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Game theory

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  • 1. Basic concepts• The payoff matrix• Nash equilibrium• Dominant strategies• Maximin strategies• Mixed strategies
  • 2. Game Theory And Oligopoly• Non cooperative games the prisoner dilemma• Cooperative games dealing with cheaters• Sequential games the ad of being first
  • 3. IntroductionIntroduced by• In 1950s , By John von Neumann and Oskar Morgenstern• Application –1. political, courtship, economic issues2. It could be used to analyze the bargaining• process between two parties : Wage rate• negotiation: unions and firms Peace talks:• between 2 countries.
  • 4. Assumptions• Assumptions Finite sets of possible action• Awareness of availability competitors strategies too Intelligent and rational• Maximize gain and minimize loss If a’s gain is b’s loss,its 0-sum game (amt of gain=amt of loss) Players act; select their stategies simultaneously
  • 5. Types of games Cooperative Non-cooperative when players can when game is not negotiate a binding cooperative it is said tocontract to play joint be non-cooperative strategies. game.
  • 6. The Payoff Matrix It is a course of action taken by 1 of the participants in a game Mixed strategies-Pure strategies don’t selects theSelects the same strategy same stategy Payoff: It is the result or outcome of the strategy Example: 2 children engaged in coin-flipping 2 competing firms whose objective is to increse their profits by price changes
  • 7. Payoff matrix Consider the competition between two department stores, each of which must what kind of clothing to promote Store 2 Promote girl’s Promote women’s cloth cloth Promote girl’s cloth 0,0 4,2Store 1 Promote 2,2 2,4 women’s cloth Profit in millions
  • 8. NASH EQUILIBRIUMA Nash Equilibrium is defined as a set of strategies such that none of the participants in the game canimprove their payoff (profits), given the strategies of the other participants. Dominant Strategies : Dominant Strategies The dominant strategy is the optimal choice for a player no matter what the opponent does. One firm will be in dominant position in terms of change in strategy. Dominant Strategy(in millions) Firm Firm 2 Firm 1 Strategy No Price Change Price Change No Price Change 10,10 100,-30 Price Change -20,30 140,25
  • 9. Max min StrategyFirm Firm 2Firm 1 Strategy No New Product New Product No New Product 4,6 3,6 New Product 6,3 2,2
  • 10. Maxmin Strategy Firm 2 Strategy No New Product New Product 4, 6 3 ,6 No NewFirm 1 Product New Product 6, 3 2 ,2 Equilibrium Nash
  • 11. Maxmin Strategy Firm 2 Strategy No New Product New Product Maximum Minimum 4, 6 3 ,6 6 3 No NewFirm 1 Product New Product 6, 3 2 ,2 6 2 Maximum Minimum 3 6 6 2 Profit in millions
  • 12. Nash Equilibrium & Maximin Point Isnt Same • Decision Criterion is not Profit-Maximisation Why So? • Its for avoiding highly unfavourable outcome • Its for avoidance of risks
  • 13. Just Remember that its 2 Step Process 1.Find Minimum(Least) Profit 2.Select maximum Out of Minimum Profit Mixed Strategy Why We Should Study This?
  • 14. Game Table• The Game of Tennis 1. For Striker: Striker chooses to serve • Best response to defend either left or right left is to Strike right Receiver defends either • Best response to defend left or right right is to Strike left• Better chance to get a 2. For receiver: Just the good return if you opposite defend in the area the striker is serving to
  • 15. Receiver - 70-30 Striker - 60-40 Percent of Payoff Chances ofExpects Throws Receiver Striker Probability Matrix Success Left Left 0.70 0.60 0.42 75% 0.315 Left Right 0.30 0.40 0.12 25% 0.030 Right Left 0.70 0.60 0.42 25% 0.105 Right Right 0.30 0.40 0.12 75% 0.090 Total Success 0.540
  • 16. Receiver – 50-50Striker - 70-30 Percent of Chances Receive Probabli Payoff of Expects Throws r Striker ty Matrix Success Left Left 0.50 0.70 0.35 75% 0.263 Left Right 0.50 0.30 0.15 25% 0.038 Right Left 0.50 0.70 0.35 25% 0.088 Right Right 0.50 0.30 0.15 75% 0.113 Total Success 0.500
  • 17. Receiver – 50-50Striker - 40-60 Percent Chances Probabli of Payoff of Expects Throws Receiver Striker ty Matrix Success Left Left 0.50 0.60 0.3 75% 0.225 Left Right 0.50 0.40 0.2 25% 0.050 Right Left 0.50 0.60 0.3 25% 0.075 Right Right 0.50 0.40 0.2 75% 0.150 Total Success 0.500
  • 18. Mixed Strategy Equilibrium•A mixed strategy equilibrium is a pair of mixed strategies that are mutual best responses.• In the tennis example, this occurred when any player chose a 50-50 mixture of left and right.
  • 19. Receiver’s Best Response Suppose p is the probability of Strikers Serving towards left Clearly•If p = 1, then the receiver should defend to the left •If p = 0, the receiver should defend to the right.
  • 20. LeftRight 1/2 P
  • 21. Best Response Suppose that the receiver goes left with probability q. Clearly,•if q = 1, the server should serve right•If q = 0, the server should serve left Server’s
  • 22. q1/2 Right Left
  • 23. Putting Things Together q Mutually best R’s best response response1/2 S’s best response 1/2 p
  • 24. Noncooperative GamesA game is considered non cooperative if it not possible tonegotiate with other participants and enter into some form ofbinding agreement. Example : Prisoners Dilemma Prisoner Prisoner 2 Prisoner 1 Strategy Don’t Confess Confess Don’t Confess 0,0 15,5 Confess 5,15 5,5
  • 25. Prisoner Prisoner 2 Remain SilentPrisoner 1 Strategy Confess Confess 5,5 0,20 Remain Silent 20,0 1,1
  • 26. cooperative Games A game is considered cooperative if it possible tonegotiate with other participants and enter intosome form of binding agreement. Firm Firm 2 Firm 1 Strategy No New New Product Product No New 30,30 10,40 Product New Product 40,10 20.20 Profit in millions
  • 27. Repeated Games•A repeated game is a game that the sameplayers play more than once In repeated games• the sequential nature of the relationshipallows for the adoption of strategies that arecontingent on the actions chosen in previousplays of the game
  • 28. Firm Firm 2Firm 1 Strategy Low-level Advertising High-level Advertising 30,30 10,40 Low-level Advertising High-level 40,10 20.20 Advertising Profit in millions
  • 29. • Any 1 Firm breaks the agreement• Adopts High-Level Advertising• Temporary Loss to other firm due to cheating• In next period, Other firm will do the same (Tit- For-Tat)• If One Firm Cuts price-Other firm will cuts price in next period.• If One firm Raise Price-Other firm will do so in next period.• Tit-For-Tat is Win-Win Situation
  • 30. Advantages•Easy to understand•Never initiates cheating•Never rewards cheating cause it punish in someway•Its about forgiving because cooperation is quicklyrestored
  • 31. Sequential Games•One Player acts First & Then other responds.•Games where players choose actions in aparticular sequence are sequential movegames.Examples: Chess, Bargaining/Negotiations.•Must look ahead in order to know what actionto choose now
  • 32. Benifits to the one Who acts firstFirm Firm 2 Strategy Low-level High-level Advertising Advertising 2,2 -5,10 Low-levelFirm 1 Advertising High-level 10,-5 -7,7 Advertising Profit in millions
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