202 research outputs found
Coalition Resilient Outcomes in Max k-Cut Games
We investigate strong Nash equilibria in the \emph{max -cut game}, where
we are given an undirected edge-weighted graph together with a set of colors. Nodes represent players and edges capture their mutual
interests. The strategy set of each player consists of the colors. When
players select a color they induce a -coloring or simply a coloring. Given a
coloring, the \emph{utility} (or \emph{payoff}) of a player is the sum of
the weights of the edges incident to , such that the color chosen
by is different from the one chosen by . Such games form some of the
basic payoff structures in game theory, model lots of real-world scenarios with
selfish agents and extend or are related to several fundamental classes of
games.
Very little is known about the existence of strong equilibria in max -cut
games. In this paper we make some steps forward in the comprehension of it. We
first show that improving deviations performed by minimal coalitions can cycle,
and thus answering negatively the open problem proposed in
\cite{DBLP:conf/tamc/GourvesM10}. Next, we turn our attention to unweighted
graphs. We first show that any optimal coloring is a 5-SE in this case. Then,
we introduce -local strong equilibria, namely colorings that are resilient
to deviations by coalitions such that the maximum distance between every pair
of nodes in the coalition is at most . We prove that -local strong
equilibria always exist. Finally, we show the existence of strong Nash
equilibria in several interesting specific scenarios.Comment: A preliminary version of this paper will appear in the proceedings of
the 45th International Conference on Current Trends in Theory and Practice of
Computer Science (SOFSEM'19
Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games
We study coordination mechanisms for Scheduling Games (with unrelated
machines). In these games, each job represents a player, who needs to choose a
machine for its execution, and intends to complete earliest possible. Our goal
is to design scheduling policies that always admit a pure Nash equilibrium and
guarantee a small price of anarchy for the l_k-norm social cost --- the
objective balances overall quality of service and fairness. We consider
policies with different amount of knowledge about jobs: non-clairvoyant,
strongly-local and local. The analysis relies on the smooth argument together
with adequate inequalities, called smooth inequalities. With this unified
framework, we are able to prove the following results.
First, we study the inefficiency in l_k-norm social costs of a strongly-local
policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy
of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all
deterministic, non-preemptive, strongly-local and non-waiting policies
(non-waiting policies produce schedules without idle times). These results
ensure that SPT is close to optimal with respect to the class of l_k-norm
social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price
of anarchy O(2^k).
Second, we consider the makespan (l_infty-norm) social cost by making
connection within the l_k-norm functions. We revisit some local policies and
provide simpler, unified proofs from the framework's point of view. With the
highlight of the approach, we derive a local policy Balance. This policy
guarantees a price of anarchy of O(log m), which makes it the currently best
known policy among the anonymous local policies that always admit a pure Nash
equilibrium.Comment: 25 pages, 1 figur
How can diversity lead to richer unity? Developing intercultural competences through "Interity"
International audienceIn this paper, an innovatory experiential teaching design, which aims to develop the intercultural competences of students in two French Graduate Engineering Schools, is described and analysed. Using a concept called "interity", developed by Demorgon, students are encouraged to negotiate a common frame of reference and action, creating unity from diversity. Our main objective is to use the diversity represented by cultural and disciplinary differences to produce new synergies. The intercultural competences which emerged are analysed using the five savoirs developed by Byram & Zarate and Demorgon's multiperspectivist approach. Successful elements of the teaching design are highlighted and suggestions for future improvements are given
Project Games
International audienceWe consider a strategic game called project game where each agent has to choose a project among his own list of available projects. The model includes positive weights expressing the capacity of a given agent to contribute to a given project The realization of a project produces some reward that has to be allocated to the agents. The reward of a realized project is fully allocated to its contributors, according to a simple proportional rule. Existence and computational complexity of pure Nash equilibria is addressed and their efficiency is investigated according to both the utilitarian and the egalitarian social function
Subset sum problems with digraph constraints
We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees
Object Allocation via Swaps along a Social Network
International audienceThis article deals with object allocation where each agent receives a single item. Starting from an initial endowment, the agents can be better off by exchanging their objects. However, not all trades are likely because some participants are unable to communicate. By considering that the agents are embedded in a social network, we propose to study the allocations emerging from a sequence of simple swaps between pairs of neighbors in the network. This model raises natural questions regarding (i) the reachability of a given assignment, (ii) the ability of an agent to obtain a given object, and (iii) the search of Pareto-efficient allocations. We investigate the complexity of these problems by providing, according to the structure of the social network, polynomial and NP-complete cases
Approximate Tradeoffs on Matroids
International audienceWe consider problems where a solution is evaluated with a couple. Each coordinate of this couple represents an agent’s utility. Due to the possible conflicts, it is unlikely that one feasible solution is optimal for both agents. Then, a natural aim is to find tradeoffs. We investigate tradeoff solutions with guarantees for the agents.The focus is on discrete problems having a matroid structure. We provide polynomial-time deterministic algorithms which achieve several guarantees and we prove that some guarantees are not possible to reach
Designing Budget-Balanced Best-Response Mechanisms for Network Coordination Games
in Springer series Lecture Notes in Computer Science, vol. 8146International audienceNetwork coordination games (NCGs) have recently received a lot of attention since they model several kinds of interaction problems in social networks. However, the performance of these games at equilibrium may be very bad. This motivates the adoption of mechanisms for inducing a socially optimal state. Many settings are naturally dynamical and thus we believe it is worth to consider the design of incentive compatible best-response mechanisms (Nisan, Schapira, Valiant, Zohar, 2011) for NCGs. Specifically, we would like to assign to players special fees in order to induce the optimum profile of an NCG. Moreover, we would like the mechanism to be budget-balanced, i.e., implementable with no cost.We show that a budget-balanced and incentive compatible best- response mechanism for inducing the optimal profile of a two-strategy NCG always exists. Moreover, for such a mechanism, we investigate other properties inspired by envy-freeness, collusion-resistance and fairness
Cost allocation protocols for network formation on connection situations
International audienceThe issue of embedding cost-awareness in the design of communication network devices and protocols has been growing at a fast rate in last years. Under certain connection situations, however, network design is not enforced by a central authority. This is the case, for instance, of power control for wireless networks, where the cost of a link is a function of the power needed to send a message to a remote node, which increases with the distance. Here each player wishes to consume as few power as possible to send its request and the main question is how to avoid that players deviate from a socially optimal network. In this paper, we study strategic games based on connection situations with the objective to coordinate self-interested agents placed on the nodes of a graph to realize a more efficient communication network. We address the problem of the design of cost allocation protocols that may guarantee the convergence of the best response dynamic and we analyze the effects of cost monotonicity and other state-dependent properties on the optimality of a protocol
Local Envy-Freeness in House Allocation Problems
International audienceWe study the fair division problem consisting in allocating one item per agent so as to avoid (or minimize) envy, in a setting where only agents connected in a given social network may experience envy. In a variant of the problem, agents themselves can be located on the network by the central authority. These problems turn out to be difficult even on very simple graph structures, but we identify several tractable cases. We further provide practical algorithms and experimental insights
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