94 research outputs found

    Multi-agent Learning For Game-theoretical Problems

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    Multi-agent systems are prevalent in the real world in various domains. In many multi-agent systems, interaction among agents is inevitable, and cooperation in some form is needed among agents to deal with the task at hand. We model the type of multi-agent systems where autonomous agents inhabit an environment with no global control or global knowledge, decentralized in the true sense. In particular, we consider game-theoretical problems such as the hedonic coalition formation games, matching problems, and Cournot games. We propose novel decentralized learning and multi-agent reinforcement learning approaches to train agents in learning behaviors and adapting to the environments. We use game-theoretic evaluation criteria such as optimality, stability, and resulting equilibria

    Online Coalition Formation Under Random Arrival or Coalition Dissolution

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    Online Coalition Formation under Random Arrival or Coalition Dissolution

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    Coalition formation considers the question of how to partition a set of nn agents into disjoint coalitions according to their preferences. We consider a cardinal utility model with additively separable aggregation of preferences and study the online variant of coalition formation, where the agents arrive in sequence and whenever an agent arrives, they have to be assigned to a coalition immediately. The goal is to maximize social welfare. In a purely deterministic model, the greedy algorithm, where an agent is assigned to the coalition with the largest gain, is known to achieve an optimal competitive ratio, which heavily relies on the range of utilities. We complement this result by considering two related models. First, we study a model where agents arrive in a random order. We find that the competitive ratio of the greedy algorithm is Θ(1n2)\Theta\left(\frac{1}{n^2}\right), whereas an alternative algorithm, which is based on alternating between waiting and greedy phases, can achieve a competitive ratio of Θ(1n)\Theta\left(\frac{1}{n}\right). Second, we relax the irrevocability of decisions by allowing to dissolve coalitions into singleton coalitions, presenting a matching-based algorithm that once again achieves a competitive ratio of Θ(1n)\Theta\left(\frac{1}{n}\right). Hence, compared to the base model, we present two ways to achieve a competitive ratio that precisely gets rid of utility dependencies. Our results also give novel insights in weighted online matching.Comment: Appears in the 31st Annual European Symposium on Algorithms (ESA 2023

    Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities

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    We study relationships between different relaxed notions of core stability in hedonic games. In particular, we study (i) q-size core stable outcomes in which no deviating coalition of size at most q exists and (ii) k-improvement core stable outcomes in which no coalition can improve by a factor of more than k. For a large class of hedonic games, including fractional and additively separable hedonic games, we derive upper bounds on the maximum factor by which a coalition of a certain size can improve in a q-size core stable outcome. We further provide asymptotically tight lower bounds for a large class of hedonic games. Finally, our bounds allow us to confirm two conjectures by Fanelli et al. [Angelo Fanelli et al., 2021][IJCAI\u2721] for symmetric fractional hedonic games (S-FHGs): (i) every q-size core stable outcome in an S-FHG is also q/(q-1)-improvement core stable and (ii) the price of anarchy of q-size stability in S-FHGs is precisely 2q/q-1

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    Socially Aware Coalition Formation with Bounded Coalition Size

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    In many situations when people are assigned to coalitions the assignment must be social aware, i.e, the utility of each person depends on the friends in her coalition. Additionally, in many situations the size of each coalition should be bounded. This paper initiates the study of such coalition formation scenarios in both weighted and unweighted settings. We show that finding a partition that maximizes the utilitarian social welfare is computationally hard, and provide a polynomial-time approximation algorithm. We also investigate the existence and the complexity of finding stable partitions. Namely, we show that the Contractual Strict Core (CSC) is never empty, but the Strict Core (SC) of some games is empty. Finding partitions that are in the CSC is computationally easy, but finding partitions that are in the SC is hard. The analysis of the core is more involved. For the weighted setting, the core may be empty. We thus concentrate on the unweighted setting. We show that when the coalition size is bounded by 3 the core is never empty, and we present a polynomial time algorithm for finding a member of the core. When the coalition size is greater, we provide additive and multiplicative approximations of the core. In addition, we show in simulation over 100 million games that a simple heuristic always finds a partition that is in the core

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Essays in Microeconomics

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    This dissertation has four chapters. The first chapter studies the testable implications of stable weighted (hedonic) coalitions. The second chapter explores an extension of Bayesian persuasion where the receiver can acquire additional information after receiving information from the sender. The third chapter studies observable implications when a decision-maker endogenously forms consideration sets. The last chapter examines weighted network formation where agents have social status concerns. Omitted proofs in each chapter are presented in the last section of each chapter. In the first chapter, we study the testable implications of a stable profile of weighted coalitions. We then apply our result to a model of weighted network formation, which subsumes aggregate matchings and the fractional stable roommates\u27 problem. In the second chapter, we study persuasion in a setting where a sender cares about a receiver\u27s action, and the receiver can acquire additional information after receiving information from the sender. Our main result indicates that the sender has considerable persuasion abilities. For binary actions, the sender always benefits from persuasion when there is a need for persuasion. For multiple actions, we give a sufficient condition for the sender to benefit from persuasion. We argue that this condition is frequently satisfied. In the third chapter, we model a decision-maker that is unable to consider all of the available alternatives due to costly attention. The decision-maker will optimally choose a subset of given alternatives by maximizing the expected utility of having that set minus the cost of attention required for considering that set. In particular, we provide a representation theorem for random choice rules where subsets of menus, which are interpreted as consideration sets, are formed by maximizing an objective function, and the probability of choosing alternatives outside this set is equal to zero. In the last chapter, we study environments where individuals allocate resources across relationships with others, creating a weighted, directed network. Value is achieved both through an exogenous factor and maintaining close connections to high-value individuals. We consider two cases corresponding to the direction benefits flow along links. In Model T (for ``taking\u27\u27) agents receive benefits through the links they create, whereas in Model G (for ``giving\u27\u27) the reverse is true: agents pass value along their links. Equilibrium and socially efficient networks are characterized. In Model G equilibrium networks do not necessarily maximize group welfare, but in Model T efficient networks and equilibrium networks coincide despite extensive network externalities

    Topological Distance Games

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    We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs -- for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.Comment: Appears in the 37th AAAI Conference on Artificial Intelligence (AAAI), 202

    Hedonic Games and Treewidth Revisited

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    We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an edge-weighted digraph G = (V,E), and the weight of an arc uv denotes the utility u gains by being in the same coalition as v. We focus on (arguably) the most basic stability question about such a game: given a graph, does a Nash stable solution exist and can we find it efficiently? We study the (parameterized) complexity of ASHG stability when the underlying graph has treewidth t and maximum degree ?. The current best FPT algorithm for this case was claimed by Peters [AAAI 2016], with time complexity roughly 2^{O(??t)}. We present an algorithm with parameter dependence (? t)^{O(? t)}, significantly improving upon the parameter dependence on ? given by Peters, albeit with a slightly worse dependence on t. Our main result is that this slight performance deterioration with respect to t is actually completely justified: we observe that the previously claimed algorithm is incorrect, and that in fact no algorithm can achieve dependence t^{o(t)} for bounded-degree graphs, unless the ETH fails. This, together with corresponding bounds we provide on the dependence on ? and the joint parameter establishes that our algorithm is essentially optimal for both parameters, under the ETH. We then revisit the parameterization by treewidth alone and resolve a question also posed by Peters by showing that Nash Stability remains strongly NP-hard on stars under additive preferences. Nevertheless, we also discover an island of mild tractability: we show that Connected Nash Stability is solvable in pseudo-polynomial time for constant t, though with an XP dependence on t which, as we establish, cannot be avoided
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