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Social hierarchy is important that can not be ignored in human socioeconomic activities and in the animal world. Here we incorporate this factor into the evolutionary game to see what impact it could have on the cooperation outcome. The…

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…

In real-world scenarios, individuals often cooperate for mutual benefit. However, differences in wealth can lead to varying outcomes for similar actions. In complex social networks, individuals' choices are also influenced by their…

Reinforcement learning (RL) relies heavily on exploration to learn from its environment and maximize observed rewards. Therefore, it is essential to design a reward function that guarantees optimal learning from the received experience.…

Self-interested individuals often fail to cooperate, posing a fundamental challenge for multi-agent learning. How can we achieve cooperation among self-interested, independent learning agents? Promising recent work has shown that in certain…

Evolution of cooperation in the prisoner's dilemma and the public goods game is studied, where initially players belong to two independent structured populations. Simultaneously with the strategy evolution, players whose current utility…

Since the earliest days of reinforcement learning, the workhorse method for assigning credit to actions over time has been temporal-difference (TD) learning, which propagates credit backward timestep-by-timestep. This approach suffers when…

Decades of scientific inquiry have sought to understand how evolution fosters cooperation, a concept seemingly at odds with the belief that evolution should produce rational, self-interested individuals. Most previous work has focused on…

A network model based on players' aspirations is proposed and analyzed theoretically and numerically within the framework of evolutionary game theory. In this model, players decide whether to cooperate or defect by comparing their payoffs…

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic…

We study the emergence of cooperative behaviors in reinforcement learning agents by introducing a challenging competitive multi-agent soccer environment with continuous simulated physics. We demonstrate that decentralized, population-based…

Spatial public goods games model collective dilemmas where individual payoffs depend on population-level strategy configurations. Most existing studies rely on evolutionary update rules or value-based reinforcement learning methods. These…

In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a…

To achieve general intelligence, agents must learn how to interact with others in a shared environment: this is the challenge of multiagent reinforcement learning (MARL). The simplest form is independent reinforcement learning (InRL), where…

Training a multi-agent reinforcement learning (MARL) model with a sparse reward is generally difficult because numerous combinations of interactions among agents induce a certain outcome (i.e., success or failure). Earlier studies have…

Growing concerns about safety and alignment of AI systems highlight the importance of embedding moral capabilities in artificial agents: a promising solution is the use of learning from experience, i.e., Reinforcement Learning. In…

Reinforcement learning (RL) algorithms aim to learn optimal decisions in unknown environments through experience of taking actions and observing the rewards gained. In some cases, the environment is not influenced by the actions of the RL…

Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world,…

Cooperative behaviors are common in humans and are fundamental to our society. Theoretical and experimental studies have modeled environments in which the behaviors of humans, or agents, have been restricted to analyze their social…

In social dilemmas self-interested learning agents face the choice between the societal benefit of cooperation and the immediate reward of defection. Significant evidence exists on the benefits of assortment mechanisms such as partner…