English
Related papers

Related papers: A fractional-order difference Cournot duopoly game…

200 papers

In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…

Numerical Analysis · Mathematics 2016-11-24 Guang-an Zou , Bo Wang

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…

Computer Science and Game Theory · Computer Science 2020-10-01 Lukáš Adam , Rostislav Horčík , Tomáš Kasl , Tomáš Kroupa

We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step…

Optimization and Control · Mathematics 2023-07-31 Stefan Clarke , Gabriele Dragotto , Jaime Fernández Fisac , Bartolomeo Stellato

We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of…

Neurons and Cognition · Quantitative Biology 2014-02-18 Ihor Lubashevsky , Bohdan Datsko

This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot-Nash equilibria for games with a continuum of players with both attractive and…

Optimization and Control · Mathematics 2014-05-07 Adrien Blanchet , Guillaume Carlier

It is well known that the Leibniz rule for the integer derivative of order one does not hold for the fractional derivative case when the fractional order lies between 0 and 1. Thus it poses a great difficulty in the calculation of…

General Mathematics · Mathematics 2019-05-16 Bichitra Kumar Lenka

Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann-Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their…

Chaotic Dynamics · Physics 2015-03-17 Vasily E. Tarasov

This work addresses competitive resource allocation in a sequential setting, where two players allocate resources across objects or locations of shared interest. Departing from the simultaneous Colonel Blotto game, our framework introduces…

Computer Science and Game Theory · Computer Science 2025-04-24 Omkar Thakoor , Rajgopal Kannan , Victor Prasanna

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti

This letter proposes a fractional-order battery model based on the Caputo definition. A closed-form time-domain solution is derived, enabling a simple recursive expression for discrete-time implementation. The model requires only the…

Systems and Control · Electrical Eng. & Systems 2025-05-20 Yangyang Xu , Hongyu Zhao , Chengzhong Zhang , Chenglin Liao

Necessary and sufficient conditions are given for the asymptotic stability and instability of a two-dimensional incommensurate order autonomous linear system, which consists of a differential equation with a Caputo-type fractional order…

Dynamical Systems · Mathematics 2017-12-14 Oana Brandibur , Eva Kaslik

In this discussion draft, we investigate five different models of duopoly games, where the market is assumed to have an isoelastic demand function. Moreover, quadratic cost functions reflecting decreasing returns to scale are considered.…

Theoretical Economics · Economics 2022-03-21 Xiaoliang Li

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on…

Numerical Analysis · Mathematics 2020-02-25 Junying Cao , Zhenning Cai

In this paper we introduce the fractional-order variant of a Gompertz-like discrete system. The chaotic behavior is suppressed with an impulsive control algorithm. The numerical integration and the Lyapunov exponent are obtained by means of…

Dynamical Systems · Mathematics 2020-04-22 Marius-F. Danca , Michal Feckan

In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov's convex regularization and via differential inclusions, the…

Chaotic Dynamics · Physics 2015-06-02 Marius-F Danca , Roberto Garrappa

This paper examines the convergence of no-regret learning in Cournot games with continuous actions. Cournot games are the essential model for many socio-economic systems, where players compete by strategically setting their output quantity.…

Computer Science and Game Theory · Computer Science 2020-02-12 Yuanyuan Shi , Baosen Zhang

This paper demonstrates the quantization of a spatial Cournot duopoly model with product choice, a two stage game focusing on non-cooperation in locations and quantities. With quantization, the players can access a continuous set of…

Quantum Physics · Physics 2015-05-19 Ramij Rahaman , Priyadarshi Majumdar , B. Basu

This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…

Dynamical Systems · Mathematics 2010-01-12 Iasson Karafyllis , Zhong-Ping Jiang , George Athanasiou

We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the…

Optimization and Control · Mathematics 2022-10-28 Filippo Fabiani , Barbara Franci , Simone Sagratella , Martin Schmidt , Mathias Staudigl

We analyze a nonlinear discrete-time Cournot duopoly game, where players have heterogeneous expectations. Two types of players are considered: boundedly rational and naive expectations. In this study we show that the dynamics of the duopoly…

Chaotic Dynamics · Physics 2016-09-08 H. N. Agiza , A. A. Elsadany