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This article introduces a class of $Nash$ games among $Stackelberg$ players ($NASPs$), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a…

Stochastic games have become a prevalent framework for studying long-term multi-agent interactions, especially in the context of multi-agent reinforcement learning. In this work, we comprehensively investigate the concept of constant-memory…

We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. Our central result shows that, among games that are `generic' (without indifferences) and that have a pure Nash equilibrium,…

Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game…

Many resources are provided by an ecological system that is vulnerable to tipping when exceeding a certain level of pollution, with a sudden big loss of ecosystem services. An ecological system is usually also a common-pool resource and…

There has been substantial progress on finding game-theoretic equilibria. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, and other fine-grained quantities have…

Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the…

Network games provide a framework to study strategic decision making processes that are governed by structured interdependencies among agents. However, existing models do not account for environments in which agents simultaneously interact…

In this paper, we explore aggregative games over networks of multi-integrator agents with coupled constraints. To reach the general Nash equilibrium of an aggregative game, a distributed strategy-updating rule is proposed by a combination…

Despite many distributed resource allocation (DRA) algorithms have been reported in literature, it is still unknown how to allocate the resource optimally over multiple interacting coalitions. One major challenge in solving such a problem…

This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…

In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action…

Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…

Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

Multi-time scale techniques, such as singular perturbations and averaging theory, have played an essential role in the development of distributed Nash equilibrium-seeking algorithms for network systems. Such techniques intrinsically rely on…

Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using…

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…

We propose a tactical homotopy-aware decision-making framework for game-theoretic motion planning in urban environments. We model urban driving as a generalized Nash equilibrium problem and employ a mixed-integer approach to tame the…

In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real…