医联体环境下患者情绪影响的分级诊疗策略演化博弈分析

doi:10.16381/j.cnki.issn1003-207x.2020.1886

Abstract

Abstract:

In recent years， with the continuous economic development， the masses have become more concerned about their own health. When they are unwell， they often skip the primary medical institutions and go directly to the second and third-level hospitals， thus causing the second and third-level hospitals to become "overcrowded." The phenomenon of few people visiting the primary medical institutions has exacerbated the unreasonable allocation of medical resources. The overkill of the second and third-level hospitals has caused a shortage of medical resources， while the idle medical resources of the primary medical institutions have caused “difficult and expensive medical treatment”. The establishment of a graded diagnosis and treatment system is an important measure to solve the problem of “difficult and expensive medical treatment” and improve the allocation of medical resources of the masses， which is related to the life and health of the masses， social stability， and the smooth development of the national medical and health undertakings. The graded diagnosis and treatment system follow the principle of patient voluntariness. The patient's willingness to cooperate has an important impact on the implementation of the graded diagnosis and treatment policy. Because the public attaches great importance to health conditions， when oneself or relatives are sick， they cannot be rational and have subjective emotions. Obviously， completely rational assumptions cannot reflect real social situations. Hence， the RDEU （rank-based expected utility） theory and game theory are combined， considering the impact of the patient's strategy under emotions on the construction of the graded diagnosis and treatment system， and a three-party evolutionary game model of the government， the medical service system and the patient is constructed. Based on the Lyapunov first rule， the stability of the strategy combination of game subjects in the three emotional states of the patient is analyzed， and MATLAB R2020a is used to simulate and analyze the impact of key elements （such as the system construction cost， the cure rate of primary medical institutions， and the government financial support amount.） on the evolution of the game system. It is found that： 1） Compared with pessimistic emotion， the evolution of the entire system is more ideal and the evolution speed is faster when patients are rational or optimistic； 2） When the cure rate of primary medical institutions is low， the patients’ best strategy is no cooperation in rational state， but when considering that patients have subjective emotions， if the construction cost of the graded diagnosis and treatment system can be lower than a certain level， the best strategy for patients will be to actively cooperate； 3） As the amount of financial subsidies increases， the willingness of the medical service system to participate in the construction of a graded diagnosis and treatment system will gradually decrease.

Key words: graded diagnosis and treatment, referral, patient emotion, RDEU theory, evolutionary game theory

CLC Number:

R197.1

Shu-hui SUN,Qiang SU. Evolutionary Game Analysis of Graded Diagnosis and Treatment Strategies Affected by Patients' Emotions under Regional Medical Association[J]. Chinese Journal of Management Science, 2023, 31(11): 288-299.

Figures/Tables 20

		患者	政府卫生部门
		患者	扶持 $g$	不扶持 $1 - g$
医疗服务系统	积极参与 $h$	配合 $p$	$S + R a - C e$ ， $H - C p l - (1 - β) (C p h - C s)$ ， $B - S$	$R a - C e$ ， $H - C p l - (1 - β) (C p h - C s)$ ， $B$
	积极参与 $h$	不配合 $1 - p$	$S + R b - C e$ ， $H - C p h$ ， $- L - S$	$R b - C e$ ， $H - C p h$ ， $- L$
	不参与 $1 - h$	配合 $p$	$R a$ ， $H - C p l - (1 - β) C p h$ ， $B$	$R a$ ， $H - C p l - (1 - β) C p h$ ， $B$
	不参与 $1 - h$	不配合 $1 - p$	$R b$ ， $H - C p h$ ， $- L$	$R b$ ， $H - C p h$ ， $- L$

医疗服务系统的策略收益	概率	等级	决策权重
$S + R a - C e$	$h p g$	$1$	$w (h p g)$
$S + R b - C e$	$h (1 - p) g$	$1 - h p g$	$w (h g) - w (h p g)$
$R a$	$(1 - h) p$	$1 - h g$	$w (p - h p + h g) - w (h g)$
$R a - C e$	$h p (1 - g)$	$1 - p - h g + h p$	$w (p + h g - h p g) - w (p - h p + h g)$
$R b$	$(1 - h) (1 - p)$	$(1 - h g) (1 - p)$	$w [1 - h (1 - p) (1 - g)]$ $- w (p + h g - h p g)$
$R b - C e$	$h (1 - p) (1 - g)$	$h (1 - p) (1 - g)$	$1 - w [1 - h (1 - p) (1 - g)]$

病患的策略收益	概率	等级	决策权重
$H - C p l - (1 - β) (C p h - C s)$	$h p$	$1$	$w (h p)$
$H - C p l - (1 - β) C p h$	$(1 - h) p$	$1 - h p$	$w (p) - w (h p)$
$H - C p h$	$1 - p$	$1 - p$	$1 - w (p)$

策略收益	概率	等级	决策权重
$B$	$p (1 - h g)$	$1$	$w (p - h p g)$
$B - S$	$h p g$	$1 - p + h p g$	$w (p) - w (p - h p g)$
$- L$	$(1 - p) (1 - h g)$	$1 - p$	$w (1 - h g + h p g) - w (p)$
$- L - S$	$h (1 - p) g$	$h (1 - p) g$	$1 - w (1 - h g + h p g)$

均衡点	特征值 $λ 1, λ 2, λ 3$	正负符号	稳定性
$(0,0, 0)$	$- C e$ ， $β C p h - C p l$ ， $0$	$(-, U, 0)$	满足 $a$ ，为 $E S S$
$(1,0, 0)$	$C e$ ， $β C p h - C p l$ $+ (1 - β) C s$ ， $- S$	$(+, U, -)$	不稳定
$(0,1, 0)$	$- C e$ ， $- (β C p h - C p l)$ ， $0$	$(-, U, 0)$	满足 $b$ ，为 $E S S$
$(0,0, 1)$	$S - C e$ ， $β C p h - C p l$ ， $0$	$(U, U, 0)$	满足 $a, c$ ，为 $E S S$
$(1,1, 0)$	$C e$ ， $- (β C p h - C p l + (1$ $- β) C s)$ ， $- S$	$(+, U, -)$	不稳定
$(1,0, 1)$	$- (S - C e)$ ， $β C p h - C p l + (1 - β) C s$ ， $S$	$(U, U, +)$	不稳定
$(0,1, 1)$	$S - C e$ ， $- (β C p h - C p l)$ ， $0$	$(U, U, 0)$	满足 $b, c$ ，为 $E S S$
$(1,1, 1)$	$- (S - C e)$ ， $- (β C p h$ $- C p l + (1 - β) C s)$ ， $S$	$(U, U, +)$	不稳定

均衡点	特征值 $λ 1, λ 2, λ 3$	正负符号	稳定性
$(0,0, 0)$	$- C e$ , $+ ∞$ , $0$	$(-, +, 0)$	不稳定
$(1,0, 0)$	$C e$ , $+ ∞$ , $- S$	$(+, +, -)$	不稳定
$(0,1, 0)$	$- C e$ , $- 0.5 (β C p h - C p l)$ , $0$	$(-, -, 0)$	$E S S$
$(0,0, 1)$	$S - C e$ , $+ ∞$ , $0$	$(U, +, 0)$	不稳定
$(1,1, 0)$	$X$ , $Y$ , $- S$	$(-, U, -)$	当满足 $d$ ，为 $E S S$
$(1,0, 1)$	$- (S - C e)$ , $+ ∞$ , $S$	$(U, +, +)$	不稳定
$(0,1, 1)$	$S - C e$ , $- 0.5 (β C p h - C p l)$ , $0$	$(U, -, 0)$	当满足 $c$ ，为 $E S S$
$(1,1, 1)$	$V$ , $W$ , $S$	$(-, U, +)$	不稳定

均衡点	特征值 $λ 1, λ 2, λ 3$	正负符号	稳定性
$(0,0, 0)$	$- C e$ , $0$ , $0$	$(-, 0,0)$	$E S S$
$(1,0, 0)$	$C e$ , $0$ , $- S$	$(+, 0, -)$	不稳定
$(0,1, 0)$	$- C e$ , $- 2 (β C p h - C p l)$ , $0$	$(-, -, 0)$	$E S S$
$(0,0, 1)$	$S - C e$ , $0$ , $0$	$(U, 0,0)$	满足 $c$ 时，为 $E S S$
$(1,1, 0)$	$M$ , $N$ , $- S$	$(-, U, -)$	满足 $d$ 时，为 $E S S$
$(1,0, 1)$	$- (S - C e)$ , $0$ , $S$	$(U, 0, +)$	不稳定
$(0,1, 1)$	$S - C e$ , $- 2 (β C p h - C p l)$ , $0$	$(U, -, 0)$	满足 $c$ 时，为 $E S S$
$(1,1, 1)$	$K$ , $T$ , $S$	$(-, -, +)$	不稳定

策略收益	概率	等级	决策权重
$H - C p l - (1 - β) (C p h - C s)$	$h p$	$1$	$w (h p)$
$H - C p h$	$1 - p$	$1 - h p$	$w (1 - p + h p) - w (h p)$
$H - C p l - (1 - β) C p h$	$(1 - h) p$	$(1 - h) p$	$1 - w (1 - p + h p)$

均衡点	特征值 $λ 1, λ 2, λ 3$	正负符号	稳定性
$(0,0, 0)$	$- C e$ , $- ∞$ , $0$	$(-, -, 0)$	$E S S$
$(1,0, 0)$	$C e$ , $+ ∞$ , $- S$	$(+, +, -)$	不稳定
$(0,1, 0)$	$- C e$ , $+ ∞$ , $0$	$(-, +, 0)$	不稳定
$(0,0, 1)$	$S - C e$ , $- ∞$ , $0$	$(U, -, 0)$	满足 $c$ 时，为 $E S S$
$(1,1, 0)$	$X$ , $Y$ , $- S$	$(-, U, -)$	满足 $d$ 时，为 $E S S$
$(1,0, 1)$	$- (S - C e)$ , $+ ∞$ , $S$	$(U, +, +)$	不稳定
$(0,1, 1)$	$S - C e$ , $+ ∞$ , $0$	$(U, +, 0)$	不稳定
$(1,1, 1)$	$V$ , $W$ , $S$	$(-, U, +)$	不稳定

均衡点	特征值 $λ 1, λ 2, λ 3$	正负符号	稳定性
$(0,0, 0)$	$- C e$ , $0$ , $0$	$(-, 0,0)$	$E S S$
$(1,0, 0)$	$C e$ , $0$ , $- S$	$(+, 0, -)$	不稳定
$(0,1, 0)$	$- C e$ , $0$ , $0$	$(-, 0,0)$	$E S S$
$(0,0, 1)$	$S - C e$ , $0$ , $0$	$(U, 0,0)$	满足 $c$ 时，为 $E S S$
$(1,1, 0)$	$M$ , $N$ , $- S$	$(-, U, -)$	满足 $d$ 时，为 $E S S$
$(1,0, 1)$	$- (S - C e)$ , $0$ , $S$	$(U, 0, +)$	不稳定
$(0,1, 1)$	$S - C e$ , $0$ , $0$	$(U, 0,0)$	满足 $c$ 时，为 $E S S$
$(1,1, 1)$	$K$ , $T$ , $S$	$(-, -, +)$	不稳定

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Evolutionary Game Analysis of Graded Diagnosis and Treatment Strategies Affected by Patients' Emotions under Regional Medical Association

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