Browsing by Subject "Opinion dynamics"
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Item Open Access Consensus as a Nash equilibrium of a dynamic game(IEEE, 2016) Niazi, Muhammad Umar B.; Özgüler, Arif Bülent; Yıldız, AykutConsensus 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.Item Open Access A Differential game model of opinion dynamics: Accord and discord as nash equilibria(Birkhauser, 2020-03) Niazi, Muhammad Umar B.; Özgüler, A. BülentThis 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 the 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.Item Open Access Multiagent systems: learning, strategic behavior, cooperation, and network formation(Elsevier, 2018) Tekin, Cem; Zhang, S.; Xu, J.; Schaar, M. van der; Djurić, P. M.; Richard., C.Many applications ranging from crowdsourcing to recommender systems involve informationally decentralized agents repeatedly interacting with each other in order to reach their goals. These networked agents base their decisions on incomplete information, which they gather through interactions with their neighbors or through cooperation, which is often costly. This chapter presents a discussion on decentralized learning algorithms that enable the agents to achieve their goals through repeated interaction. First, we discuss cooperative online learning algorithms that help the agents to discover beneficial connections with each other and exploit these connections to maximize the reward. For this case, we explain the relation between the learning speed, network topology, and cooperation cost. Then, we focus on how informationally decentralized agents form cooperation networks through learning. We explain how learning features prominently in many real-world interactions, and greatly affects the evolution of social networks. Links that otherwise would not have formed may now appear, and a much greater variety of network configurations can be reached. We show that the impact of learning on efficiency and social welfare could be both positive or negative. We also demonstrate the use of the aforementioned methods in popularity prediction, recommender systems, expert selection, and multimedia content aggregation.Item Open Access A noncooperative dynamic game model of opinion dynamics in multilayer social networks(2017-08) Niazi, Muhammad Umar B.How do people living in a society form their opinions on daily or prevalent topics? A noncooperative di erential (dynamic) game model of opinion dynamics, where the agents' motives are shaped by how susceptible they are to others' in uence, how stubborn they are, and how quick they are willing to change their opinions on socially prevalent issues is considered here. The agents connected through a multilayer network interact with each other on a set of issues (layers) for a nite time duration. They express their opinions, listen to others' and, hence, mutually in uence each other. The tendency of agents to interact with people of similar traits, known as homophily, restricts them in their own localities, which may correspond to ethnicity but may as well be the ideological ones. This governs their interpersonal in uences and is the cause of clustering in the network. As the agents build their biases, they also create conceptions about the correlation between the issues. As a result, antagonistic interactions arise if the agents see each other as holding inconsistent opinions on the issues according to their individual conceptions. This way the interpersonal in uence becomes ine ective leading to con ict and disagreement between the agents. The dynamic game formulated here takes these subtle issues into account. The game is proved to admit a unique Nash equilibrium under a mild necessary and su cient condition. This condition is argued to be ful lled if there is some harmony of views among the agents in the network. The harmony may be in the form of similarity in pairwise conceptions about the issues but may also be a collective agreement on the status of a leader in the network. Since the agents do not seek any social motive in the game but their own individual motives, the existence of a Nash equilibrium can be interpreted as an emergent collective behavior out of the noncooperative actions of the agents.Item Open Access Opinion dynamics of stubborn agents under the presence of a troll as differential game(Scientific and Technical Research Council of Turkey - TUBITAK,Turkiye Bilimsel ve Teknik Arastirma Kurumu, 2021-11-30) Yıldız, A.; Özgüler, Arif BülentThe question of whether opinions of stubborn agents result in Nash equilibrium under the presence of troll is investigated in this study. The opinion dynamics is modelled as a differential game played by n agents during a finite time horizon. Two types of agents, ordinary agents and troll, are considered in this game. Troll is treated as a malicious stubborn content maker who disagrees with every other agent. On the other hand, ordinary agents maintain cooperative communication with other ordinary agents and they disagree with the troll. Under this scenario, explicit expressions of opinion trajectories are obtained by applying Pontryagin’s principle on the cost function. This approach provides insight into the social networks that comprise a troll in addition to ordinary agents