Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2309.14317

Online and Offline Dynamic Influence Maximization Games Over Social Networks

Melih Bastopcu·S. Rasoul Etesami·Tamer Başar
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we consider dynamic influence maximization games over social networks with multiple players (influencers). The goal of each influencer is to maximize their own reward subject to their limited total budget rate constraints. Thus, influencers need to carefully design their investment policies considering individuals' opinion dynamics and other influencers' investment strategies, leading to a dynamic game problem. We first consider the case of a single influencer who wants to maximize its utility subject to a total budget rate constraint. We study both offline and online versions of the problem where the opinion dynamics are either known or not known a priori. In the singe-influencer case, we propose an online no-regret algorithm, meaning that as the number of campaign opportunities grows, the average utilities obtained by the offline and online solutions converge. Then, we consider the game formulation with multiple influencers in offline and online settings. For the offline setting, we show that the dynamic game admits a unique Nash equilibrium policy and provide a method to compute it. For the online setting and with two influencers, we show that if each influencer applies the same no-regret online algorithm proposed for the single-influencer maximization problem, they will converge to the set of $\epsilon$-Nash equilibrium policies where $\epsilon=O(\frac{1}{\sqrt{K}})$ scales in average inversely with the number of campaign times $K$ considering the average utilities of the influencers. Moreover, we extend this result to any finite number of influencers under more strict requirements on the information structure. Finally, we provide numerical analysis to validate our results under various settings.

Explore related subjects

cs.GTcs.MAcs.SYeess.SYmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Melih Bastopcu, S. Rasoul Etesami, Tamer Başar. 2023-09-25. Online and Offline Dynamic Influence Maximization Games Over Social Networks. https://arxiv.org/abs/2309.14317

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗