arXiv subjects

Angelo Fanelli

Publications and source records attributed to Angelo Fanelli.

12 recordsLinked to original sources

arXiv2024

Individually Stable Dynamics in Coalition Formation over Graphs

Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of stability, has attracted a lot of attention. However, the natural process by which players, starting from any feasible state, strive to reach an equilibrium after a series of unilateral improving deviations, has been less studied. We investigate the convergence of dynamics towards individually stable outcomes under the following perspective: what are the most general classes of preferences and graph topologies guaranteeing convergence? To this aim, on the one hand, we cover a hierarchy of preferences, ranging from the most general to a subcase of additively separable preferences, including individually rational and monotone cases. On the other hand, given that convergence may fail in graphs admitting a cycle even in our most restrictive preference class, we analyze acyclic graph topologies such as trees, paths, and stars.

cs.GT↗

arXiv2024

Minimizing Rosenthal's Potential in Monotone Congestion Games

Congestion games are attractive because they can model many concrete situations where some competing entities interact through the use of some shared resources, and also because they always admit pure Nash equilibria which correspond to the local minima of a potential function. We explore the problem of computing a state of minimum potential in this setting. Using the maximum number of resources that a player can use at a time, and the possible symmetry in the players' strategy spaces, we settle the complexity of the problem for instances having monotone (i.e., either non-decreasing or non-increasing) latency functions on their resources. The picture, delineating polynomial and NP-hard cases, is complemented with tight approximation algorithms.

cs.GT↗

arXiv2020

Local Aggregation in Preference Games

In this work we introduce a new model of decision-making by agents in a social network. Agents have innate preferences over the strategies but, because of the social interactions, the decision of the agents are not only affected by their innate preferences but also by the decision taken by their social neighbors. We assume that the strategies of the agents are embedded in an {approximate} metric space. Furthermore, departing from the previous literature, we assume that, due to the lack of information, each agent locally represents the trend of the network through an aggregate value, which can be interpreted as the output of an aggregation function. We answer some fundamental questions related to the existence and efficiency of pure Nash equilibria.

cs.GT↗

arXiv2019

On approximate pure Nash equilibria in weighted congestion games with polynomial latencies

We study natural improvement dynamics in weighted congestion games with polynomial latencies of maximum degree $d\geq 1$. We focus on two problems regarding the existence and efficiency of approximate pure Nash equilibria, with a reasonable small approximation factor, in these games. By exploiting a simple technique, we firstly show that such a game always admits a $d$-approximate potential function. This implies that every sequence of $d$-approximate improvement moves by the players leads to a $d$-approximate pure Nash equilibrium. As a corollary, we also obtain that, under mild assumptions on the structure of the players' strategies, the game always admits a constant approximate potential function. Secondly, using a simple potential function argument, we are able to show that a $(d+\delta)$-approximate pure Nash equilibrium of cost at most $(d+1)/(d+\delta)$ times the cost of an optimal state always exists, for $\delta\in [0,1]$.

cs.GT↗

arXiv2016

An almost ideal coordination mechanism for unrelated machine scheduling

Coordination mechanisms aim to mitigate the impact of selfishness when scheduling jobs to different machines. Such a mechanism defines a scheduling policy within each machine and naturally induces a game among the selfish job owners. The desirable properties of a coordination mechanism includes simplicity in its definition and efficiency of the outcomes of the induced game. We present a broad class of coordination mechanisms for unrelated machine scheduling that are simple to define and we identify one of its members (mechanism \Dcoord) that is superior to all known mechanisms. \Dcoord\ induces potential games with logarithmic price of anarchy and only constant price of stability. Both bounds are almost optimal.

cs.GT↗

arXiv2015

Ride Sharing with a Vehicle of Unlimited Capacity

A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle travels through the graph, carrying each object from its origin to its destination without any bound on the number of objects that can be simultaneously transported. The vehicle starts and terminates its ride at given nodes, and the goal is to compute a minimum-cost ride satisfying all requests. This ride sharing problem is shown to be tractable on paths by designing a $O(h \log h+n)$ algorithm, with $h$ being the number of distinct requests and with $n$ being the number of nodes in the path. The algorithm is then used as a subroutine to efficiently solve instances defined over cycles, hence covering all graphs with maximum degree $2$. This traces the frontier of tractability, since $\bf NP$-hard instances are exhibited over trees whose maximum degree is $3$.

cs.DM↗

arXiv2014

Short sequences of improvement moves lead to approximate equilibria in constraint satisfaction games

We present an algorithm that computes approximate pure Nash equilibria in a broad class of constraint satisfaction games that generalize the well-known cut and party affiliation games. Our results improve previous ones by Bhalgat et al.~(EC 10) in terms of the obtained approximation guarantee. More importantly, our algorithm identifies a polynomially-long sequence of improvement moves from any initial state to an approximate equilibrium in these games. The existence of such short sequences is an interesting structural property which, to the best of our knowledge, was not known before. Our techniques adapt and extend our previous work for congestion games (FOCS 11) but the current analysis is considerably simpler.

cs.GT↗

arXiv2011

Approximate Pure Nash Equilibria in Weighted Congestion Games: Existence, Efficient Computation, and Structure

We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential function arguments. Unfortunately, this proof of existence is inefficient and computing equilibria is such games is a {\sf PLS}-hard problem. The situation gets worse when superlinear latency functions come into play; in this case, the Nash dynamics of the game may contain cycles and equilibria may not even exist. Given these obstacles, we consider approximate equilibria as alternative solution concepts. Do such equilibria exist? And if so, can we compute them efficiently? We provide positive answers to both questions for weighted congestion games with polynomial latency functions by exploiting an "approximation" of such games by a new class of potential games that we call $\Psi$-games. This allows us to show that these games have $d!$-approximate equilibria, where $d$ is the maximum degree of the latency functions. Our main technical contribution is an efficient algorithm for computing O(1)-approximate equilibria when $d$ is a constant. For games with linear latency functions, the approximation guarantee is $\frac{3+\sqrt{5}}{2}+O(\gamma)$ for arbitrarily small $\gamma>0$; for latency functions with maximum degree $d\geq 2$, it is $d^{2d+o(d)}$. The running time is polynomial in the number of bits in the representation of the game and $1/\gamma$. As a byproduct of our techniques, we also show the following structural statement for weighted congestion games with polynomial latency functions of maximum degree $d\geq 2$: polynomially-long sequences of best-response moves from any initial state to a $d^{O(d^2)}$-approximate equilibrium exist and can be efficiently identified in such games as long as $d$ is constant.

cs.GT↗

arXiv2011

On the Impact of Fair Best Response Dynamics

In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from the price of anarchy, within a polynomially bounded number of best responses. We focus on the well known class of congestion games and we show that, if each player is allowed to play at least once and at most $\beta$ times any $T$ best responses, states with approximation ratio $O(\beta)$ times the price of anarchy are reached after $T \lceil \log \log n \rceil$ best responses, and that such a bound is essentially tight also after exponentially many ones. One important consequence of our result is that the fairness among players is a necessary and sufficient condition for guaranteeing a fast convergence to efficient states. This answers the important question of the maximum order of $\beta$ needed to fast obtain efficient states, left open by [9,10] and [3], in which fast convergence for constant $\beta$ and very slow convergence for $\beta=O(n)$ have been shown, respectively. Finally, we show that the structure of the game implicitly affects its performances. In particular, we show that in the symmetric setting, in which all players share the same set of strategies, the game always converges to an efficient state after a polynomial number of best responses, regardless of the frequency each player moves with.

cs.GT↗

arXiv2011

Enforcing efficient equilibria in network design games via subsidies

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.

cs.GT↗

arXiv2011

Efficient computation of approximate pure Nash equilibria in congestion games

Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {\sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes O(1)-approximate Nash equilibria in these games. In particular, for congestion games with linear latency functions, our algorithm computes $(2+\epsilon)$-approximate pure Nash equilibria in time polynomial in the number of players, the number of resources and $1/\epsilon$. It also applies to games with polynomial latency functions with constant maximum degree $d$; there, the approximation guarantee is $d^{O(d)}$. The algorithm essentially identifies a polynomially long sequence of best-response moves that lead to an approximate equilibrium; the existence of such short sequences is interesting in itself. These are the first positive algorithmic results for approximate equilibria in non-symmetric congestion games. We strengthen them further by proving that, for congestion games that deviate from our mild assumptions, computing $\rho$-approximate equilibria is {\sf PLS}-complete for any polynomial-time computable $\rho$.

cs.GT↗

arXiv2010

Dynamics of Profit-Sharing Games

An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each team's profit is given by a convex function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.

cs.GT↗