Foraging motion of swarms with leaders as Nash equilibria

Yildiz, Aykut; Özgüler, A.B.

doi:10.1016/j.automatica.2016.07.024

Cited by 12 publications

(2 citation statements)

References 19 publications

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“…The optimal control of consensus model and control through a leader model in [2] also use integral cost functions and has similarities to our model except that the objective in their case is control of consensus via external actions. The noncooperative dynamic game model here is inspired by the foraging biological swarm models in [16], [20], and [21].…”

Section: Introductionmentioning

confidence: 99%

Consensus as a Nash Equilibrium of a Dynamic Game

Niazi

Özgüler

Yildiz

2016

2016 12th International Conference on Signal-Image Technology &Amp; Internet-Based Systems (SITIS)

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Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.Comment: 7 pages, 9 figure, Pre-print from the Proceedings of the 12th International Conference on Signal Image Technology and Internet-based Systems (SITIS), 201

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Section: Introductionmentioning

confidence: 99%

Consensus as a Nash Equilibrium of a Dynamic Game

Niazi

Özgüler

Yildiz

2016

2016 12th International Conference on Signal-Image Technology &Amp; Internet-Based Systems (SITIS)

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“…Integral cost functions are also employed in [2] with a quite different objective of external control of consensus via suitable inputs. The dynamic game on multiple issues studied here is inspired by the foraging swarm models in [37,44,45].…”

Section: Introductionmentioning

confidence: 99%

A Differential Game Model of Opinion Dynamics: Accord and Discord as Nash Equilibria

Niazi

Özgüler

2020

Dyn Games Appl

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This paper presents a noncooperative differential (dynamic) game model of opinion dynamics with open-loop information structure. In this game, the agents' motives are shaped by their expectations of the nature of others' opinions as well as how susceptible they are to get influenced by others, how stubborn they are, and how quick they are willing to change their opinions on a set of issues in a prescribed time interval. These motives are independently formed by all agents. The existence of a Nash equilibrium in the network means that a collective behavior emerges out of local interaction rules and these individual motives. We prove that a unique Nash equilibrium may exist in the game under quite different circumstances. It may exist not only if there is a harmony of perceptions among the agents of the network, but also when agents have different views about the correlation among issues. The first leads to an accord in the network usually expressed as a partial consensus, and the second to a discord in the form of oscillating opinions. In case of an accord, the harmony in the network may be in the form of similarity in pairwise conceptions about the issues but may also be an agreement on the status of a "leader" in the network. A Nash equilibrium may fail to exist only if the network is in a state of discord.

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Reinforcement Learning Based Reciprocal Decision‐Making in Multi‐Player Pursuit‐Evasion Differential Games

Lu,

Yang

2024

Intl J Robust & Nonlinear

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This paper investigates reciprocal decision‐making in multi‐player pursuit‐evasion (MPE) differential games by analyzing altruistic decision‐making among players. The irrational decision‐making motivated by altruism is modeled by introducing a distance term between cooperative players and common adversaries into the original performance function. Based on the new performance function, the Nash policy under irrationality is first sought using the maximum principle, based on which reinforcement learning is proposed to approximate the Nash policy. Subsequently, sufficient conditions are proposed to determine whether irrational decision‐making is egoistic or altruistic and whether reciprocity is generated under altruistic decision‐making among players. Finally, the effectiveness of the proposed results is verified by a numerical example.

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Foraging motion of swarms with leaders as Nash equilibria

Cited by 12 publications

References 19 publications

Consensus as a Nash Equilibrium of a Dynamic Game

Consensus as a Nash Equilibrium of a Dynamic Game

A Differential Game Model of Opinion Dynamics: Accord and Discord as Nash Equilibria

Reinforcement Learning Based Reciprocal Decision‐Making in Multi‐Player Pursuit‐Evasion Differential Games

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