Three Person Games
Simple extensions of two person games
All players have two strategies
o 8 possible outcomes in the game
o Denominated as the payoff for each player
First number is for player one, second for two, third for three
o Player one is red, pla
Sequential Games
Static games: Expressed in normal form that are simultaneous nature
Sequential games: one person moves and then another person moves
Compare extensive form games with analogous games
Example:
o Macro Corp has developed a new product. It i
Nash Equilibrium Problems
Review:
o Absent a dominant strategy, the best strategy for a player depends on
the strategy selected by the opposing player
o A Nash Equilibrium can be viewed as a set of strategies resulting in an
outcome that represents each p
Prisoners Dilemma
Prisoners Dilemma
o Dominant strategies achieve worst social outcome
o Each player has a dominant strategy to defect
o Paradox of rationality
o Collective action problem
o Only one solution
o Would preplay communication affect the outcom
Nash Equilibrium in Mixed Strategies
Mixed strategy is a strategy that involves a random selection from two or more
pure strategies
o According to a particular probability distribution
o Randomizing ones own choice this way is called a mixed strategy
When
Introduction to Nash Equilibrium
Nash Equilibrium
What is it?
Why is it important?
How do you find it?
Introduction
Nash Equilibrium is generally recognized as the single most important principle
of modern game theory
The Nash Equilibrium is a genera
Hawk vs. Dove Games
If both players are hawks, they will fight each other for they prey
o Ultimately one may win or both may get a piece
o Both will incur a cost
If one player is a dove, he will give in
o If both players are doves, they will share
The bes
Equilibrium Selection
Sometimes a focal point (Schelling point) can be an effective tool for helping the
players to independently focus on one of the competing Nash Equilibrium
outcomes, and as such to make strategy selections leading to the best game
sol
Equilibrium Path
Some say that the equilibrium outcome is, by definition, a SPNE in an extensive
form game with sequential moves, because a Nash equilibrium is determined at
every decision node along the equilibrium path
o However, more formally, a SPNE i
Chicken Game
Chicken Game
o The name of the game is derived from a dangerous game played by disaffected
teenagers in California in the mid-1950s
Boys would go out in a deserted road with their cars
The boys would face each other and would be right on th