【正文】 not 169。2020 Pearson Education, Inc. Chapter 13 60 Extensive Form of a Game ? Extensive Form of a Game ? Representation of possible moves in a game in the form of a decision tree ? Allows one to work backward from the best oute for Firm 1 169。2020 Pearson Education, Inc. Chapter 13 58 Modified Product Choice Problem ?If firms both announce their decisions independently and simultaneously, they will both pick sweet cereal and both will lose money ?What if Firm 1 sped up production and introduced new cereal first? ?Now there is a sequential game ?Firm 1 will think about what Firm 2 will do 169。2020 Pearson Education, Inc. Chapter 13 56 Sequential Games ?Players move in turn, responding to each other’s actions and reactions ?Ex: Stackelberg model (ch. 12) ?Responding to a petitor’s ad campaign ?Entry decisions ?Responding to regulatory policy 169。2020 Pearson Education, Inc. Chapter 13 54 Oligopolistic Cooperation in the Water Meter Industry ?Significant economies of scale ?Both long term relationship and economies of scale represent barriers to entry ?Hard for new firms to enter market ?If firms were to cooperate, could earn significant monopoly profits ?If pete aggressively to gain market share, profits will fall to petitive levels 169。2020 Pearson Education, Inc. Chapter 13 52 Oligopolistic Cooperation in the Water Meter Industry ?Characteristics of the Market ?Four producers of water meters ? Rockwell International ? Badger Meter ? Neptune Water Meter Company ? Hersey Products ? Rockwell has about 35% of market share ? Badger, Neptune, and Hersey bined have about a 50 to 55% share 169。2020 Pearson Education, Inc. Chapter 13 50 TitforTat Strategy ?If firms don’t believe their petitors are rational or think perhaps they aren’t, cooperative behavior is a good strategy ?Most managers don’t know how long they will be peting with their rivals ?In a repeated game, prisoner’s dilemma can have cooperative oute 169。2020 Pearson Education, Inc. Chapter 13 48 TitforTat Strategy ?What if the game is infinitely repeated? ?Competitors repeatedly set price every month, forever ?Titfortat strategy is rational ? If petitor charges low price and undercuts firm ? Will get high profits that month but know I will lower price next month ? Both of us will get lower profits if keep undercutting, so not rational to undercut 169。2020 Pearson Education, Inc. Chapter 13 46 Pricing Problem Firm 1 Low Price High Price Low Price High Price Firm 2 10, 10 100, 50 50, 50 50, 100 169。2020 Pearson Education, Inc. Chapter 13 44 The Battle of the Sexes ? Pure Strategy ?Both watch wrestling ?Both watch opera ? Mixed Strategy ?Jim chooses wrestling ?Joan chooses wrestling Jim Wrestling Opera Wrestling Opera Joan 2,1 0,0 1,2 0,0 169。2020 Pearson Education, Inc. Chapter 13 42 Mixed Strategy ?One reason to consider mixed strategies is when there is a game that does not have any Nash equilibriums in pure strategy ?When allowing for mixed strategies, every game has a Nash equilibrium ?Mixed strategies are popular for games like poker ?A firm might not find it reasonable 169。 probability and tails with 189。2020 Pearson Education, Inc. Chapter 13 40 Matching Pennies ? Pure strategy: No Nash equilibrium ?No bination of head and tails leaves both players better off ? Mixed strategy: Random choice is a Nash equilibrium Player A Heads Tails Heads Tails Player B 1, 1 1, 1 1, 1 1, 1 169。2020 Pearson Education, Inc. Chapter 13 38 Mixed Strategy ?Pure Strategy ?Player makes a specific choice or takes a specific action ?Mixed Strategy ?Player makes a random choice among two or more possible actions, based on a set of chosen probabilities 169。2020 Pearson Education, Inc. Chapter 13 36 Prisoners’ Dilemma Confess Don’t Confess Confess Don’t Confess Prisoner B 5, 5 1, 10 2, 2 10, 1 169。2020 Pearson Education, Inc. Chapter 13 34 Maximin Strategy ?If both are rational and informed ?Both firms invest ?Nash equilibrium ?If Player 2 is not rational or pletely informed ?Firm 1’s maximin strategy is to not invest ?Firm 2’s maximin strategy is to invest ?If 1 knows 2 is using a maximin strategy, 1 would invest 169。2020 Pearson Education, Inc. Chapter 13 32 Maximin Strategy Firm 1 Don’t invest Invest Firm 2 0, 0 10, 10 20, 10 100, 0 Don’t invest Invest ? Observations ?Dominant strategy Firm 2: Invest ?Firm 1 should expect Firm 2 to invest ?Nash equilibrium ? Firm 1: invest ? Firm 2: Invest ?This assumes Firm 2 understands the game and is rational 169。2020 Pearson Education, Inc. Chapter 13 30 The Nash Equilibrium Revisited ?Maximin Strategies Scenario ?Two firms pete selling file encryption software ?They both use the same encryption standard (files encrypted by one software can be read by the other advantage to consumers) ?Firm 1 has a much larger market share than Firm 2 ?Both are considering investing in a new encryption standard 169。2020 Pearson Education, Inc. Chapter 13 28 Beach Location Game ?Scenario ?Two petitors, Y and C, selling soft drinks ?Beach is 200 yards long ?Sunbathers are spread evenly along the beach ?Price Y = Price C ?Customer will buy from the closest vendor 169。2020 Pearson Education, Inc. Chapter 13 26 Product Choice Problem Crispy Sweet Crispy Sweet Firm 2 5, 5 10, 10 5, 5 10, 10 169。2020 Pearson Education, Inc. Chapter 13 24 The Nash Equilibrium Revisited ?Dominant Strategy ?“I’m doing the best I can no matter what you do. You’re doing the best you can no matter what I do.” ?Nash Equilibrium ?“I’m doing the best I can given what you are doing. You’re doing the best you can given what I am doing.” ?Dominant strategy is a speci