Game theory

Game theory is the study of strategic decision making.

After taking this course, I realized that many of my daily issues can be transformed into a game theory problem and then be solved by helping me to decide which strategy to choose.

We’ve learned many methods (we choose the one that suits our problem).

1-Methods for 2-person games: - Dominated strategies

-      Minimax criterion

-      Analytical method 2x2

-      Graphical method mx2 and 2xn

-      Simplex method mxn

2- Methods for N-persons games: - The core

-Shapley value

The aim of this project is to show how game theory exists in my surroundings constantly through demonstrating some solved examples.

"You treat world history as a mathematician does mathematics, in which nothing but laws and formulae exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal shallow, mathematical present."
 Hermann Hesse

Example 1

My dad makes candles for churches for a living.

 In North Lebanon where we live, he has only one factory as a competitor.  

All the churches in our area are obliged to buy candles from one of them.

How are the churches going to choose their seller? Logically they will choose the cheapest one.

The other contestant (B) and my dad are free to sell 10 kg of candles (1000 candle ) for 10$, 13$ or 16$. Note that making 10 kg will costs 3$.

Obviously, it’s a zero sum game since each participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s).

The players: player 1-> my dad

                   Player 2-> contestant B

There is 3 strategies for each one (10$-13$-16$).

(for exp:        A11: 3.5 ₌ (10-3)/2                    A12: 7=10-3)       

Solving this Nash equilibrium example, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy, we obtain (3.5 , 3.5) as a solution.

                                                   Example 2

My grandmother has 100$ and wants to give it to me and my cousin Nancy. Nancy and I will have to follow a strategy to gain as much as money as we can (the 3 strategies: crying, screaming, giving logical arguments of why we deserve it).

Crying wins over both screaming and good arguments (since grandma is a very sensitive person).

Good arguments win over screaming.

(Crying > good arguments > screaming)

If both of us followed the same strategy we will get 50$ each. 

Since it is a zero-sum game, we can solve it by dominance strategy.

Therefore the best strategy is crying which lead to me getting as much as my cousin (50 $). 

Example 3

My 2 brothers Michel and Elias are going out to the movies with their friends. They are going to ask my parents for money.

 Mom has planned to give 100$ to my brothers. If both of them came to her each one will get 50$, if only one of them did, he will get 100$.

My dad’s strategy is to give 60$ for whom ask him for money whether both of them did or just one of them.

Solving this Nash equilibrium example we obtain 2 solutions: (100,60) and (60,100) since in those 2 cases no one of them has an incentive to deviate from his chosen strategy after considering the other one’s choice. Therefore each one of my brothers should ask money from one of my parents. ( they should not ask the same one for money)