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GOA: Game Theory application in my school community

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One of the things that I have noticed that is a problem in my community is parking at my school. Recently, one of the buildings has been shut down due to the school undertaking a construction project that will renovate it. As a result, one of the parking lots is undergoing renovation as well, limiting the amount of parking on campus. This has led to a large number of people parking of campus. One of the places that is a popular parking spot is the curb outside of one of the houses. However, the owner of the house has put up cinder blocks restricting parking at the house, forcing people to either park far away from school or risk hitting one which makes parking there much more difficult. These cinder blocks are in fact illegally placed, but they still remain outside the house. Legally, you are allowed to park there, but the cinder blocks remain there, illegally inhibiting people’s ability to park. In addition to this, the owner of the house has also illegally planted bushes in part on part of the area outside of her house. She can also plant bushes outside her house, which are easier to park over but she is less likely to get into legal trouble as a result of planting these bushes. She has a reputation of complaining to the school about everything that happens there for the past 10 years. This includes dances, events, construction, and in this case people parking outside her house.

 

A- Park there

B- Don’t Park there

C- Place bushes

D- Place cinder blocks

E- Don’t place anything

Homeowner
C D E
Student A (2,-1) (1,-4) (3,-1)
B (-2,2) (0,1) (-3,3)

 

AC has a value of (2,-1).

  • Student: Parking over bushes is an impediment to parking there but not as much as it would be if there were cinder blocks there.
  • Homeowner: Planting bushes outside of her house are in fact illegal, but she is much less likely to get in legal trouble for them than the cinder blocks.

BC has a value of (-3,3)

  • Student: Parking over the bushes is in fact an impediment to parking there, but not parking there does in fact incur a negative cost because of the fact that parking there is not that difficult and not parking there forces the student to take a long walk.
  • Homeowner: If planting bushes there serves as an effective deterrent this is definitely a good thing for the homeowner. However, this is not ideal for her as she still does face some possible legal consequences.

AD has a value of (1,-4)

  • Student: Parking over the cinder blocks is more risky than parking near the bushes, but not so risky that it has a negative value.
  • Homeowner: If the student parks over the cinder blocks, the cinder blocks were both ineffective in accomplishing their goal, and she faces a greater risk of legal consequences for the illegally placed cinder blocks.

BD has a value of (-1,1)

  • Student: The student will have to make a long walk, but the increased cost of parking there negates the values. This is assigned a neutral value as a result.
  • Homeowner: The cinder blocks are a more effective deterrent but if a student doesn’t park there they will face more legal consequences than they would if they planted bushes.

AE has a value of (3,-1)

  • Student: The student saves a lot of time walking around and in addition, there are no risks to parking there.
  • Homeowner: They have to deal with a student parking outside of their house for the school day, but they don’t have to deal with any legal consequences.

BE has a value of (-3,3)

  • Student: Not parking there when there are no risks, consequences, or obstacles to parking there simply doesn’t makes sense.
  • Homeowner: They didn’t have to place any obstacles outside the house or risk any legal consequences yet still, nobody parked there.

When we try and solve the game created we are able to solve for the nash equilibrium and the pareto optimality to find the solutions to this game.

 

Nash Equilibrium

  • Student: In this game, it is always better for the student to park at the house than it is to park somewhere else, regardless of the obstacles that the homeowner places outside her house.
  • Homeowner: For the homeowner, it is always beneficial for them never to place anything, and as a result, not placing anything is their ideal strategy.
  • Solution: The solution to this game is for the student to park there and for the woman not to place any obstacles outside of her house.

Pareto Optimality: The solution to this game using the pareto optimality is for the student to park there and for the woman not to place anything as it achieves the best net value which is a value of 2.

 

From this we can see that if both of the parties involved act rationally, the homeowner will place nothing outside her home and the student will park there. However, the homeowner has shown repeatedly that she does not in fact act rationally. Despite the fact that her best option is to not place anything outside of her house, she has shown that she wants to place obstacles outside of her house in order to prevent people from parking there. In addition to the outcomes that are listed above, there are many outcomes which this game does not account for. The homeowner has the option of calling the police and telling them that the cars are parked illegally. The homeowner has the option of calling the school and telling them that there are students parking illegally outside her house. Also, the homeowner has the option to sue the students parking there. She has previously called the police, the school, and threatened to sue a student for parking outside of her house.

 

Since the homeowner has shown that she often does not act rationally, and that there are many different results given many different decisions that parties make along the way, I feel that a payoff tree is a good way to represent the many different possibilities the for outcomes that may happen as a result of the decisions that each party makes.

 

Payoff Tree

A=Place cinder blocks

B=Plant bushes

C=Place nothing

D=Park there

E=Don’t park there

F=Call Police

G=Call School

H=Sue

I=Fight Suit

J=Don’t Fight Suit

ADF= (1,-6)         BE=(-2,2)

ADG= (0,-5)        CDF=(2,-1)

ADZ= (1,-4)         CDG=(1,-1)

ADHI= (-1,-6)      CDZ=(3,-1)

ADHJ=(0,-3)        CDHI=(1,-3)

AE=(0,1)              CDHJ=(2,0)

BDF=(1,-1)           CE=(-3,3)

BDG=(0,-1)

BDZ=(2,-1)

BDHI=(0,-3)

BDHJ=(1,0)

From this payoff tree, we can see that with the increased number of options that each party was given led to many different outcomes. From the payoff tree, the game should result in the homeowner not restricting access to parking on her lawn, the student parking there, the homeowner suing and the student not contesting the lawsuit and agreeing not to park there. This is somewhat problematic when we realize that this game is not being played just once, but actually every single day when the student goes to school. Due to this there are some important compromises that both sides need to make in order to create the best outcome. The best way that the two parties can come to a compromise is to agree not to contact any outside authorities. Intervention by the school, police, or a lawsuit will only have negative consequences for both sides. In exchange for both agreeing not to get involved into the conflict, the student agrees that they will only park there every other day and the woman agrees to let the student park there every other day. This will achieve a significantly better outcome for both sides as the intervention on the part of the school, police, and a lawsuit only results in a net negative. The student and homeowner will both be willing to get rid of the risk of this net negative in order to get rid of the possible risk.

 

Call to action:

Overall, the solution to this problem is to compromise and work out a solution between the two parties, as involving a third party will only result negatively for both sides. What I learned from analyzing this situation is that in order to find the best solution to a problem and solve a conflict, the best way to go about solving it is to put aside your differences, disagreements, emotions, and assumptions and solve it with the other person to secure a good outcome for both of you. As a call to action, I encourage all of you reading this to make sure that you take these lesson about co-operative problem solving to heart.

 

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COMMENTS: 1
  1. May 07, 2018 by Ryan

    What an interesting project! I like how to connected game theory to something that affects you directly. I like your explanation and inclusion of the Nash Equilibrium; such an interesting theory. Great job!

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