Stochastic games form the foundational mathematical framework for describing multiagent interactions and underpin the theoretical foundations of multiagent reinforcement learning (MARL) and optimal decision making. However, previous research has typically focused on either two-agent settings or large-scale well-mixed agent populations, where the considered interaction scenarios were far from realistic. In this article, we consider structured populations where agents can interact with immediate neighbors. By using the pair-approximation method, we develop a new dynamical model to describe the $Q$ -learning dynamics in stochastic games on regular graphs. Through comparisons with agent-based simulation results, we validate the accuracy of our dynamical model across various stochastic games, population structures, and algorithm parameters. Our research thus provides both qualitative and quantitative insights into the effects of state transition rules and graph topologies in population dynamics. In particular, we show that, under certain conditions, state transitions can significantly promote the evolution of cooperation in social dilemmas. We also explored the effects of agent degree on cooperation, and unlike previous findings, we show that this can have either positive or negative implications for cooperation depending on the transition rules.

Reciprocity plays a crucial role in maintaining cooperation in human societies and AI systems. In this paper, we focus on reciprocity within multichannel games and examine how cooperation evolves in this context. We propose a unified framework that allows us to evaluate the reputations of interdependent actions across multiple channels while simultaneously exploring both direct and indirect reciprocity mechanisms. We identify partner and semi-partner strategies under both forms of reciprocity, with the former leading to full cooperation and the latter resulting in partial cooperation. Through equilibrium analysis, we characterize the conditions under which full cooperation and partial cooperation emerge. Moreover, we show that when players can link multiple interactions, they learn to coordinate their behavior across different games to maximize overall cooperation. Our findings provide new insights into the maintenance of cooperation across various reciprocity mechanisms and interaction patterns.

In this article, we introduce a new theory for payoff control in multichannel learning environments, where agents interact with each other over multiple channels and each channel is a repeated normal form game. We propose two payoff control strategies-partial control and full control-that allow a single agent to set an upper bound to the opponent's expected payoffs summed across all channels, even if the opponent is a reinforcement learning agent. We prove that a partial (or full) control strategy can be obtained by solving a system of inequalities, and characterize the conditions under which such a partial (or full) control strategy exists. We show that by utilizing these control strategies, the agent can influence the opponent's learning evolution and direct it toward a desired viable equilibrium. Our experiments confirm the effectiveness of our theory for payoff control in a wide range of multichannel learning environments.

Understanding and predicting the behavior of large-scale multiagents in games remains a fundamental challenge in multiagent systems. This article examines the role of heterogeneity in equilibrium formation by analyzing how smooth regret matching drives a large number of heterogeneous agents with diverse initial policies toward unified behavior. By modeling the system state as a probability distribution of regrets and analyzing its evolution through the continuity equation, we uncover a key phenomenon in diverse multiagent settings: the variance of the regret distribution diminishes over time, leading to the disappearance of heterogeneity and the emergence of consensus among agents. This universal result enables us to prove convergence to quantal response equilibria in both competitive and cooperative multiagent settings. This work advances the theoretical understanding of multiagent learning and offers a novel perspective on equilibrium selection in diverse game-theoretic scenarios.

Modeling the dynamics of multi-agent learning has long been an important research topic. The focus of previous research has been either on 2-agent settings or well-mixed infinitely large agent populations. In this paper, we consider the scenario where n Q-learning agents locate on regular graphs, such that agents can only interact with their neighbors. We examine the local interactions between individuals and their neighbors, and derive a formal model to capture the Q-value dynamics of the entire population. Through comparisons with agent-based simulations on different types of regular graphs, we show that our model describes the agent learning dynamics in an exact manner.

In order to improve resource utilization of software evolution processes, reduce the cost of resource management, on the basis of classifying and describing the resources, introduced 3S technology to analysis and manage the typical resources in area of Software Evolution Processes, and with the updating principle of GIS Database, proposed a framework of Management Resources System, and also designed an algorithm of Management Resources System. Studies have shown that the approach based on 3S to resources management of software evolution processes, improving resource utilization, managing resources dynamically, according to the requirement to apply for and allocate resources, and other resource management objectives can be achieved.

Software evolution process model (EPM) is created in terms of a formal evolution process meta-model (EPMM) and semi-formal approach to modeling based on EPMM [1]. In order to better manage and control the software evolution process and make the best of existing software technology, the method to transform any EPM to its execution model based logic programming has been proposed. Completeness of conversion depends on completeness of the rules, that is, all the expressions of the original model are found the correspondence in the target model. Since transformation rules are proposed based on precondition or post-condition types of activities in anyone EPM, this need to prove that activity type set in anyone EPM is completeness set. To this end, the precondition and post-condition of activities in EPM are classified based on analyzing all expressions in EPMs and the semantics of the activity execution. Type completeness set of activity’s precondition and its post-condition is presented. Lastly we prove that the activity type set in anyone EPM is completeness set by mathematical induction.