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GAME THEORY study of how people interact and make decisions (Applications,…
GAME THEORY study of how people interact and make decisions
History
1950:
John Nash
invents concept of Nash equilibrium
1944:
“Theory of Games and Economic Behavior” by
von
Neumann and Morgenstern
1928:
von Neumann
wrote a key paper in 1928
Key Elements
Payoffs:
What are their incentives?
Information:
What do they know?
Strategies:
What are their options?
Rationality:
How do they think?
Players
: Who is interacting?
Game Types
Simultaneous and sequential
Perfect information and imperfect information
Zero sum and non-zero sum
Finite & Infinite Strategies
Cooperative or non-cooperative
Applications
Political Science
Military Strategy
Economics
Psychology
Biology
Philosophy
Computer Science
Game Playing
Mathematics
Logic
Strategy
Pure Strategy
Minimax Principle
Maxmin principle
Mixed Strategy
Algebric Method
Graphical Method
Arithmetic Method
Matrix Method
Examples
Penalty shoot-outs in soccer matches
Serving and receiving in Tennis
Individual Plays in a game of American Football
Altheletes choosing to dope or not to dope
Split or Steal in Golden Balls
Speed dating
A game of Rock, Paper, Scissor
Closed bid auctions
The Prisoner's Dilemma
Major Assumptions
Repetition:
most instances involve repetitive solution
Payoff:
the payoff is fixed and determined in advanced
Conflicting Goals:
there is a conflict of interest between them
Information Availability:
each player knows all possible courses of action open to the opponent as well as anticipated payoffs
Timing:
the conflicting parties decide simultaneously
Players:
there are finite number of competitors
Nash Equilibrium
no player has an incentive to deviate from his chosen strategy after considering an opponent's choice.
A game may have multiple Nash Equilibria or none at all.
named after its inventor,
John Nash
, an American mathematician
each player's strategy is optimal when considering the decisions of other players.
To quickly test if the Nash equilibrium exists, reveal each player's strategy to the other players. If no one changes his strategy, then the Nash Equilibrium is proven.