Machine learning and artificial intelligence methods have achieved remarkable success, matching and even surpassing human capabilities in various complex tasks. However, many demonstrations have generally neglected a critical part of the intelligence that is prevalent in the real world, namely, the one that emerges from the collective of interconnected individuals with diverse capabilities, perspectives and experiences.

To explore this fact, the current dissertation utilizes mathematical models of collaborative learning and reasoning. These models are based on the following two concepts: Bayesian inference, which is used to model how agents update their beliefs in the face of uncertain data, and graphs, which represent the communication links and information exchange among individuals.

Through these models, the current work examines the effect of dynamic models on learning, as well as the implications of causal interactions among agents on their decisions. In particular, this work is structured around (i) the effect of different information exchange procedures on learning, (ii) the need to adapt to changing environments, and (iii) the cause-and-effect relationships that arise among interacting agents over a graph. The net effect of our study is a collection of new results and design tools that strengthen our understanding of multi-agent networks.

A critical part of collaboration among agents is how information is exchanged among them. The first part of the dissertation examines how information is (i) fused and (ii) shared within a social network of interacting agents, and how these processes affect the learning capabilities of the network. In particular, the learning rates of the network are compared under both arithmetic and geometric fusion rules. The effect of network connectivity and information diversity is also clarified, in addition to the impact of random and partial information sharing.

The second part of the dissertation examines network behavior under changing environments, where the unknown state of nature is assumed to follow a hidden Markov model (HMM). The work examines the agents' ability to track the evolving state. It also considers the more challenging case of partially observable Markov decision processes (POMDP), where agents are able to take actions based on certain sequential policies. By acknowledging the uncertainties present in real-world scenarios and tackling them through cooperative state estimation, the methods devised in this work can facilitate the practical application of multi-agent reinforcement learning.

The first two parts of the dissertation address how procedural and environmental factors influence agent behavior. In the final part, the work focuses on the cause-and-effect relationships between agents. Specifically, causal inference tools are developed to determine how agents impact other agents' decisions and how this influence diffuses through the network. Expressions are derived for the total effects of agents over time in terms of the instantaneous direct effects, and an algorithm is devised to learn the causal effects from observational data.