3. Consider the following payoff matrix for a complementary investment game:WCGa.Do Not InvestC.Investb. What is the Nash equilibrium?Do Not InvestWhat is the maximin solution?0Does either firm have a dominant strategy?-100BB00Invest020d. How do your answers change if BB loses 5 if it invests and WCG doesn't invest?11010

Game theory helps in the decision-making of the players on the basis of different payoffs. A player…

3. Consider the following payoff matrix for a complementary investment game: WCG a. Do Not Invest Invest b. What is the Nash equilibrium? Do Not Invest -100 Does either firm have a dominant strategy? C. What is the maximin solution? 0 BB 0 0 Invest 0 20 d. How do your answers change if BB loses 5 if it invests and WCG doesn't invest? 5 10

3. Consider the following payoff matrix for a complementary investment game: WCG a. Do Not Invest Invest b. What is the Nash equilibrium? Do Not Invest -100 Does either firm have a dominant strategy? C. What is the maximin solution? 0 BB 0 0 Invest 0 20 d. How do your answers change if BB loses 5 if it invests and WCG doesn't invest? 5 10

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter15: Oligopoly And Strategic Behavior

Section: Chapter Questions

Problem 17P

See similar textbooks

Similar questions

on 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.
7. Solving for dominant strategies and the Nash equilibrium Suppose Rajiv and Simone are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Rajiv chooses Right and Simone chooses Right, Rajiv will receive a payoff of 5 and Simone will receive a payoff of 5.
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; 5
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…
A st SW B st 2,1 5, 15 2. Consider the game of chicken above. SW 11,4 3,5 a. Find all Nash equilibrium in pure strategies. b. Say that player A uses a mixed strategy, where she picks st with prob. 0.55 and sw with prob. 0.45. What is B's expected payoffs from choosing pure st and pure sw? c. Player B uses a mixed strategy and wants A to choose sw. What is the minimum prob. p, for which B needs to play st so A will choose sw.
Question > Consider the following matrix game where Player 1 moves first then Player 2 observes player 1's move and responds. Draw the game tree for the sequential move game and then determine all the Nash equilibria. Player 1 Strategy A Strategy B Strategy C Strategy D -3, -2 10, 12 9, 20 Player 2 Please show each step on how to get the answer. Thank you! Strategy E 13,7 17, 17 12, 21 Strategy F 20,8 22, 16 19, 19
7. Solving for dominant strategies and the Nash equilibrium Suppose Ethan and Cadence are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Ethan chooses Up and Cadence chooses Down, Ethan will receive a payoff of 6 and Cadence will receive a payoff of 4. Ethan Up Down Cadence Up 4,3 6, 7 Down 6, 4 7,6 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Ethan chooses and Cadence chooses
4. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner's payoff is 10 and the loser's payoff is –10. • When paper (P) beats rock, the winner's payoff is 5 and the loser's payoff is -5. • When scissors beats paper, the winner's payoff is 2 and the loser's payoff is -2. • In case of ties, both players receive 0 payoff.
8.1 Consider the following game: Player 1 A B C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1.1 E 0,0 1,1 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..
. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
7. Solving for dominant strategies and the Nash equilibrium Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of 6 and Aaliyah will receive a payoff of 4. Russell Up Down Aaliyah Up 6,3 3,3 Down 6,4 7,4 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses and Aaliyah chooses
7. Solving for dominant strategies and the Nash equilibrium Suppose Rashard and Alyssa are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Rashard chooses Up and Alyssa chooses Down, Rashard will receive a payoff of 6 and Alyssa will receive a payoff of 8. Rashard Up Down Alyssa Up 4,6 7,5 Down 6,8 3,7 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Rashard chooses and Alyssa chooses