相关论文: Discriminants of multilinear systems

Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions on the size of their coefficients. We accomplish this by…

In practical applications, decision-makers with heterogeneous dynamics may be engaged in the same decision-making process. This motivates us to study distributed Nash equilibrium seeking for games in which players are mixed-order (first-…

Multiagent learning is a necessary yet challenging problem as multiagent systems become more prevalent and environments become more dynamic. Much of the groundbreaking work in this area draws on notable results from game theory, in…

In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among…

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…

Existing settings of decentralized learning either require players to have full information or the system to have certain special structure that may be hard to check and hinder their applicability to practical systems. To overcome this, we…

In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradient-play, augmented with a dynamic internal-model based component,…

Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical…

The maximal number of totally mixed Nash equilibria in games of several players equals the number of block derangements, as proved by McKelvey and McLennan.On the other hand, counting the derangements is a well studied problem. The numbers…

We discuss and solve a model for a game with many players, where a subset of truely deciding players is embedded into a hierarchy of dependent agents. These interdependencies modify the game matrix and the Nash equilibria for the deciding…

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…

We give a bracket polynomial expression for intermediate terms between discriminant and resultant for pair of binary forms. As an application of the bracket polynomial expression, we give an algebraic proof of the algebraic independence of…

In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show…

We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…

We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on…

We initiate the study of how to perturb the reward in a zero-sum Markov game with two players to induce a desirable Nash equilibrium, namely arbitrating. Such a problem admits a bi-level optimization formulation. The lower level requires…

In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant $2$, and provide a database of such bases. One of our motivations is…

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…