Related papers: Inverse maximum theorems and some consequences
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
In another paper with the same name\cite{frame}, we proposed a new representation of Game Theory, but most results are given by specific examples and argument. In this paper, we try to prove the conclusions as far as we can, including a…
This paper presents an exact penalization theory of the generalized Nash equilibrium problem (GNEP) that has its origin from the renowned Arrow-Debreu general economic equilibrium model. While the latter model is the foundation of much of…
The recent theory of sequential games and selection functions by Mar- tin Escardo and Paulo Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is…
As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the…
In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…
In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost…
For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
We show that the problem of deciding whether in a multi-player perfect information recursive game (i.e. a stochastic game with terminal rewards) there exists a stationary Nash equilibrium ensuring each player a certain payoff is Existential…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
The Generalized Nash Equilibrium Problem refers to the question of the existence of a Nash equilibrium in an abstract economy. This model is due to Kenneth J. Arrow and Gerard Debreu in their pioneering work from 1954. An abstract economy…
We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it. The scheme is implemented with a single spin qubit system and two entangled qubit system. The Nash Equilibrium…
A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems…
We consider the inverse problem of dynamic games, where cost function parameters are sought which explain observed behavior of interacting players. Maximum entropy inverse reinforcement learning is extended to the N-player case in order to…
The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we…
This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…