9 research outputs found
Stable Invitations
We consider the situation in which an organizer is trying to convene an
event, and needs to choose a subset of agents to be invited. Agents have
preferences over how many attendees should be at the event and possibly also
who the attendees should be. This induces a stability requirement: All invited
agents should prefer attending to not attending, and all the other agents
should not regret being not invited. The organizer's objective is to find the
invitation of maximum size subject to the stability requirement. We investigate
the computational complexity of finding the maximum stable invitation when all
agents are truthful, as well as the mechanism design problem when agents may
strategically misreport their preferences.Comment: To appear in COMSOC 201
Bargaining for coalition structure formation
Many multiagent settings require a collection of agents
to partition themselves into coalitions. In such cases, the agents may
have conflicting preferences over the possible coalition structures
that may form. We investigate a noncooperative bargaining game to
allow the agents to resolve such conflicts and partition themselves
into non-overlapping coalitions. The game has a finite horizon and
is played over discrete time periods. The bargaining agenda is de-
fined exogenously. An important element of the game is a parameter
0 ≤ δ ≤ 1 that represents the probability that bargaining ends
in a given round. Thus, δ is a measure of the degree of democracy
(ranging from democracy for δ = 0, through increasing levels of
authoritarianism as δ approaches 1, to dictatorship for δ = 1). For
this game, we focus on the question of how a player’s position on the
agenda affects his power. We also analyse the relation between the
distribution of the power of individual players, the level of democracy,
and the welfare efficiency of the game. Surprisingly, we find
that purely democratic games are welfare inefficient due to an uneven
distribution of power among the individual players. Interestingly,
introducing a degree of authoritarianism into the game makes
the distribution of power more equitable and maximizes welfare
Approximately Socially-Optimal Decentralized Coalition Formation
Coalition formation is a central part of social interactions. In the emerging
era of social peer-to-peer interactions (e.g., sharing economy), coalition
formation will be often carried out in a decentralized manner, based on
participants' individual preferences. A likely outcome will be a stable
coalition structure, where no group of participants could cooperatively opt out
to form another coalition that induces higher preferences to all its members.
Remarkably, there exist a number of fair cost-sharing mechanisms (e.g.,
equal-split, proportional-split, egalitarian and Nash bargaining solutions of
bargaining games) that model practical cost-sharing applications with desirable
properties, such as the existence of a stable coalition structure with a small
strong price-of-anarchy (SPoA) to approximate the social optimum. In this
paper, we close several gaps on the previous results of decentralized coalition
formation: (1) We establish a logarithmic lower bound on SPoA, and hence, show
several previously known fair cost-sharing mechanisms are the best practical
mechanisms with minimal SPoA. (2) We improve the SPoA of egalitarian and Nash
bargaining cost-sharing mechanisms to match the lower bound. (3) We derive the
SPoA of a mix of different cost-sharing mechanisms. (4) We present a
decentralized algorithm to form a stable coalition structure. (5) Finally, we
apply our results to a novel application of peer-to-peer energy sharing that
allows households to jointly utilize mutual energy resources. We also present
and analyze an empirical study of decentralized coalition formation in a
real-world P2P energy sharing project
-fractional Core Stability in Hedonic Games
Hedonic Games (HGs) are a classical framework modeling coalition formation of
strategic agents guided by their individual preferences. According to these
preferences, it is desirable that a coalition structure (i.e. a partition of
agents into coalitions) satisfies some form of stability. The most well-known
and natural of such notions is arguably core-stability. Informally, a partition
is core-stable if no subset of agents would like to deviate by regrouping in a
so-called core-blocking coalition. Unfortunately, core-stable partitions seldom
exist and even when they do, it is often computationally intractable to find
one. To circumvent these problems, we propose the notion of
-fractional core-stability, where at most an
-fraction of all possible coalitions is allowed to core-block. It
turns out that such a relaxation may guarantee both existence and
polynomial-time computation. Specifically, we design efficient algorithms
returning an -fractional core-stable partition, with
exponentially decreasing in the number of agents, for two fundamental classes
of HGs: Simple Fractional and Anonymous. From a probabilistic point of view,
being the definition of -fractional core equivalent to requiring
that uniformly sampled coalitions core-block with probability lower than
, we further extend the definition to handle more complex sampling
distributions. Along this line, when valuations have to be learned from samples
in a PAC-learning fashion, we give positive and negative results on which
distributions allow the efficient computation of outcomes that are
-fractional core-stable with arbitrarily high confidence.Comment: Accepted as poster at NeurIPS 202
Análise da estabilidade de jogos hedônicos
Orientadores: Rafael Crivellari Saliba Schouery, Eduardo Candido XavierDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Jogos hedônicos são jogos de formação de coalizão nos quais os agentes apenas se importam ou são influenciados pelos agentes na mesma coalizão que eles estão. Os agentes podem formar qualquer coalizão que eles queiram e cada agente tem um perfil de preferência, uma ordem fraca sobre o conjunto de coalizões que o contém indicando sua preferência. Um jogo hedônico é definido por um conjunto de agentes e seus perfis de preferência. Classicamente, o resultado de tais jogos é uma partição do conjunto de agentes. Nesta dissertação, nós revisamos alguns resultados da literatura a respeito da existência de resultados Nash estáveis, do preço da anarquia e estabilidade, da existência de partições no núcleo e da complexidade de computar um resultado que está no núcleo. Estudamos o modelo de jogos hedônicos que permite a formação de coalizões com sobreposição. Esta extensão permite a representação de vários cenários como interações sociais, grupos de trabalhos e formação de redes. Nós apresentamos um modelo para jogos fracionários com sobreposição de coalizões e mostramos que o núcleo não é vazio para jogos representados por circuitos, caminhos e grafos bipartidos com emparelhamento perfeito. Nós também apresentamos um modelo para jogos hedônicos aditivamente separáveis com sobreposição de coalizões. Mais ainda, mostramos que, para jogos hedônicos aditivamente separáveis simétricos com sobreposição de coalizões, o bem-estar social de qualquer estrutura de coalizão é no máximo o bem-estar social ótimo da versão do jogo sem sobreposição de coalizõesAbstract: Hedonic games are coalition formation games where the agents only care or are influenced by agents in the same coalition as they are. Agents may form any coalition they want, and every agent has a preference profile, a weak ordering on the set of coalitions that contains it. A hedonic game is defined by a set of agents and their profile preferences. Classically, the outcome of such games is a partition of the agent set. We review some literature results regarding the existence of Nash stable outcomes, the price of anarchy and stability, the existence of core stable partitions, and the complexity to compute a Core stable outcome. We extend the hedonic games model by allowing the formation of overlapping coalitions. This extension permits the representation of many scenarios by hedonic games, such as social interactions, working groups, and network formation. We give a model for fractional hedonic games with overlapping coalitions and we show that the core is not empty for games represented by cycles, paths, and bipartite graphs with perfect matching. We also give a model for additively separable hedonic games with overlapping coalitions. Moreover, we show that for symmetric additively separable hedonic games with overlapping coalitions, the social welfare of any coalition structure is at most the optimal social welfare of the game version without overlapping coalitionsMestradoCiência da ComputaçãoMestre em Ciência da ComputaçãoCAPE
Coordination Games on Weighted Directed Graphs
We study strategic games on weighted directed graphs, where each player’s payoff is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed nonnegative integer bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. We identify natural classes of graphs for which finite improvement or coalition-improvement paths of polynomial length always exist, and consequently a (pure) Nash equilibrium or a strong equilibrium can be found in polynomial time. The considered classes of graphs are typical in network topologies: simple cycles correspond to the token ring local area networks, whereas open chains of simple cycles correspond to multiple independent rings topology from the recommendation G.8032v2 on Ethernet ring protection switching. For simple cycles, these results are optimal in the sense that without the imposed conditions on the weights and bonuses, a Nash equilibrium may not even exist. Finally, we prove that determining the existence of a Nash equilibrium or of a strong equilibrium is NP-complete already for unweighted graphs, with no bonuses assumed. This implies that the same problems for polymatrix games are strongly NP-hard. </jats:p