Related papers: Robust equilibria in continuous games: From strate…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and…
We study learnability of mixed-strategy Nash Equilibrium (NE) in general finite games using higher-order replicator dynamics as well as classes of higher-order uncoupled heterogeneous dynamics. In higher-order uncoupled learning dynamics,…
We know that the Nash equilibria of a game cannot be computed efficiently unless $P = PPAD$. But can they be learned? Are there dynamics that (1) can be computed efficiently by the players at each strategy profile and (2) are guaranteed to…
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…
Following the ideas laid out in Myerson (1996), Hofbauer (2000) defined a Nash equilibrium of a finite game as sustainable if it can be made the unique Nash equilibrium of a game obtained by deleting/adding a subset of the strategies that…
We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that…
Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known…
We analyze inertial coordination games: dynamic coordination games with an endogenously changing state that depends on (i) a persistent fundamental players privately learn about over time; and (ii) past play. The speed of learning…
We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash…
We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and…
This paper studies the global Nash equilibrium problem of leader-follower multi-agent dynamics, which yields consensus with a privacy information encrypted learning algorithm. With the secure hierarchical structure, the relationship between…
We investigate the degree of discontinuity of several solution concepts from non-cooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria are dealt with. Formally,…
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…
Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…
Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…
In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well…