called top-only preferences, which violates the assumption, and develop a class of exchange mechanisms that satisfy all those properties. Each mechanism in the class utilizes one instance of the mechanisms introduced by Saban and Sethuraman (2013). We also find a class of preference domains called m-chotomous preferences, where the assumption fails and these properties are incompatible.

It is a well known fact that in extensive form games with perfect information, there is a Nash equilibrium with support of size one. This doesn't hold for games with imperfect information, where the size of minimal support can be larger. We present a dependency between the level of uncertainty and the minimum support size. For many games, there is a big disproportion between the game uncertainty and the number of actions available. In Bayesian extensive games with perfect information, the only uncertainty is about the type of players. In card games, the uncertainty comes from dealing the deck. In these games, we can significantly reduce the support size. Our result applies to general-sum extensive form games with any finite number of players.

We consider a classic social choice problem in an online setting. In each round, a decision maker observes a single agent's preferences overa set of $m$ candidates, and must choose whether to irrevocably add a candidate to a selection set of limited cardinality $k$. Each agent's (positional) score depends on the candidates in the set when he arrives, and the decision-maker's goal is to maximize average (over all agents) score. We prove that no algorithm (even randomized) can achieve an approximationfactor better than $O(\frac{\log\log m}{\log m})$. In contrast, if the agents arrive in random order, we present a $(1 - \frac{1}{e} - o(1))$-approximatealgorithm, matching a lower bound for the off-line problem.We show that improved performance is possible for natural input distributionsor scoring rules. Finally, if the algorithm is permitted to revoke decisions at a fixedcost, we apply regret-minimization techniques to achieve approximation $1 - \frac{1}{e} - o(1)$ even for arbitrary inputs.

The growing Electric Vehicles' (EVs) popularity among commuters creates new challenges for the smart grid. The most important of them is the uncoordinated EV charging that substantially increases the energy demand peaks, putting the smart grid under constant strain. In order to cope with these peaks the grid needs extra infrastructure, a costly solution. We propose an Adaptive Management of EV Storage (AMEVS) algorithm, implemented through a learning agent that acts on behalf of individual EV owners and schedules EV charging over a weekly horizon. It accounts for individual preferences so that mobility service is not violated but also individual benefit is maximized. We observe that it reshapes the energy demand making it less volatile so that fewer resources are needed to cover peaks. It assumes Vehicle-to-Grid discharging when the customer has excess capacity. Our agent uses Reinforcement Learning trained on real world data to learn individual household consumption behavior and to schedule EV charging. Unlike previous work, AMEVS is a fully distributed approach. We show that AMEVS achieves significant reshaping of the energy demand curve and peak reduction, which is correlated with customer preferences regarding perceived utility of energy availability. Additionally, we show that the average and peak energy prices are reduced as a result of smarter energy use.

An important subclass of social choice functions, so-called majoritarian (or C1) functions, only take into account the pairwise majority relation between alternatives. In the absence of majority ties--e.g., when there is an odd number of agents with linear preferences--the majority relation is antisymmetric and complete and can thus conveniently be represented by a tournament. Tournaments have a rich mathematical theory and many formal results for majoritarian functions assume that the majority relation constitutes a tournament. Moreover, most majoritarian functions have only been defined for tournaments and allow for a variety of generalizations to unrestricted preference profiles, none of which can be seen as the unequivocal extension of the original function. In this paper, we argue that restricting attention to tournaments is justified by the existence of a conservative extension, which inherits most of the commonly considered properties from its underlying tournament solution.

In this paper, we discuss a computational approach to the cognitivetask of social planning. First, we specify a class of planningproblems that involve an agent who attempts to achieve its goalsby altering other agents' mental states. Next, we describe SFPS,a flexible problem solver that generates social plans of this sort,including ones that include deception and reasoning about otheragents' beliefs. We report the results for experiments on socialscenarios that involve different levels of sophistication and thatdemonstrate both SFPS's capabilities and the sources of its power.Finally, we discuss how our approach to social planning has beeninformed by earlier work in the area and propose directions foradditional research on the topic.

We study a mechanism design problem for exchange economies where each agent is initially endowed with a set of indivisible goods and side payments are not allowed. We assume each agent can withhold some endowments, as well as misreport her preference. Under this assumption, strategyproofness requires that for each agent, reporting her true preference with revealing all her endowments is a dominant strategy, and thus implies individual rationality. Our objective in this paper is to analyze the effect of such private ownership in exchange economies with multiple endowments. As fundamental results, we first show that the revelation principle holds under a natural assumption and that strategyproofness and Pareto efficiency are incompatible even under the lexicographic preference domain. We then propose a class of exchange rules, each of which has a corresponding directed graph to prescribe possible trades, and provide necessary and sufficient conditions on the graph structure so that they satisfy strategyproofness.

Realistic multi-agent team applications often feature dynamic environments with soft deadlines that penalize late execution of tasks. This puts a premium on quickly allocating tasks to agents, but finding the optimal allocation is NP-hard due to temporal and spatial constraints that require tasks to be executed sequentially by agents. We propose FMC_TA, a novel task allocation algorithm that allows tasks to be easily sequenced to yield high-quality solutions. FMC_TA first finds allocations that are fair (envy-free), balancing the load and sharing important tasks between agents, and efficient (Pareto optimal) in a simplified version of the problem. It computes such allocations in polynomial or pseudo-polynomial time (centrally or distributedly, respectively) using a Fisher market with agents as buyers and tasks as goods. It then heuristically schedules the allocations, taking into account inter-agent constraints on shared tasks. We empirically compare our algorithm to state-of-the-art incomplete methods, both centralized and distributed, on law enforcement problems inspired by real police logs. The results show a clear advantage for FMC_TA both in total utility and in other measures commonly used by law enforcement authorities.

We present and analyze a mechanism for the Combinatorial Public Project Problem (CPPP). The problem asks to select k out of m available items, so as to maximize the social welfare for autonomous agents with combinatorial preferences (valuation functions) over subsets of items. The CPPP constitutes an abstract model for decision making by autonomous agents and has been shown to present severe computational hardness, in the design of truthful approximation mechanisms. We study a non-truthful mechanism that is, however, practically relevant to multi-agent environments, by virtue of its natural simplicity. It employs an Item Bidding interface, wherein every agent issues a separate bid for the inclusion of each distinct item in the outcome; the k items with the highest sums of bids are chosen and agents are charged according to a VCG-based payment rule. For fairly expressive classes of the agents' valuation functions, we establish existence of socially optimal pure Nash and strong equilibria, that are resilient to coordinated deviations of subsets of agents. Subsequently we derive tight worst-case bounds on the approximation of the optimum social welfare achieved in equilibrium. We show that the mechanism's performance improves with the number of agents that can coordinate, and reaches half of the optimum welfare at strong equilibrium.