Browsing by Subject "Dynamic game theory"

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Open Access
A Differential game model of opinion dynamics: Accord and discord as nash equilibria
(Birkhauser, 2020-03) Niazi, Muhammad Umar B.; Özgüler, A. Bülent
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 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.
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.
Open Access
Partially informed agents can form a swarm in a nash equilibrium
(Institute of Electrical and Electronics Engineers, 2015) Yildiz, A.; Ozguler, A. B.
Foraging swarms in one-dimensional motion with incomplete position information are studied in the context of a noncooperative differential game. In this game, the swarming individuals act with partial information as it is assumed that each agent knows the positions of only the adjacent ones. It is shown that a Nash equilibrium solution that exhibits many features of a foraging swarm such as movement coordination, self-organization, stability, and formation control exists. © 1963-2012 IEEE.