Çok takımlı öğrenmenin temellerine doğru: Yakınsama, iş birliği ve denge

Outcomes in modern socio-technical systems are increasingly shaped not by isolated individuals, but by teams of intelligent agents that coordinate internally while competing externally. This thesis focuses on the emerging grand challenge of how intelligent agents (human or artificial) learn and act as teams in complex and dynamic environments. We address two strategic environments: inter-team competition in repeated normal-form games and intra-team cooperation in dynamic, stochastic environments. We establish a unified framework based on epoch-based stochastic approximation and differential inclusions to overcome non-stationarity induced by simultaneous learning. For inter-team competition, we introduce Zero-Sum Potential Team Games (ZSPTGs), generalizing potential and zero-sum polymatrix games. We propose Team-Fictitious-Play (Team-FP), a decentralized dynamic using smoothed best responses to teammate history and opponent beliefs. We prove empirical averages under Team-FP converge almost surely to a near Team-Nash Equilibrium (TNE), quantifying error via exploration parameters. Addressing intra-team cooperation where standard dynamics often fail, we develop Logit-Q dynamics. Combining log-linear learning with Q-learning, this method allows simultaneous learning of value functions and policies without model knowledge. We prove almost sure convergence to the efficient stationary equilibrium, validated by coupling the non-stationary process with a tractable quasi-stationary reference. Finally, numerical experiments validate our theoretical findings and demonstrate effective coordination.