We investigate hedonic games under enemies aversion and friends appreciation, where every agent considers other agents as either a friend or an enemy. We extend these simple preferences by allowing each agent to also consider other agents to be neutral. Neutrals have no impact on her preference, as in a graphical hedonic game. Surprisingly, we discover that neutral agents do not simplify matters, but cause complexity. We prove that the core can be empty under enemies aversion and the strict core can be empty under friends appreciation. Furthermore, we show that under both preferences, deciding whether the strict core is nonempty, is NP NP -complete. This complexity extends to the core under enemies aversion. We also show that under friends appreciation, we can always find a core stable coalition structure in polynomial time.

Given a set of voters V , a set of candidates C, and voters' preferences over the candidates, multiwinner voting rules output a fixed-size subset of candidates (committee). Under the Chamberlin-Courant multiwinner voting rule, one fixes a scoring vector of length |C|, and each voter's 'utility' for a given committee is defined to be the score that she assigns to her most preferred candidate in that committee; the goal is then to find a committee that maximizes the joint utility of all voters. The joint utility is typically identified either with the sum of all voters' utilities or with the utility of the least satisfied voter, resulting in, respectively, the utilitarian and the egalitarian variant of the Chamberlin-Courant's rule. For both of these cases, the problem of computing an optimal committee is NP-hard for general preferences, but becomes polynomial-time solvable if voters' preferences are single-peaked or single-crossing. In this paper, we propose a family of multiwinner voting rules that are based on the concept of ordered weighted average (OWA) and smoothly interpolate between the egalitarian and the utilitarian variants of the Chamberlin-Courant rule. We show that under moderate constraints on the weight vector we can recover many of the algorithmic results known for the egalitarian and the utilitarian version of Chamberlin-Courant's rule in this more general setting.

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a first-in-first-out queue and may wait: an edge is associated with a capacity, which defines how many agents-pertime-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.(a) Static routing games were a crucial testbed for the Price of Anarchy, a concept that bounds a game's loss of efficiency due to selfish behaviors.

We investigate markets with a set of students on one side and a set of colleges on the other. A student and college can be linked by a weighted contract that defines the student's wage, while a college's budget for hiring students is limited. Stability is a crucial requirement for matching mechanisms to be applied in the real world. A standard stability requirement is coalitional stability, i.e., no pair of a college and group of students has any incentive to deviate. We find that a coalitionally stable matching is not guaranteed to exist, verifying the coalitional stability for a given matching is coNP-complete, and the problem of finding whether a coalitionally stable matching exists in a given market, is SigmaP2-complete: NPNP-complete. Other negative results also hold when blocking coalitions contain at most two students and one college. Given these computational hardness results, we pursue a weaker stability requirement called pairwise stability, where no pair of a college and single student has an incentive to deviate. Unfortunately, a pairwise stable matching is not guaranteed to exist either. Thus, we consider a restricted market called a typed weighted market, in which students are partitioned into types that induce their possible wages. We then design a strategy-proof and Pareto efficient mechanism that works in polynomial-time for computing a pairwise stable matching in typed weighted markets.

In a multi-objective game, each individual's payoff is a vectorvalued function of everyone's actions. Under such vectorial payoffs, Paretoefficiency is used to formulate each individual's best-response condition, inducing Pareto-Nash equilibria as the fundamental solution concept. In this work, we follow a classical game-theoretic agenda to study equilibria. Firstly, we show in several ways that numerous pure-strategy Pareto-Nash equilibria exist. Secondly, we propose a more consistent extension to mixed-strategy equilibria. Thirdly, we introduce a measurement of the efficiency of multiple objectives games, which purpose is to keep the information on each objective: the multi-objective coordination ratio. Finally, we provide algorithms that compute Pareto-Nash equilibria and that compute or approximate the multi-objective coordination ratio.