Strategic Stochastic Coordination and Learning In Regular Network Games

Coordination is a desirable feature in many multi-agent systems, such as robotic, social and economic networks, allowing the execution of tasks that would be impossible by individual agents. This thesis addresses two problems in stochastic coordination where each agent make decisions strategically, taking into account the decisions of its neighbors over a regular network. In the first problem, we study the coordination in a team of strategic agents choosing to undertake one of the multiple tasks. We adopt a stochastic framework where the agents decide between two distinct tasks whose difficulty is randomly distributed and partially observed. We show that a Nash equilibrium with a simple and intuitive linear structure exists for textit{diffuse} prior distributions on the task difficulties. Additionally, we show that the best response of any agent to an affine strategy profile can be nonlinear when the prior distribution is not diffuse. Then, we state an algorithm that allows us to efficiently compute a data-driven Nash equilibrium within the class of affine policies. In the second problem, we assume that the payoff structure of the coordination game corresponds to a single task allocation scenario whose difficulty is perfectly observed. Since there are multiple Nash equilibria in this game, the agents must use a distributed stochastic algorithm know as textit{log linear learning} to play it multiple times. First, we show that this networked coordination game is a potential game. Moreover, we establish that for regular networks, the convergence to a Nash equilibrium depends on the ratio between the task-difficulty parameter and the connectivity degree according to a threshold rule. We investigate via simulations the interplay between rationality and the degree of connectivity of the network. Our results show counter-intuitive behaviors such as the existence of regimes in which agents in a network with larger connectivity require less rational agents to converge to the Nash equilibrium with high probability. Simultaneously, we examined the characteristics of both regular graphical coordination games and non-regular graphical games using this particular bi-matrix game model.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Computer Engineering

Department dc:contributor.department

Electrical and Computer Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2023

Author dc:creator

• Wei, Yi

Chairs dc:contributor.committeechair

• Pereira da Silva, Luiz Antonio
• Muller Vasconcelos, Marcos

Committee member dc:contributor.committeemember

• Dhillon, Harpreet Singh

• Game Theory
• Multi-agent system
• Coordination
• Global Games
• Incomplete Information Games
• Potential Games
• Log-linear Learning
• Task Allocation
• Regular Graph
• Irregular Graph

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:37600

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/115127