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Game theory

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  • 1. ProgressiveEducationSociety’sModernCollegeOf Engineering DepartmentOfComputerEngineering By Soumyashree Bilwar Department Of Computer Engineering
  • 2. Overview  What is Game Theory ( layman’s language)  Game Theory (Formal Definition)  Major Assumptions  Types Of Games  Representation Of Games  Nash Equilibrium  Popular Games  Prisoner’s Dilemma  Chicken Game  General and applied uses  Conclusion  References
  • 3. Game Theory????? Lets us first understand what is a Game?? Game, in the mathematical sense, is defined as strategic situation in which there are multiple participants. Is Sudoku a "game" ? No. Is Chess a "game" ? Yes.
  • 4. What is Game Theory? (layman’s language) Game Theory is one way of studying how an individual or a group makes a strategic choice. Practical applications in everyday life:  Friends choosing where to go for dinner  Gamblers betting in a card game  Diplomats negotiating a treaty  Commuters deciding how to go to work
  • 5. What is Game Theory? (Formal Definition ) Game Theory is a set of tools and techniques for decisions under uncertainty involving two or more intelligent opponents in which each opponent aspires to optimize his own decision at the expense of the other opponents.
  • 6. Major Assumptions  Players – the number of participants may be two or more. A player can be a single individual or a group with the same objective.  Timing – the conflicting parties decide simultaneously.  Conflicting Goals – each party is interested in maximizing his or her goal at the expense of the other.
  • 7. Major Assumptions(cont)  Repetition – most instances involve repetitive solution.  Payoff – the payoffs for each combination of decisions are known by all parties.  Information Availability – all parties are aware of all pertinent information. Each player knows all possible courses of action open to the opponent as well as anticipated payoffs
  • 8. Types of Games: Cooperative or non-cooperative Symmetric and asymmetric Zero-sum and non-zero-sum Simultaneous and sequential Perfect information and imperfect information Combinatorial games Infinitely long games Discrete and continuous games Many-player and population games Metagames
  • 9. Representation of games Type 1:Extensive form-> Tree Point of choice for a player. The player is specified by a number listed by the vertex. Possible action for that player. Payoffs
  • 10. Representation of games Type 2: Normal form-> Matrix 4,3 -1,-1 0,0 3,4 Player 1 chooses Up Player 1 chooses Down Player 2 chooses Left Player 2 chooses Right Normal form or payoff matrix of a 2-player, 2-strategy game Payoffs Player1 chooses Rows Player2 chooses Columns
  • 11. Nash Equilibrium John Nash John Nash was a mathematician and an economist.  He developed several theories in economics .  He was a Princeton and CMU graduate.  His most important contribution was the theory of Nash equilibrium  He is the person portrayed in the movie “A beautiful mind”.
  • 12. What is Nash Equilibrium ? For any two groups that do not co-operate there will be a point at which neither group can benefit from unilateral action , and that the groups will hold their strategies constant at this point. The Nash equilibrium is not usually the most effective strategy; it is only the best one without co-operation. Through co-operation it is only that both parties will be able to increase their utility.
  • 13. Some of the popular Games of Game Theory Prisoner's dilemma Battle of the sexes Deadlock Rock, Paper, Scissors Trust game Cake cutting Chicken (aka hawk-dove) Traveller's dilemma
  • 14. Prisoner’s Dilemma Prisoner B stays silent Prisoner B confesses Prisoner A stays silent Each serves 1 month Prisoner A: 1 year Prisoner B: goes free Prisoner A confesses Prisoner A: goes free Prisoner B: 1 year Each serves 3 months http://pespmc1.vub.ac.be/PRISDIL.html Cooperation is usually analysed in game theory by means of a non-zero-sum game called the "Prisoner's Dilemma“. The prisoner's dilemma is meant to study short term decision-making .
  • 15. Analysisof Prisoner’sDilemma Each player gains when both stay silent. (one month)  One player stays silent and other confesses then one who confesses will gain more. (confess- freed, silent-1 year)  If both confess , both lose (or gain very little) but not as much as the "cheated" silent prisoner whose cooperation is not returned. (3 months) Prisoner’s Dilemma has single Nash equilibrium. Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the United States. It is an example of the prisoner's dilemma game tested by real people
  • 16. Chicken Game Driver B Swerve Driver B Straight Driver A Swerve Tie , Tie Lose, Win Driver A Straight Win , Lose Crash http://pespmc1.vub.ac.be/PRISDIL.html Chicken is a famous game where two people drive on a collision course straight towards each other. Whoever swerves is considered a 'chicken' and loses, but if nobody swerves, they will both crash.
  • 17. Analysis of Chicken Game Both lose when both swerve.  One player wins when one swerves and other goes straight.  If both go straight, both lose(lose more than what they would have lost when both swerve. Because if both go straight they CRASH)  Chicken Game has 2 Nash Equilibrium.
  • 18. General and applied uses  Economics and business E.g. modelling competing behaviours of interacting agents , auctions, bargaining, social network formation.  Political Science E.g. public choice, social choice, players are voters, politicians , states.  Biology E.g. evolution , mobbing, animal communication  Computer Science and logic E.g. game semantics, online algorithms , equilibrium in games and peer to peer systems, time complexity  Philosophy E.g. co ordination games , convention , common knowledge
  • 19. Conclusion Game theory is exciting because although the principles are simple, the applications are far- reaching. Game theory is the study of cooperative and non cooperative approaches to games and social situations in which participants must choose between individual benefits and collective benefits. Game theory can be used to design credible commitments, threats, or promises, or to assess propositions and statements offered by others.
  • 20. References  Research papers and books  Game Theory at Work by James D. Miller  Thinking Strategically: Competitive Edge in Business, Politics and Everyday Life by Avinash Dixit  Existence of Equilibrium in Discrete Market Games by Somdeb Lahiri  URL  http://en.wikipedia.org/wiki/Game_theory  http://faculty.lebow.drexel.edu/mccainr/top/eco/gam e/game-toc.html  http://www2.owen.vanderbilt.edu/mike.shor/courses /game-theory/quiz/problems2.html  http://en.wikipedia.org/wiki/Nash_equilibrium
  • 21. Feedback and Question????