Game Theory Primer

• Game theory is a way of strategic interactions between self-interested people. It relates to how self-interested participants would behave in strategic interactions. 
• A game in general is any interaction between two or more people where the outcomes depend on what every body does or what every body has.  

Source: Coursera, Game theory course.

The questions to ask:

• What action should a player of the game take?
• Would all users behave the same in this scenario?
• What global behavior patterns should a system designer expect?
• For what changes to the numbers would behavior be the same?
• What effect would communication have?
• Repetitions? (Finite? Infinite?) 
• Does it matter if I believe that my opponent is rational?

What does it mean to say that the agent is self-interested?

• It does not mean that they want to harm others or only care about themselves. 
• only that the agent has his own description of states of the world that it likes, and acts based on this description. 

Each agent has a utility function. 

• quantifies degrees of preference across alternatives
• explains the impacts of uncertainty
• Decision-theoretic rationality: act to maximize expected utility. There is a basic theorem (von Neumann and Morgenstern, 1944) that derives the existence of a utility function from a more basic preference ordering and axioms of such offerings. 

Defining a game: Key Ingredients

• Players: who are decision makers? 
• people? governments? companies?
• Actions: Enter a bid in auction? Decide whether to end a strike? Decide when to sell a stock? Decide who to vote?
• Payoffs? 
• What motivates players? Do they care about some profits? Do they care about other players? 

Defining Games: Two Standard Representations

• Normal form (a.k.a. Matrix Form, Strategic Form) List what payoffs get as a function of their actions
• It is as if players moved simultaeneously
• But strategies encode many things 

 Prisoner's dilemma in any game:

• a,a: both cooperate and both get highest possible reward. 
• d,d: both defect and both get least possible reward. 
• b,c: one cooperates and the other defects --> the defector gets the most benefit and the cooperator gets the least benefit. 
• c,b: symmetric to the above. One cooperates and the other defects. The defector gets the most benefits, and the cooperator gets the least benefit as in c > a > d > b.