Nash equilibria in nonzero-sum differential games with impulse control

Sadana, Utsav; Reddy, Puduru Viswanadha; Zaccour, Georges

doi:10.1016/j.ejor.2021.03.025

Cited by 19 publications

(7 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the CLSC of the Nash equilibrium game (NG), the manufacturer ω P m and the retailer has the same strength and no one is in the absolute leading position for P r . So, in NG the decisions of both parties depend on each other's behaviour [96][97][98]. Proposition 5.…”

Section: Nash Equilibrium Game Pricing (Ng)mentioning

confidence: 98%

A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference

Pan

Lin

2021

Axioms

View full text Add to dashboard Cite

This paper focuses on the pricing problem of a two-stage closed-loop supply chain (CLSC) considering the cross-channel recycling and channel preference based on a single manufacturer and a single traditional retailer. The pricing decision problem raises from the manufacturer’s direct sales and the retailer’s retailing including recycling. Managers need to focus on intelligible management considering consumer channel preferences, cross-channel recovery and pricing strategies. According to game theory, centralized and decentralized CLSC decision models are used to provide an efficient solution to managers for the pricing problem. The centralized model consists of differential and uniform pricing strategy and the decentralized model consists of manufacturer-led Stackelberg, retailer-led Stackelberg and Nash equilibrium game, respectively. The impact of cross-channel recycling rate and channel preference on pricing and profitability in a two-stage CLSC system is explained elaborately in this study. The results show that cross-channel recovery rates and consumer channel preferences have a direct significant impact on pricing strategies including profit allocation decisions in CLSC. It demonstrated that different channel preferences leading to different pricing strategies and decision for manufacturers and retailers choices. Manufacturer’s pricing decreases when channel preferences are constant and cross-channel recovery rates increase. Retailer’s pricing remains stable as the cross-channel recovery rate has less affected on it. Furthermore, if the cross-channel recovery rates increase, then the manufacturers pricing decreases and retailers pricing increases. This information will be a helpful guideline for the manager to select suitable pricing strategies based on the company scenario.

show abstract

Section: Nash Equilibrium Game Pricing (Ng)mentioning

confidence: 98%

A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference

Pan

Lin

2021

Axioms

View full text Add to dashboard Cite

show abstract

“…Recent papers by Cosso [21] and El Asri and Mazid [30] consider dynamic programming approach for zero-sum stochastic DGs where both players use only impulse control. Works by Aïd et al [1], Basei et al [8], Campi and De Santis [18] and Sadana et al [54,55] study some nonzero-sum DGs with impulse controls. We mention that in [1] authors studied a DG between two notions that have different targets for the currency exchange rate, and provided a system of QVIs that needs to be solved in order to compute the NE.…”

Section: Below By (H) and (H Cmentioning

confidence: 99%

“…We mention that in [1] authors studied a DG between two notions that have different targets for the currency exchange rate, and provided a system of QVIs that needs to be solved in order to compute the NE. In [54] the necessary and sufficient conditions for the existence of an open-loop NE for a class of DGs with impulse control were formulated. Impulse control 1 INTRODUCTION problems are typically solved using two main approaches, one based on Bellman's [9] DPP, and another using Pontryagin's maximum principle [15] to compute the value function (see e.g.…”

Section: Below By (H) and (H Cmentioning

confidence: 99%

A Differential Game Control Problem in Finite Horizon with an Application to Portfolio Optimization

Asri¹,

Lalioui²

2022

Preprint

View full text Add to dashboard Cite

This paper considers a new class of deterministic finite-time horizon, two-player, zero-sum differential games (DGs) in which the maximizing player is allowed to take continuous and impulse controls whereas the minimizing player is allowed to take impulse control only. We seek to approximate the value function, and to provide a verification theorem for this class of DGs. We first, by means of dynamic programming principle (DPP) in viscosity solution (VS) framework, characterize the value function as the unique VS to the related Hamilton-Jacobi-Bellman-Isaacs (HJBI) double-obstacle equation. Next, we prove that an approximate value function exists, that it is the unique solution to an approximate HJBI double-obstacle equation, and converges locally uniformly towards the value function of each player when the time discretization step goes to zero. Moreover, we provide a verification theorem which characterizes a Nash-equilibrium for the DG control problem considered. Finally, by applying our results, we derive a new continuous-time portfolio optimization model, and we provide related computational algorithms.

show abstract

“…For instance, in the research of optimal control of delay system, see Yu; 26 for near-optimal control problems, see Huang and Zhang; 27 and for differential game problems, see Sadana et al. 28 It is worth pointing out that the stochastic control problems stated above all assume that the controller can obtain all the information of the control system, that is, the noise of the state equation can be completely observed. But in reality, due to the interference of external noise, the information we obtained is often incomplete.…”

Section: Introductionmentioning

confidence: 99%

Maximum principle for partially observed stochastic recursive optimal control problems involving impulse controls

Zhang

2022

Optim Control Appl Methods

View full text Add to dashboard Cite

This article focuses on a stochastic recursive optimal control problem involving impulse control under partially observed information and obtains the related maximum principle. Unlike the classical literature, both the regular control (considering the nonconvexity of the domain) and the impulse control (where the domain is convex) are considered in the framework. In virtue of two types of variational methods, spike variation and convex variation, the Pontryagin maximum principle is established. In addition, to demonstrate the validity of the results, this article investigates a differential game problem as an application.

show abstract

Nash equilibria in nonzero-sum differential games with impulse control

Cited by 19 publications

References 48 publications

A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference

A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference

A Differential Game Control Problem in Finite Horizon with an Application to Portfolio Optimization

Maximum principle for partially observed stochastic recursive optimal control problems involving impulse controls

Contact Info

Product

Resources

About