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Game theory
- 1. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Basics of Game Theory The Study of Mathematical Models of Conflict and Cooperation Shubham Kumar Nigam shubhamkumarnigam@gmail.com Department of Computer Science and Technology IIEST,Shibpur,Howrah 28 June 2016
- 2. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Outline 1 What is Game Theory ?? 2 History and impact of game theory 3 Basics of Game Theory Informal definitions Formal definitions 4 Types of Game Cooperative and Non-Cooperative 5 Examples 6 Applications of Game Theory
- 3. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games What is Game Theory ?? Game theory is the study of how people interact and make decisions. Or, Game theory is the formal study of decision-making where the outcome of a participants choice of action, depends on the actions of other participants.
- 4. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games History and impact of game theory
- 5. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games History and impact of game theory John von-Neumann wrote a key paper in 1928. 1944: Theory of Games and Economic Behavior by von Neumann and Morgenstern. 1950: John Nash invents concept of Nash equilibrium. Game theory booms after this . . . 1994: Harsanyi, Nash, and Selten win Nobel Prize in economics for game theory work.
- 6. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Contents 1 What is Game Theory ?? 2 History and impact of game theory 3 Basics of Game Theory Informal definitions Formal definitions 4 Types of Game Cooperative and Non-Cooperative 5 Examples 6 Applications of Game Theory
- 7. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Informal definitions: Key terms: Players: Who is interacting? Strategies: What are their options? Payoffs: What are their incentives? Information: What do they know? Rationality: How do they think?
- 8. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Contents 1 What is Game Theory ?? 2 History and impact of game theory 3 Basics of Game Theory Informal definitions Formal definitions 4 Types of Game Cooperative and Non-Cooperative 5 Examples 6 Applications of Game Theory
- 9. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Formal definitions: Some formal definitions are: Game: A game in normal form consists of: A list of players i = 1....n A finite set of strategies Si for each player i A utility function or Payoffs ui for each player i, where ui : (S1xS2x.....xSn) ⇒ R. So, utility is the method of assigning numbers to outcomes from the preferences of the players.
- 10. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Formal definitions A Nash equilibrium is a set of strategies s1 ∈ S1....sn ∈ Sn, such that for each player i: si = arg maxs ui (s1, , si-1, s, si+1,...., sn)
- 11. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Types of Game A game with only one player is usually called a decision problem. Cooperative and Non-Cooperative Zero sum and non zero sum
- 12. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Contents 1 What is Game Theory ?? 2 History and impact of game theory 3 Basics of Game Theory Informal definitions Formal definitions 4 Types of Game Cooperative and Non-Cooperative 5 Examples 6 Applications of Game Theory
- 13. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Cooperative and Non-Cooperative A non-cooperative game is one in which players make decisions independently. Cooperative game theory: A cooperative game is a game where groups of players may enforce cooperative behaviour. Hence, the game is a competition between coalitions of players, rather than between individual players.
- 14. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Example 1:Decision making under uncertainty Would one rather go to the movies or to the beach? It is believed that there is a 40% chance that it will rain. The person will enjoy a movie whether it rains or not: U(movie, sun) = U(movie, rain) = 1. The person will not enjoy the beach if it is rainy, but I will have great time if it is sunny: U(beach, rain) = -1, U(beach, sun) = 2. (subjective expected utility)SEU(movie) = 1. SEU(beach) = .4(-1)+.6(2) = .8 . Thus, the person will rather go to the movies.
- 15. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Example 2:Zero sum games ”In zero sum games (ex. chess), one player’s gain is the other’s loss, while in non-zero sum games (ex. business agreements), it is possible for both players to simultaneously gain or lose.” Payoffs to P1/P2 Player 2 chooses A Player 2 chooses B Player 1 chooses A Player 1 chooses B -7/7 -4/4 2/-2 -1/1 Solution: P1 always prefers B; P2 (knowing this) prefers Bb to Ba. The value of the game for P1 is −1.
- 16. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Example 3: Non-zero sum games Payoffs to P1/P2 Player 2 chooses A Player 2 chooses B Player 1 chooses A Player 1 chooses B 4/4 0/2 2/0 1/1 Solution: Aa is a Nash equilibrium - each player gets 4 at Aa, but only 2 if he plays B instead.
- 17. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Example 4: The Prisoner’s Dilemma The district attorney of a small town is holding two prisoners as suspects in an armed robbery case. Being experienced with the criminal mentality, he tells each prisoner the following: ”If you both confess, you’ll get the standard sentence for armed robbery. If neither of you confess, I’ll have to lower the sentence to illegal possession of firearms.” ”But if you confess and your partner doesn’t, we’ll have enough evidence to give him the harshest possible sentence. In return for your assistance, we’ll let you go free.” What should each player do, cooperate with the other prisoner (telling the district attorney nothing) or defect (admit the crime in return for a lighter sentence)?
- 18. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Solution : The Prisoner’s Dilemma Each prisoner thinks: • ”If my partner defects, I’ll get a harsh sentence if I cooperate or a standard sentence if I defect.” •”If my partner cooperates, I’ll get a light sentence if I cooperate or go free if I defect.” •”So I should defect no matter what my partner does.” And he admits his guilt to the D.A. In a one-shot in Prisoner’s Dilemma, defection strictly dominate cooperation, so mutual defection is clearly the only rational outcome (i.e. the unique Nash equilibrium).
- 19. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Applications of Game Theory Economists auctions of radio spectrum licenses for cell phone innovated antitrust policy program that matches medical residents to hospitals Computer scientists new software algorithms and routing protocols Game AI Military strategists nuclear policy and notions of strategic deterrence Biologists what species have the greatest likelihood of extinction
- 20. Basics of Game Theory Shubham Kumar Nigam What is Game Theory ?? History and impact of game theory Basics of Game Theory Informal definitions Formal definitions Types of Game Cooperative and Non-Cooperative Examples Decision making under uncertainty Zero sum games Non-zero sum games Thank You!