arXiv subjects

Vincenzo Auletta

Publications and source records attributed to Vincenzo Auletta.

10 recordsLinked to original sources

arXiv2024

Stochastic Multi-round Submodular Optimization with Budget

In this work, we study the Stochastic Budgeted Multi-round Submodular Maximization (SBMSm) problem, where we aim to adaptively maximize the sum, over multiple rounds, of a monotone and submodular objective function defined on subsets of items. The objective function also depends on the realization of stochastic events, and the total number of items we can select over all rounds is bounded by a limited budget. This problem extends, and generalizes to multiple round settings, well-studied problems such as (adaptive) influence maximization and stochastic probing. We show that, if the number of items and stochastic events is somehow bounded, there is a polynomial time dynamic programming algorithm for SBMSm. Then, we provide a simple greedy $1/2(1-1/e-ε)\approx 0.316$-approximation algorithm for SBMSm, that first non-adaptively allocates the budget to be spent at each round, and then greedily and adaptively maximizes the objective function by using the budget assigned at each round. Finally, we introduce the {\em budget-adaptivity gap}, by which we measure how much an adaptive policy for SBMSm is better than an optimal partially adaptive one that, as in our greedy algorithm, determines the budget allocation in advance. We show that the budget-adaptivity gap lies between $e/(e-1)\approx 1.582$ and $2$.

cs.DS↗

arXiv2023

Election Manipulation in Social Networks with Single-Peaked Agents

Several elections run in the last years have been characterized by attempts to manipulate the result of the election through the diffusion of fake or malicious news over social networks. This problem has been recognized as a critical issue for the robustness of our democracy. Analyzing and understanding how such manipulations may occur is crucial to the design of effective countermeasures to these practices. Many studies have observed that, in general, to design an optimal manipulation is usually a computationally hard task. Nevertheless, literature on bribery in voting and election manipulation has frequently observed that most hardness results melt down when one focuses on the setting of (nearly) single-peaked agents, i.e., when each voter has a preferred candidate (usually, the one closer to her own belief) and preferences of remaining candidates are inversely proportional to the distance between the candidate position and the voter's belief. Unfortunately, no such analysis has been done for election manipulations run in social networks. In this work, we try to close this gap: specifically, we consider a setting for election manipulation that naturally raises (nearly) single-peaked preferences, and we evaluate the complexity of election manipulation problem in this setting: while most of the hardness and approximation results still hold, we will show that single-peaked preferences allow to design simple, efficient and effective heuristics for election manipulation.

cs.GT↗

arXiv2022

On the Impact of Social Media Recommendations on Opinion Consensus

We consider a discrete opinion formation problem in a setting where agents are influenced by both information diffused by their social relations and from recommendations received directly from the social media manager. We study how the "strength" of the influence of the social media and the homophily ratio affect the probability of the agents of reaching a consensus and how these factors can determine the type of consensus reached. In a simple 2-symmetric block model we prove that agents converge either to a consensus or to a persistent disagreement. In particular, we show that when the homophily ratio is large, the social media has a very low capacity of determining the outcome of the opinion dynamics. On the other hand, when the homophily ratio is low, the social media influence can have an important role on the dynamics, either by making harder to reach a consensus or inducing it on extreme opinions. Finally, in order to extend our analysis to more general and realistic settings we give some experimental evidences that our results still hold on general networks.

cs.SI↗

arXiv2021

Belief-Invariant and Quantum Equilibria in Games of Incomplete Information

Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as communication equilibria, belief-invariant equilibria, and correlated equilibria, all of which contain the familiar Nash equilibria. The notion of belief-invariant equilibrium appeared in game theory in the 90s. However, the class of non-signalling correlations associated to belief-invariance arose naturally already in the 80s in the foundations of quantum mechanics. In the present work, we explain and unify these two origins of the idea and study the above classes of equilibria, together with quantum correlated equilibria, using tools from quantum information but the language of (algorithmic) game theory. We present a general framework of belief-invariant communication equilibria, which contains correlated equilibria and quantum correlated equilibria as special cases. Our framework also contains the theory of Bell inequalities and their violations due to non-locality, which is a question of intense interest in the foundations of quantum mechanics, and it was indeed the original motivation for the aforementioned studies. Moreover, in our framework we can also model quantum games where players have conflicting interests, a recent developing topic in physics. We then use our framework to show new results related to the social welfare of equilibria. Namely, we exhibit a game where belief-invariance is socially better than any correlated equilibrium, and a game where all non-belief-invariant communication equilibria have a suboptimal social welfare. We also show that optimal social welfare can sometimes be achieved by quantum mechanical correlations, which do not need an informed mediator to be implemented, and go beyond the classical shared randomness approach.

cs.GT↗

arXiv2017

Metastability of Logit Dynamics for Coordination Games

Logit Dynamics [Blume, Games and Economic Behavior, 1993] are randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability distribution biased toward strategies promising higher payoffs. This process defines an ergodic Markov chain, over the set of strategy profiles of the game, whose unique stationary distribution is the long-term equilibrium concept for the game. However, when the mixing time of the chain is large (e.g., exponential in the number of players), the stationary distribution loses its appeal as equilibrium concept, and the transient phase of the Markov chain becomes important. It can happen that the chain is "metastable", i.e., on a time-scale shorter than the mixing time, it stays close to some probability distribution over the state space, while in a time-scale multiple of the mixing time it jumps from one distribution to another. In this paper we give a quantitative definition of "metastable probability distributions" for a Markov chain and we study the metastability of the logit dynamics for some classes of coordination games. We first consider a pure $n$-player coordination game that highlights the distinctive features of our metastability notion based on distributions. Then, we study coordination games on the clique without a risk-dominant strategy (which are equivalent to the well-known Glauber dynamics for the Curie-Weiss model) and coordination games on a ring (both with and without risk-dominant strategy).

cs.GT↗

arXiv2016

Discrete Preference Games in Heterogeneous Social Networks: Subverted Majorities and the Swing Player

We study discrete preference games in heterogeneous social networks. These games model the interplay between a player's private belief and his/her publicly stated opinion (which could be different from the player's belief) as a strategic game in which the players' strategies are the opinions and the cost of an opinion in a state is a convex combination through a parameter $α\in[0,1]$ of two factors: the disagreement between the player's opinion and his/her internal belief and the number of neighbors whose opinions differ from the one of the player. The parameter $α$ models how stubborn a player is: players with large $α$ change their opinion only if many neighbors disagree with his/her belief. We consider social networks that are heterogeneous in the sense that the parameter $α$ can vary from player to player. We ask if it is possible that the belief shared by the majority of the players does not coincide with the opinion that is publicly announced by the majority of the players in an equilibrium state. Our main result is a characterization of the social networks that admit an initial belief assignment for which there exists a sequence of best response moves that reach an equilibrium in which the initial majority is subverted. Our characterization is effective in the sense that can be tested efficiently and the initial belief assignment that can be subverted can be computed in time polynomial in the number of players. Our result is actually stronger as we show that in each initial belief assignment that can be subverted, subversion is actually obtained in a very strong way: it only takes one move of a single player, the swing player, to lead the social network to a point of no return in which any rational move from any player leads to a subverted majority.

cs.GT↗

arXiv2015

Minority Becomes Majority in Social Networks

It is often observed that agents tend to imitate the behavior of their neighbors in a social network. This imitating behavior might lead to the strategic decision of adopting a public behavior that differs from what the agent believes is the right one and this can subvert the behavior of the population as a whole. In this paper, we consider the case in which agents express preferences over two alternatives and model social pressure with the majority dynamics: at each step an agent is selected and its preference is replaced by the majority of the preferences of her neighbors. In case of a tie, the agent does not change her current preference. A profile of the agents' preferences is stable if the preference of each agent coincides with the preference of at least half of the neighbors (thus, the system is in equilibrium). We ask whether there are network topologies that are robust to social pressure. That is, we ask if there are graphs in which the majority of preferences in an initial profile always coincides with the majority of the preference in all stable profiles reachable from that profile. We completely characterize the graphs with this robustness property by showing that this is possible only if the graph has no edge or is a clique or very close to a clique. In other words, except for this handful of graphs, every graph admits at least one initial profile of preferences in which the majority dynamics can subvert the initial majority. We also show that deciding whether a graph admits a minority that becomes majority is NP-hard when the minority size is at most 1/4-th of the social network size.

cs.GT↗

arXiv2013

Logit Dynamics with Concurrent Updates for Local-Interaction Games

Logit choice dynamics are a family of randomized best response dynamics based on the logit choice function [McFadden, 1974], used for modeling players with limited rationality and knowledge. In this paper we study the all-logit dynamics, where at each time step all players concurrently update their strategies according to the logit choice function. In the well studied one-logit dynamics [Blume, 1993] instead at each step only one randomly chosen player is allowed to update. We study properties of the all-logit dynamics in the context of local interaction games, a class of games that has been used to model complex social phenomena and physical systems. In a local interaction game, players are the vertices of a social graph whose edges are two-player potential games. Each player picks one strategy to be played for all the games she is involved in and the payoff of the player is the sum of the payoffs from each of the games. We prove that local interaction games characterize the class of games for which the all-logit dynamics is reversible. We then compare the stationary behavior of one-logit and all-logit dynamics. Specifically, we look at the expected value of a notable class of observables, that we call decomposable observables. We prove that the difference between the expected values of the observables at stationarity for the two dynamics depends only on the rationality level beta and on the distance of the social graph from a bipartite graph. In particular, if the social graph is bipartite then decomposable observables have the same expected value. Finally, we show that the mixing time of the all-logit dynamics has the same twofold behavior that has been highlighted in the case of the one-logit: for some games it exponentially depends on the rationality level beta, whereas for other games it can be upper bounded by a function independent from beta.

cs.GT↗

arXiv2012

Convergence to Equilibrium of Logit Dynamics for Strategic Games

We present the first general bounds on the mixing time of the Markov chain associated to the logit dynamics for wide classes of strategic games. The logit dynamics with inverse noise beta describes the behavior of a complex system whose individual components act selfishly and keep responding according to some partial ("noisy") knowledge of the system, where the capacity of the agent to know the system and compute her best move is measured by the inverse of the parameter beta. In particular, we prove nearly tight bounds for potential games and games with dominant strategies. Our results show that, for potential games, the mixing time is upper and lower bounded by an exponential in the inverse of the noise and in the maximum potential difference. Instead, for games with dominant strategies, the mixing time cannot grow arbitrarily with the inverse of the noise. Finally, we refine our analysis for a subclass of potential games called graphical coordination games, a class of games that have been previously studied in Physics and, more recently, in Computer Science in the context of diffusion of new technologies. We give evidence that the mixing time of the logit dynamics for these games strongly depends on the structure of the underlying graph. We prove that the mixing time of the logit dynamics for these games can be upper bounded by a function that is exponential in the cutwidth of the underlying graph and in the inverse of noise. Moreover, we consider two specific and popular network topologies, the clique and the ring. For games played on a clique we prove an almost matching lower bound on the mixing time of the logit dynamics that is exponential in the inverse of the noise and in the maximum potential difference, while for games played on a ring we prove that the time of convergence of the logit dynamics to its stationary distribution is significantly shorter.

cs.GT↗

arXiv2011

Mixing Time and Stationary Expected Social Welfare of Logit Dynamics

We study "logit dynamics" [Blume, Games and Economic Behavior, 1993] for strategic games. This dynamics works as follows: at every stage of the game a player is selected uniformly at random and she plays according to a "noisy" best-response where the noise level is tuned by a parameter $β$. Such a dynamics defines a family of ergodic Markov chains, indexed by $β$, over the set of strategy profiles. We believe that the stationary distribution of these Markov chains gives a meaningful description of the long-term behavior for systems whose agents are not completely rational. Our aim is twofold: On the one hand, we are interested in evaluating the performance of the game at equilibrium, i.e. the expected social welfare when the strategy profiles are random according to the stationary distribution. On the other hand, we want to estimate how long it takes, for a system starting at an arbitrary profile and running the logit dynamics, to get close to its stationary distribution; i.e., the "mixing time" of the chain. In this paper we study the stationary expected social welfare for the 3-player CK game, for 2-player coordination games, and for two simple $n$-player games. For all these games, we also give almost tight upper and lower bounds on the mixing time of logit dynamics. Our results show two different behaviors: in some games the mixing time depends exponentially on $β$, while for other games it can be upper bounded by a function independent of $β$.

cs.GT↗