Related papers: Mapping Game Theory to Quantum Systems: Nash Equil…
The Nash equilibrium problem is a widely used tool to model non-cooperative games. Many solution methods have been proposed in the literature to compute solutions of Nash equilibrium problems with continuous strategy sets, but, besides some…
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…
We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\delta>0$, an…
Distributed Nash equilibrium (NE) seeking problem for multi-coalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This paper considers a…
We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the…
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…
In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…
The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring…
Computing a Nash equilibrium (NE) is a central task in computer science. An NE is a particularly appropriate solution concept for two-agent settings because coalitional deviations are not an issue. However, even in this case, finding an NE…
This work studies Nash equilibria for games where a mixture of coordinating and anti-coordinating agents, with possibly heterogeneous thresholds, coexist and interact through an all-to-all network. Whilst games with only coordinating or…
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…
We consider the problem of approximating Nash equilibria of $N$ functions $f_1,\dots, f_N$ of $N$ variables. In particular, we deduce conditions under which systems of the form $$ \dot u_j(t)=-\nabla_{x_j}f_j(u(t)) $$ $(j=1,\dots, N)$ are…
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…
We develop a non-cooperative game-theoretic model for the problem of graph minor-embedding to show that optimal compiling of adiabatic quantum programs in the sense of Nash equilibrium is possible.
In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information…
In this tutorial, we present a computational overview on computing Nash equilibria in Integer Programming Games ($IPG$s), $i.e.$, how to compute solutions for a class of non-cooperative and nonconvex games where each player solves a…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…
We study the problem of computing an approximate Nash equilibrium of a game whose strategy space is continuous without access to gradients of the utility function. Such games arise, for example, when players' strategies are represented by…