A Stay-in-a-Set Game without a Stationary Equilibrium

Hansen, Kristoffer Arnsfelt; Raskin, Mikhail

doi:10.4204/eptcs.305.6

Cited by 3 publications

References 22 publications

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A Note on Game Theory and Verification

Bouyer¹

2019

Automated Technology for Verification and Analysis

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We present some basics of game theory, focusing on matrix games. We then present the model of multiplayer stochastic concurrent games (with an underlying graph), which extends standard finite-state models used in verification in a multiplayer and concurrent setting; we explain why the basic theory cannot apply to that general model. We then focus on a very simple setting, and explain and give intuitions for the computation of Nash equilibria. We then give a number of undecidability results, giving limits to the approach. Finally we describe the suspect game construction, which (we believe) captures and explains well Nash equilibria and allow to compute them in many cases.

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A Note on Game Theory and Verification

Bouyer¹

2019

Automated Technology for Verification and Analysis

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Nurse allocation in hospital: hybridization of linear regression, fuzzy set and game-theoretic approaches

2022

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Sufficient numbers of staff are required for any hospital for providing better services to patients with satisfactory treatment. In most hospitals, the patient's treatment and care depend on the availability of nurses. Less number of nurses are a reason for average care and treatment to patients, whereas more than the required number of nurses may cause wastage of expenditure and manpower. More importantly, an additional number of nurses may be assigned to some hospitals where a sufficient number of nurses are not available. Moreover, nurses are of different categories such as qualified nurses having experience in providing service to patients, qualified nurses without having experience, and nurses without qualification but have experience. The expenditure also depends on categories of nurses' appointments. To reach an equilibrium point in appointing nurses, we propose a hybridization model using linear regression, fuzzy set theory and game-theoretic approaches. Regression analysis is implemented for prediction based on different fuzzy membership values of independent variables. We implement two concepts of game theory, the Nash equilibrium and the perfect Nash equilibrium. Implementing the Nash equilibrium, different equilibria values are generated and by implementing perfect Nash equilibrium, a subgame is generated to reach one equilibrium value. We have illustrated the proposed approach using a case study in which the linear regression approach is implemented to predict the patients’ arrival rate based on the monetary standard of the patient, communication facilities, patients curing chances, and patient choice towards the hospital, where these four features are quantified using fuzzy membership values. Nash equilibrium decides all possible ways of the nurses' allocations and perfect Nash equilibrium assist to reach an appropriate allocation. Thus, the hybridization of the regression approach, fuzzy membership and game theory approaches finalize the exact allocation of nurses. Finally, a comparative analysis is given to demonstrate the effectiveness of the proposed approach.

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∃ℝ-Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games

Hansen¹,

Sølvsten²

2020

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A Stay-in-a-Set Game without a Stationary Equilibrium

Abstract: We give an example of a finite-state two-player turn-based stochastic game with safety objectives for both players which has no stationary Nash equilibrium. This answers an open question of Secchi and Sudderth.

Cited by 3 publications

References 22 publications

A Note on Game Theory and Verification

A Note on Game Theory and Verification

Nurse allocation in hospital: hybridization of linear regression, fuzzy set and game-theoretic approaches

∃ℝ-Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games

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