Calculate nash and sequential stability

Assignment Help Game Theory

Reference no: EM132479483

Decision Analysis Question 1:

An environmental dispute is occurring between an Environmental Agency and a company called Goldamorous Ltd. The company operated a gold mine for two decades. The Environmental Agency discovered heavy metals that are carcinogenic in a nearby drinking water source. The company had been disposing of processed fine particles of crushed rocks in a landfill site located near the water aquifer used for drinking water. Because the aquifer became contaminated with heavy metals, the Environmental Agency ordered Goldamorous Ltd. to pay for the full cost of remediating the water. Goldamorous appealed the decision and requested that the Environmental Agency share the cleanup cost. The Environmental Agency has two strategies: to Modify (M) or Do Not Modify (DM) its initial control order. The company Goldamorous Ltd. has two strategies: to Accept (A) or Do Not Accept (DA) the control order.

Environmental Agency

Modify (M) Do Not Modify (DM)

Accept (A)

Goldamorous Ltd.

Do Not Accept (DA)

5,5

A,M

1,10

A,DM

1,0

DA,M

2,2

DA,DM

Part 1. (a) Write the above game in the integrated graph form assuming all moves are reversible.

Part 1. (b) Also, write the model in option form.

Part 1. (d) Calculate Nash and Sequential (SEQ) stability for each state and decision maker. Be sure to provide representative calculations for each of the two stability definitions for which you have one example in normal form, an example in option form and another calculation in graph form. Use the table below to indicate your findings for which a check mark means stable, G stands for Goldamorous Ltd., Env represents Environmental Agency, and E means Equilibrium and U mean unstable.

States	Nash			SEQ
States	G	Env	E	G	Env	E
1 A,M
2 A,DM
3 DA,M
4 DA,DM

Please present your sample calculations for 1. (d) in the space provided below and on the next page.

Strategic Decision Analysis

Two Decision Makers Conflict Resolution

Question 1

Tables 1 and 2 show Syrian and Iraq preference vectors. Use this information to identify the following:

Syrian and Iraq possible unilateral improvements (UIs).

Syrian and Iraq individual stability analysis. Indicate rational states using an "r", sequentially stable states having unilateral improvements using an "s", unstable states using a "u".

Identify the equilibrium states for the dispute. Mark with "E" any state that is stable for both DMs, and with "x" the states that are not equilibrium for the game.

Kindly, show your calculation in Table 3.

Table 1:

Preference Vector for Syria

DM	Options	States
Syria	1. Release Water	N N	N	Y	N	Y
	2. Escalate	N Y	Y	N	N	N
Iraq	3.Attack	N	NYNY			Y FixIraq'sStrategy

1 3 6 2 4 5

Table 2:

Preference Vector for Iraq

States

Syria 1. ReleaseWater

2.Escalate

Fix Syrian

Strategy

Iraq

3. Attack

Label

Preference Vector for Syria

Table 3:

Stability Analysis Tableau

Syria
Overall stability Syrian Stability
Preference Vector	1	3	6	2	4	5
UIs

Iraq Iraq Stability
Iraq Preference Vector	2	4	6	1	5	3
UIs

Question 2
In Table 4, indicate rational states using an "r", sequentially stable states having unilateral improvements using an "s", unstable states using a "u", equilibrium state using "E", and with "x" the states that are not equilibrium for the game.

Table 4:

Stability Analysis Tableau

DM A
Overall stability DM A Stability
Preference Vector	10	5	32	33	0	1	4	8	9	20	24	25	26	21
UIs				5	32	5	32	23	5	32	32	5	10	5
						33	0	0	33	0	0	33		33
								4	1	4	4	1		1
										8	8	9		9
											20			25

DM B DM B Stability
Preference Vector	21	20	24	25	0	1	4	8	9	5	26	32	33	10
UIs		21		24		0			8	4	24		32	8
											25			9

Attachment:- Strategic Decision Analysis.zip

Reference no: EM132479483

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