Research on the unification of dominant and subjectivity of ideological and political education in colleges and universities based on big data technology

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Payment matrix when the school “ineffective incentives”

		Tutor
		Carefully cultivate (y)	Careless cultivation (1-y)
Student	Active learning (x)	As + rL − CsAt + (1 − r)L − CtAu + Lu + Eu	As − CsAt + EtAu
	Passive learning (1 − x)	0At − CtAu	0AtAu

Payment matrix when the school “effective incentives”

		Tutor
		Carefully cultivate (y)	Careless cultivation (1-y)
Student	Active learning(x)	As + rL − (Cs − Bq)At + (1 − r)L − [Ct − B(1 − q)]Au + Lu + Bu − Cu	As − (Cs − Bq)At + EtAu + Bu − Cu
	Passive learning (1 − x)	0At − [Ct − B(1 − q)]Au + Bu − Cu	0AtAu + Bu − Cu

Local stability of equilibrium points (Cases 1, 2)

	Case 1	Case 1	Case 1	Case 2	Case 2	Case 2
Equalization point	det J	trJ	Stability	det J	trJ	Stability
E1(0, 0, 0)	-	+	Unstable point	-	+	Unstable point
E2(0, 0, 1)	-	-	Unstable point	+	+	Unstable point
E3(0, 1, 0)	+	+	Unstable point	+	+	Unstable point
E4(0, 1, 1)	+	+	Unstable point	-	-	Unstable point
E5(1, 0, 0)	+	-	ESS	+	-	ESS
E6(1, 0, 1)	-	-	ESS	-	-	ESS
E7(1, 1, 0)	-	-	ESS	-	-	ESS
E8(1, 1, 1)	+	+	ESS	+	+	ESS

Three-party game model

Education subject 1		Act 1		Act 2
Education subject 2		Act 1	Act 2	Act 1	Act 2
Education subject 3	Act 1	Revenue value	Revenue value	Revenue value	Revenue value
	Act 2	Revenue value	Revenue value	Revenue value	Revenue value

The eigenvalue of the equilibrium point

Equalization point	Eigenvalue λ1	Eigenvalue λ2	Eigenvalue λ3
E1(0, 0, 0)	As − Cs	−Ct	Bu − Cu
E2(0, 0, 1)	As + Bq − Cs	B(1 − q) − Ct	−(Bu − Cu)
E3(0, 1, 0)	As + rL − Cs	Ct	Bu − Cu
E4(0, 1, 1)	As + rL + Bq − Cs	−[B(1 − q) − Ct]	−(Bu − Cu)
E5(1, 0, 0)	−(As − Cs)	L(1 − r) − Ct − Et	Bu − Cu
E6(1, 0, 1)	−(As + Bq − Cs)	L(1 − r) + B(1 − q) − Ct − Et	−(Bu − Cu)
E7(1, 1, 0)	−(As + rL − Cs)	−[L(1 − r) − Ct − Et]	Bu − Cu − Eu
E8(1, 1, 1)	−(As + rL + Bq − Cs)	−[L(1−r)+B(1−q)−Ct−Et]$$ - \left[ {L(1 - r) + B(1 - q) - {C_t} - {E_t}} \right]$$	−(Bu − Cu − Eu)