**My Focus**

Game theory is aboutfinging an optimal solution for different players in any situation that can be modeled using a game. The purpose of this project is to look into the ways in which we can assign values to different players in a game. In this project I will analyses two parts of game theory, the process of playing the game, and formulation of the game.

What does that mean? For a quick thought example If someone rolls a 6-sided dice what it’s the probability that they will roll a 1? Using what we know about game theory the answer is a 1/6 percent chance. And the result is random. However, what if the dice rolled had all 1’s then the chance of rolling a one in 100%. In game theory multiple charts are made of games based off relative payoffs to predict an opponent’s move or decision so that the player can get the largest possible pay off. My project will specifically focus on the game of politics and different ways politicians can analyses their political opponents, play the game, along with the process in which politicians can create games in which participant can play strategies that allow them a higher chance of winning either policy or elections.

In my first examples I will go over a simple example that I have made up and assigned values to arbiterly.

**A simple Example**

Policy Platform Decision | Republican | |||||

Republican | Democrat | Moderate | Moderate &Rep | Moderate & Lib | ||

Democrat | Republican | (0 ,5) | (2,2) | (1,7) | (0,9) | (2, 6) |

Democrat | (5,5) | (5,0) | (5,8) | (5,10) | (4,7) | |

Moderate | (6,5) | (7,1) | (5,7) | (4,8) | (4,5) | |

Mod & Rep | (3,4) | (4,1) | (3,8) | (3,7) | (5,6) | |

Mod & Lib | (8,4) | (7,3) | (7,8) | (5,7) | (7,7) |

**1) Creating a Model **

When starting a Game one must show the options available for each player.

Republican | Democrat | Moderate | Moderate & Rep | Moderate & Lib | |

Republican | |||||

Democrat | |||||

Moderate | |||||

Mod & Rep | |||||

Mod & Lib |

**2) Next**

The hardest part of game theory is assigning the values to the different players.

When assigning pay offs for different players you can visually display them as a coordinate point (Rows, Column) where the left side is the value of the paler being modeled on the rows, and the right number is that of the play being modeled in the columns (hence row and column)

In this game for ease I assigned values based on my initial instinct for a state congressman election based on my previous knowledge of my home state Texas.

the explanation for these values are under the graph

- Please skip to the next caption to void my explanations.

Policy Platform Decision | Republican | |||||

Republican | Democrat | Moderate | Moderate &Rep | Moderate & Lib | ||

Democrat | Republican | (0 ,5) | (2,2) | (1,7) | (0,9) | (2, 6) |

Democrat | (5,5) | (5,0) | (5,8) | (5,10) | (4,7) | |

Moderate | (6,5) | (7,1) | (5,7) | (4,8) | (4,5) | |

Mod & Rep | (3,4) | (4,1) | (3,8) | (3,7) | (5,6) | |

Mod & Lib | (8,4) | (7,3) | (7,8) | (5,7) | (7,7) |

*RR : liberal will waste too much time trying to get republicans to vote for them*

*DR: both will have a similar outcome as liberals are voting for democrats and traditionally conservatives vote conservative*

*M,R: without any mid line policies moderates who might have voted republican will now be forced to vote with democrats to match ideals*

*MR,R: democratic nominee wasted time on republicans that could better be used on moderates and liberals*

*Mod & liberal : moderates and liberals allows the democratic candidate get the generally more liberal/democratic voters to be on there side along with a majority of the moderate favoring the more neutral policies over hard core conservative policies from republicans.*

*R,D: democratic candidate is trying to get hard republican on his/her side and republicans are trying same with democrats, and is not very effective on pre decided voters*

*D,D: democrats get all democratic voters, and republican get none*

*M,D: appealing moderates gets a lot of moderate cotes along with s few democratic votes, but republican to get a few away*

*M&R,D: wasting time on republican makes moderate persuasion less effective, and republicans still win a few democrats through heavy advertising*

*M&l ,D: liberal maximize on both moderates and there base, making getting votes easier, while republican still struggle with democrats*

*R,m: Republican capitalist on moderates while still getting some of their base while democrat waste time on republicans*

*D,M: Dems get all Dem base, but lode moderates and normal republican wit default to rep ballet*

*M,M: being in Texas gives republican a better chance based on of the idea because texas is republican, a republican will be elected.*

*M&R,M: Dems Waste time on republican so more moderate votes go to republicans*

*M&l, M: Get liberal and moderate vote, but more moderates and republicans vote republican off president.*

*R,MR : republican focus on moderate leaning group an republican base, while democratic candidate focuses on republican base.*

*D,MR democrats get the democratic base out o vote, but the republican get most moderate and republican votes*

*M,MR: dem get some moderates, but repub gets both moderates and Republicans*

*MR, MR: when playing the same cards, republican candidate gets more of the moderate and republican votes because Texas is historically republican.*

*DL,MR: democrats get dem base republicans get republican base, but also more moderates because Texas is historically republican.*

*R,ML : republican reaches out to liberal base and moderates, but some of the advertising by Dems to republicans worked.*

*D,ML: democrats will get majority democratic vote, republican get most republican base and a few liberals*

*M,ML , this is a real tight, as Dem dedicate of their strength on moderates and they already have there liberal bias, but Republican win slightly due to the slight favor of moderates and the conservative base that is thought to win .*

*MR,ML, Both are trying to get the opposite party and moderate, but republican have a slight advantage due to moderate favor.*

*ML,ML Moth go for moderates and liberal, but the slight factoring of republican in elation make them split even*

**Calculating the Games Solution**

To solve for the percent each person should play given that there is no nash equilibrium is found. in order to do this two different graphs need to be made based on the (Rows, Column) points. This can be done my making two matrices. 1 Rows, and 1 Column

**Republican strategy**** in Dem game.**

is there a single solution ?

to answer this question we can draw arrow as seen above to find different solutions

steps

- Arrows are drawn horizontally to the highest numbers
- Arrow are drawn vertically to the highest number
- Solutions is the point in which multiple arrows meet
- If multiple arrows meet the percentage of players needs to be found.

Because there are multiple point we need to show the parentage of each strategy each play should play of what strategy.

- by assigning values to each of the columns and solving for X we can create a matrix and solve a system of equations.

0x+2y+1z+0W+2(1-x-y-z-w) =5x+5 y+5z+5w+4(1-x-y-z-w)

2y+1z+ =5x+5y+5z+5w+2(1-x-y-z-w)

0=5x+3y+4z+5w+2(1-x-y-z-w)

0=5x+3y+4z+5w+ 2-2x-2y-2z-2w

0=3x+y+2z+3w+ 2

3x+y+2z+3w+ = -2

0x+2y+1z+0W+2(1-x-y-z-w) = 6x+7y+5z+4w+4(1-x-y-z-w)

2y+1z = 6x+7y+5z+4w+2(1-x-y-z-w)

0= 6x+5y+4z+4w+ 2-2x-2y-2z-2w

4x+3y+2z+2w+ 2=0

4x+3y+2z+2w= -2

0x+2y+1z+0W+2(1-x-y-z-w) = 3x+4y+3z+3w+5(1-x-y-z-w)

2y+1z= 3x+4y+3z+3w+3(1-x-y-z-w)

2y+1z = 3x+4y+3z+3w + 3-3x-3y-3z-3w

2y+1z = +y + 3

Y+z=3

0x+2y+1z+0W+2(1-x-y-z-w) = 8x+7y+7z+5w+7(1-x-y-z-w)

2y+1z= 8x+7y+7z+5w+5(1-x-y-z-w)

0 = 8x+5y+6z+5w+5(1-x-y-z-w)

0= 8x+5y+6z+5w +5-5x-5y-5z-5w

0= 3x+z+5

3x+z = -5

**Democratic strategy**** in rep game**

5x+5y+5z+4w+4(1-x-y-z-w) = 2x+0y+1z+1w+3(1-x-y-z-w)

5x+5y+5z+4w +(1-x-y-z-w) = 2x +z + w

3x+5y+4z+3w + 1-x-y-z-w = 0

2x+4y+3z+2w=-1

7x+8y+7z+8w+8(1-x-y-z-w) = 2x+0y+1z+1w+3(1-x-y-z-w)

7x+8y+7z+8w+5(1-x-y-z-w) = 2x+1z+1w

5x+8y+6z+7w + 5(1-x-y-z-w) =0

5x+8y+6z+7w + 5-5x-5y-5z-5w =0

0x+3y+z+2w +5 = 0

3y+z+2w =-5

9x+10y+8z+7w+7(1-x-y-z-w) = 2x+0y+1z+1w+3(1-x-y-z-w)

9x+10y+8z+7w+4(1-x-y-z-w) = 2x+0y+1z+1w

7x+10y+7z+6w+4(1-x-y-z-w) = 0

7x+10y+7z+6w + 4-4x-4y-4z-4w = 0

3x+6y+3z+2w = -4

6x+7y+5z+6w+7(1-x-y-z-w) = 2x+0y+1z+1w+3(1-x-y-z-w)

6x+7y+5z+6w+4(1-x-y-z-w) = 2x+0y+1z+1w

4x+7y+4z+5w+4(1-x-y-z-w) = 0

4x+7y+4z+5w+4-4x-4y-4z-4w= 0

0x+3y+0z+w+4 = 0

3y+w= -4

Parietal optimal solution: This shows the optimal solution for each runner for each outcome. By drawing a line on the outside we establish the highest possible win rates.

**Simplify **

Zero Sum solution :

I this Game can also be made simpler using only 3 values. <Win, Lose, Tie>

-1 ==> (-1,1)

By observing this model we are able to look at how each candidate should analise his/her campaign. -1 mean a win for the republican , while a 1 = a win for the democrat. When looking at game given above you will notice that there are more possibilities for a republican to win than a liberal. This is because i created this data using my home state Texas which has a historical republican bias towards candidates. In Order for a democrat to win the best chance they have is to choose a Moderate or liberal strategy. This is because out of all solutions this allows them the possibility of two wins and one tie we’re all other possibilities result in only two wins and no tie. This is only the case if the republican candidate is playing randomly. A candidate vested in the art of game theory will look at this and find inorder to get the highest probability of wins i need to have a moderate , or a moderate/rep based platform. This allows for the republican candidate to win 100% of the time regardless of what the other candidate does.

While looking at this it is clear the democratic candidate cannot win my party platform and ideas alone, but must instead look for another way to discredit a candidate it make them look better. By doing this the values of the original can change resulting in a different solution.

**So far: **we have looked at a made up example over how a candidate could make a decision on the policy he/she should run in an election. This example was based off of vaguely defined interpretations that were meant to show you the way game theory is can be applied. we will now shifted focuses to how this applies to games in the political sphere and to your daily lives.

**How does this apply to politics? **

3 way

**How politicians scope out there opponent**

when politicians scope out their opponent they often have well versed pole in their campaign gather information on the other candidates. which candidate will be the largest threat to m candidate? What does this candidate dislike, what are their habits, tendencies, possible policies? Where are opportunities I can twist what they say to benefit my candidate.

These are the questions that every candidate must ask in order get all their information’s they need. Large amounts of data collection are crucial to scoping out one’s opponent. The more information one finds, the more games that a player can create and the more scenarios and variable the payer has. By knowing what your opponent might do and will do based on what they have done a politician, or more accurately a campaign director, can shape a campaign to take many different courses of action. But this required knowing what path that the campaign can take to receive large pay offs of voters.

The following is a short audio clip from my Government teacher

** 2. How to model a game**

How we model a game is the hardest part of Game theory. It involves both setting numerical values to differ outcomes of a game. In addition, when setting up a game like seen in the first examples the variable I assign values, or voters to a candidate based on how I view a situation. How do I know these values are right? A game with incorrect variable will more easily have an incorrect solution be known

Take one example during the JFK v. Nixon election. in the USA’s first election to televise a presidential debate. Prior to the debate Both candidates had agreed not to use makeup. Both candidates endued up doing so. Simple decisions like this can be model as games like so

JFK: Use makeup | Don’t use makeup | |

NIX: Use makeup | (10,10) | (10,0) |

Don’t use makeup | (0,10) | (10,10) |

The obvious choice from a simple game such as this is to use male up because there is no reason to not where make up. now this is of course ignoring variable like personal pride which must normally be considered, however for the strict example we will ignore extraneous variables and only use 2×2 matrixes for ease.

How did I assign those variables?

Both use Make up: look better in front of a TV audience. The first of its kind do both people benefit more from looking good

JFK uses, NIX dose: JFK will look much better in front of a TV audience while imponent will look shabby

JFK doesn’t, Nixon Does: Nixon will look much better in front of a TV audience while imponent will look shabby

Neither uses: the audience will probably not notice the difference, unless on person looks better naturally than the other (witch I will ignore, because I don’t have a way to quantify)

Of course, many more variables will need to be added like how much money to spend on make up who will do it, professional, self-applied. What make up to use. All of these are variables that must be considers making an accurate model.

Ultimately JFK had a professional apply his makeup will Nixon applied only over the counter product “lazy shave”.

In addition to this JFK’s campaign knew from their research that Nixon sweat easily, and that the debate room was intentionally make cooler. JFK’s campaign manager had this temperature raised during the debate, making his appoint look sluggish. This shows just how important both understanding the value of the information you have when creating a game. If you gather a lot of information but have no concept of how you can use it then it is useless. Is the JFK campaign had the information of Nixon’s sweating tendencies, but deemed them unimportant then the game models where the manager would turn up the heat was monitored?

——————JFK JFK——————————————————————————————————–

**Turn up temp Do nothing VS. Turn up temp Do nothing**

0,0 0,0 10,-10 0,0

what this Game model means

variable, variable == JFKs Pay off, Nixon’s

- because Nixon doesn’t have any knowledge of what JFK is doing he has no ability to play so only Nixon’s choices are shown.

In the first game doing nothing and turning the temperature up different pay offs, but the rest of turning the temperature up is a negative, so why bother putting any work in to change the temperature. In the second scenario JFK gets a payoff and damages his opponent, making acting and Turning up the heat worthwhile.

** 3. How to introduce new variables.**

Lastly when there is no longer any course of action you can take you can add in more variables. This is seen often in politics, by damaging there appoints reputation. Spread lies, or making false assumption that the people believe, or will hurt their chances of election.

Thomas Jefferson was an expert at this and when he was running for president he had his friend print pamphlets spreading rumors about his opponent John Adams. Hesitated that Adams wants to go to war and had a very disagree able personality. This spread of lies based on people’s fears to help him get vote, or at least take votes away from his opponent was the inclusion of ne variables into a game.

**How is this Applicable to you ?**

Humans have a special ability to think. By using the techniques in game theory to accurately model real life situations you can accurately see the situation in front of you and you can change the variables and options you have to better increase your chances of winning.

Sources :

http://news.gallup.com/poll/226556/state-partisanship-shifts-toward-democratic-party-2017.aspx (general sense of state)

https://www.fec.gov/data/elections/senate/TX/2014/(money spent spent by politicians)

https://www.hayshighguidon.com/opinion/2016/04/04/political-parties-are-damaging-american-politics/ (pic of rep & dem fihgting )

https://giphy.com/gifs/studiosoriginals-vote-election-2016-3oriO15V1jJGz4Wq2c egal go vote giff

https://nimd.org/inndem2017-innovating-democracy-conference/ (inivaing democracy pic )

https://listverse.com/2014/01/18/10-worst-dirty-tricks-in-american-politics/ (exaples of games)

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