WHAT IS " game theory"?

 
Game theory is the study of mathematical models of strategic interaction between rational decision-makers. t has applications in all fields of social science, as well as in logic and computer science.

1 of 6 :: game theory is nothing but the science of decision making

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2 OF 6 :; not a classic " prisoner's dilemma " situation?

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3 OF 6 : ultimatum game :: Nick’s idea - change Ibrahim’s payoff in the outcome

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4 OF 6 :: simplest version of the ultimatum game:

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5 OF 6 :: ultimatum : game

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 6 OF 6 :: Nash EquilibriA using Calculus

Game theory is looking at human interactions through the lens of mathematics. Now, here is the situation With up to ten years in prison at stake, will Wanda rat Fred out? Now that is a classic game theory situation used to analyze what is called a "prisoner's dilemma".

The Golden Balls’ “split or steal” differs from the classic Prisoner’s Dilemma in a key way, and the difference brings about a different dominant strategy.

In the classic Prisoner’s Dilemma, the "dominant strategy" is "always to betray" the other prisoner, or steal, in the Golden Balls example.

But the entire point of the Prisoner’s dilemma is that the two participants are separated and "cannot communicate" — that’s why they are "prisoners".

If you can "communicate", as these two contestants clearly can, the game changes entirely. Because the dominant strategy (which the girl in the clip employs) is to steal, you have to assume that the person up against you is going to steal.

II. NICK'S STRATEGY (THIRD VIDEO) -          THE " ULTIMATUM GAME "
     
So instead of trying to convince them to split with you, why not simply announce that you are going to steal, no matter what? (Strategy Nick uses).

You can even make a contract to give them back a certain amount of the winnings, buying off their cooperation.

If you convince them that you are going to steal no matter what, they are going to have to resign to accepting whatever you hand out to them, because otherwise they’ll get nothing.

In doing so you will in fact turn the situation into another well-known game: called the "ultimatum game".

Nick donated the winnings to charity. Fundamentally, his play was based on altruism.

               ~ Know the terms ~

Strategy: 
In game theory, player's strategy is any of the options he or she can choose in a setting where the outcome depends not only on his own actions but on the action of others. A player's strategy will determine the action the player will take at any stage of the game.

Dominant strategy: 
A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other. Hence, a strategy is dominant if it is always better than any other strategy, for any profile of other players' actions.

Altruism:  Is the principle or practice of concern for the welfare of others. It is a traditional virtue in many cultures and a core aspect of various religious traditions and secular worldviews, though the concept of "others" toward whom concern should be directed can vary among cultures and religions.

" We find that those who can propose offers hold substantial bargaining leverage over their opponents. "

How to solve Nash Equilibria  (the plural of equilibrium) using Calculus.