2. Provide the normal-form expression to the extensive-form game below, and find all pure-strategy Nash equilibria there. Find the subgame-perfect Nash equilibrium then. A X B B F G F G A 0 60 9 5 B 3 5 12 10
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- Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…Consider the following game: Sarah R S T Peter X 9, 6 4, 4 6, -3 Y 6, 6 7, 6 2, 2 Z 9, 7 1, 5 6, 7 How many (pure strategy) Nash equilibria does this game have?Tucker and Eddie are playing the following game. Tucker can choose A or B and Eddie can choose C or D. The first payoff is for Tucker, the second for Eddie. Eddie Tucker C D A 3, 2 4, 3 B 4, 5 3, 4 Identify the Nash equilibrium(s) in this game. What rational game theoretic advice would you offer Tucker and Eddie on how to play this game? If Tucker and Eddie follow your advice, what payoff should each expect? Show your work.
- 2. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.Consider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium OHawk, Dove ODove, Hawk O Hawk, Hawk O Hawk, Hawkon 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
- 2. Brad and Angelina have agreed to meet up for their first date. Neither of them can remember the exact location where they arranged to meet up and have forgotten their phones at home. Their payoff matrix can be described as follows: Brad The Hive Le Monde a) What is the Nash equilibrium in this game? Angelina The Hive 5; 5 0; 0 Le Monde 0; 0 5; 5ROWENA 2 Answer 1: 2 Answer 2: 2 Answer 3: 1 Earth Water Wind Answer 4: Fire of the Nash equilibrium, (Rowena's 1 Colin's 3 3 North 1.3 This simultaneous game has two Nash equilibria. The Nash equilibrium, (Rowena's 2 , Colin's 1,2 3,2 2,0 COLIN South 3,1 1,2 2,1 3,0 East 0,2 2,3 1,1 West 1.1 1,1 0,3 2,2 ) has a greater joint payoff than thatQuick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No The Ice Cream Guys $3.99 $4.99 Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 Treats The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would they agree upon, if any? a) Both…
- 5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…rock paper scissors rock 0. -3 0. раper scissors -1 -1 3. 0. (a) Show that xT= (,) and yT= (,) together are not a Nash equilibrium 3' 3 3131 for this modified game.