A zero-sum game between a singular stochastic controller and a discretionary stopper

Hernández–Hernández, Daniel; Simon, Robert Samuel; Zervos, Mihail

doi:10.1214/13-aap986

Cited by 25 publications

(24 citation statements)

References 27 publications

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“…Finally, we derive explicit descriptions of Pareto-optimal policies when N = 2. This complements the existing literature on Nash equilibrium for stochastic two player games (De Angelis & Ferrari, 2018;Dianetti & Ferrari, 2020;Hernandez-Hernandez et al, 2015;Kwon & Zhang, 2015). Analytical comparison between the Pareto-optimal and the Nash equilibrium solutions demonstrates the role of regulator in the interbank lending game.…”

Section: A Class Of Stochastic Differential Games Of Singular Controlsupporting

confidence: 63%

Pareto Optima for a Class of Singular Control Games

Cont

Guo

2020

SSRN Journal

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We study a class of N -player stochastic differential games of singular control, motivated by the study of a dynamic model of interbank lending with benchmark rates. We describe Pareto optima for this game and show how they may be achieved through the intervention of a regulator, whose policy is a solution to a singular stochastic control problem. Pareto optima are characterized in terms of the solution to a new class of Skorokhod problems with piecewise-continuous free boundary.Pareto optimal policies are shown to correspond to the enforcement of endogenous bounds on interbank lending rates. Analytical comparison between Pareto optima and Nash equilibria for the case of two players allows to quantify the impact of regulatory intervention on the stability of the interbank rate.

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Section: A Class Of Stochastic Differential Games Of Singular Controlsupporting

confidence: 63%

Pareto Optima for a Class of Singular Control Games

Cont

Guo

2020

SSRN Journal

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“…The game between a controller and a stopper has been studied by Hernández-Hernández et al [26] for the case driven by a diffusion process, where they obtained general results on the verification lemma and gave some explicitly solvable examples.…”

Section: 4mentioning

confidence: 99%

Optimality of Two-Parameter Strategies in Stochastic Control

Yamazaki

2018

XII Symposium of Probability and Stochastic Processes

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In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are first chosen by the two continuous/smooth fit conditions, and then the optimality of the corresponding strategy is shown by verification arguments. Under the setting driven by a spectrally one-sided Lévy process, these procedures can be efficiently done thanks to the recent developments of scale functions. In this note, we illustrate these techniques using several examples where the optimal strategy as well as the value function can be concisely expressed via scale functions. AMS 2010 Subject Classifications: 60G51, 93E20, 49J40

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“…The paper showed the value of the game as a random process. Hernandez-Hernandez et al (2015) have studied Stochastic Differential Equation. The game is between controller called minimizer and stopper called maximizer.…”

Section: Games In Social Systemsmentioning

confidence: 99%

Game theory models for communication between agents: a review

Farooqui

Niazi²

2016

Complex Adapt Syst Model

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In the real world, agents or entities are in a continuous state of interactions. These inter- actions lead to various types of complexity dynamics. One key difficulty in the study of complex agent interactions is the difficulty of modeling agent communication on the basis of rewards. Game theory offers a perspective of analysis and modeling these interactions. Previously, while a large amount of literature is available on game theory, most of it is from specific domains and does not cater for the concepts from an agent- based perspective. Here in this paper, we present a comprehensive multidisciplinary state-of-the-art review and taxonomy of game theory models of complex interactions between agents.Comment: 31 pages, 7 figure

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A zero-sum game between a singular stochastic controller and a discretionary stopper

Cited by 25 publications

References 27 publications

Pareto Optima for a Class of Singular Control Games

Pareto Optima for a Class of Singular Control Games

Optimality of Two-Parameter Strategies in Stochastic Control

Game theory models for communication between agents: a review

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