On games with coordinating and anti-coordinating agents

Vanelli, Martina; Arditti, Laura; Como, Giacomo; Fagnani, Fabio

doi:10.1016/j.ifacol.2020.12.2848

Cited by 12 publications

(14 citation statements)

References 10 publications

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“…Hence, since (ζ, δ) ∈ Ψ, it holds that A(x(T − 1)) ≤ τ ζ + 1, which contradicts (27), completing the proof.…”

Section: Proving Invariancementioning

confidence: 84%

“…Finally, the equilibrium x * satisfies the first condition of Theorem 2 as A(x * ) = 31 ∈ [27,42]. The second condition is also satisfied since L(z) = R(z) = ∅.…”

Section: Denote the Type Of The Initially Active Agent Bymentioning

confidence: 99%

“…In [8], any network of all coordinators or all anticoordinators who update their strategies asynchronously, that is one at a time, is guaranteed to equilibrate. In [27], [28], sufficient conditions for existence of and finite-time convergence to equilibrium in heterogeneous mixed populations of coordinators and anticoordinators are shown. Although structured populations are often more popular as they model the heterogeneity in neighbors, many real-world populations are well-mixed, where individuals know the total number or ratio of others who have chosen a particular strategy.…”

Section: Introductionmentioning

confidence: 99%

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Characterizing Oscillations in Heterogeneous Populations of Coordinators and Anticoordinators

Ramazi¹,

Roohi²

2022

Preprint

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Oscillations often take place in populations of decision makers that are either a coordinator, who takes action only if enough others do so, or an anticoordinator, who takes action only if few others do so. Populations consisting of exclusively one of these types are known to reach an equilibrium, where every individual is satisfied with her decision. Yet it remains unknown whether oscillations take place in a population consisting of both types, and if they do, what features they share. We study a wellmixed population of individuals, which are either a coordinator or anticoordinator, each associated with a possibly unique threshold and initialized with the strategy A or B. At each time, an agent becomes active to update her strategy based on her threshold: an active coordinator (resp. anticoordinator) updates her strategy to A (resp. B) if the portion of other agents who have chosen A exceeds (falls short of) her threshold, and updates to B (resp. A) otherwise. We define the state of the population dynamics as the distribution over the thresholds of those who have chosen A. We show that the population can admit several minimally positively invariant sets, where the solution trajectory oscillates. We explicitly characterize a class of positively invariant sets, prove their invariance, and provide a necessary and sufficient condition for their stability. Our results highlight the possibility of non-trivial, complex oscillations in the absence of noise and population structure and shed light on the reported oscillations in nature and human societies.

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“…Hence, since (ζ, δ) ∈ Ψ, it holds that A(x(T − 1)) ≤ τ ζ + 1, which contradicts (27), completing the proof.…”

Section: Proving Invariancementioning

confidence: 84%

“…Finally, the equilibrium x * satisfies the first condition of Theorem 2 as A(x * ) = 31 ∈ [27,42]. The second condition is also satisfied since L(z) = R(z) = ∅.…”

Section: Denote the Type Of The Initially Active Agent Bymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Characterizing Oscillations in Heterogeneous Populations of Coordinators and Anticoordinators

Ramazi¹,

Roohi²

2022

Preprint

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“…The standard literature on coordination games (Ramazi, Riehl, and Cao 2016;Bramoullé and Kranton 2015;Apt, Simon, and Wojtczak 2015;Vanelli et al 2019;Apt, Simon, and Wojtczak 2019;Jackson and Zenou 2015) only consists of the first term, namely α|N (i, x, x i )|. The second term, namely C i (1 − x i ) could be easily incorporated into the coordination game setting, e.g., (Vanelli et al 2019), but is not often considered. The third term, which captures herd immunity has not been considered before.…”

Section: Preliminaries and Formulationmentioning

confidence: 99%

“…There is a certain dis-utility an individual gets by not conforming to their social contacts; on the other hand, the individual gets a utility by conforming to its social contacts. This phenomenon can be viewed as a coordination games, which has been very well studied (Ramazi, Riehl, and Cao 2016;Bramoullé and Kranton 2015;Apt, Simon, and Wojtczak 2015;Vanelli et al 2019;Apt, Simon, and Wojtczak 2019;Jackson and Zenou 2015;Adam, Dahleh, and Ozdaglar 2012). In its basic form, the utility of a node in a coordination game is a function of the number of neighbors having the same state as the node.…”

Section: Introductionmentioning

confidence: 99%

Persistence of Anti-vaccine Sentiment in Social Networks Through Strategic Interactions

Ahsan-Ul-Haque

Thakur

Bielskas

et al. 2021

AAAI

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Vaccination is the primary intervention for controlling the spread of infectious diseases. A certain level of vaccination rate (referred to as "herd immunity'') is needed for this intervention to be effective. However, there are concerns that herd immunity might not be achieved due to an increasing level of hesitancy and opposition to vaccines. One of the primary reasons for this is the cost of non-conformance with one's peers. We use the framework of network coordination games to study the persistence of anti-vaccine sentiment in a population. We extend it to incorporate the opposing forces of the pressure of conforming to peers, herd-immunity and vaccination benefits. We study the structure of the equilibria in such games, and the characteristics of unvaccinated nodes. We also study Stackelberg strategies to reduce the number of nodes with anti-vaccine sentiment. Finally, we evaluate our results on different kinds of real world social networks.

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Social Diffusion Dynamics in Cyber–Physical–Human Systems

Zino

Cao

2023

Cyber–Physical–Human Systems

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On games with coordinating and anti-coordinating agents

Cited by 12 publications

References 10 publications

Characterizing Oscillations in Heterogeneous Populations of Coordinators and Anticoordinators

Characterizing Oscillations in Heterogeneous Populations of Coordinators and Anticoordinators

Persistence of Anti-vaccine Sentiment in Social Networks Through Strategic Interactions

Social Diffusion Dynamics in Cyber–Physical–Human Systems

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