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We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
Understanding the behavior of no-regret dynamics in general $N$-player games is a fundamental question in online learning and game theory. A folk result in the field states that, in finite games, the empirical frequency of play under…
In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…
This paper combines ideas from Q-learning and fictitious play to define three reinforcement learning procedures which converge to the set of stationary mixed Nash equilibria in identical interest discounted stochastic games. First, we…
Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…
Recently, the eco-evolutionary game theory which describes the coupled dynamics of strategies and environment have attracted great attention. At the same time, most of the current work is focused on the classic two-player two-strategy game.…
Mixed extension has played an important role in game theory, especially in the proof of the existence of Nash equilibria in strategic form games. Mixed extension can be regarded as continuous relaxation of a strategic form game. Recently,…
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its…
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has…
Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this…
In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are…
The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally…
In this paper, we propose a passivity-based methodology for analysis and design of reinforcement learning in multi-agent finite games. Starting from a known exponentially-discounted reinforcement learning scheme, we show that convergence to…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
The cornerstone underpinning deep learning is the guarantee that gradient descent on an objective converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, where there are multiple…
We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost functionals. Our approach ensures that all system…
We study a multi-agent decision problem in population games, where agents select from multiple available strategies and continually revise their selections based on the payoffs associated with these strategies. Unlike conventional…
The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…
Motivated by game-theoretic models of crowd motion dynamics, this paper analyzes a broad class of distributed games with jump diffusions within the recently developed $\alpha$-potential game framework. We demonstrate that analyzing the…