Instructions: Enter a numeric response corresponding to the number of the definition listed above. a. A repeated game: b. Cooperative equilibrium: c. Simultaneous game: d. Payoff matrix: e. Nash equilibrium: 5
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- t 0886951] Two firms are competing in a market by simultaneously deciding the quality of their manufactured product. The payoff matrix for this competition is depicted in the image. Firm 1 This game can be solved by deleting dominated strategies. Use this tactic to identify all pure-strategy Nash equilibria in this game. Low Medium High 53 54 66 Low A. Firm 1 chooses high and Firm 2 chooses high. 25 34 43 B. Firm 1 chooses low and Firm 2 chooses high. 43 68 77 C. Firm 1 chooses medium and Firm 2 chooses medium. Firm 2 Medium D. Firm 1 chooses medium and Firm 2 chooses low. 12 45 E. Firm 1 chooses low and Firm 2 chooses low. 74 96 89 F. Firm 1 chooses high and Firm 2 chooses low. High G. Firm 1 chooses medium and Firm 2 chooses high. 39 48 H. Firm 1 chooses low and Firm 2 chooses medium. I. Firm 1 chooses high and Firm 2 chooses medium. 50 21Number Definition A table that shows the payoffs each firm earns from every combination of firm strategies 1 An agreement among firms to charge the same price or otherwise not to compete An option that is better than any alternative option regardless of what the other firm does An outcome of a strategic game from which neither rival wants to deviate A game outcome in which players seek to increase their mutual payoff A practice where one firm initiates a price change and the other firms follow the leader A game in which the firms choose their strategies at the same time One firm's gain must equal the other firm's loss A game in which the sum of the two firms' outcomes is positive 4 6. 7 8. 9. Firms select their optimal strategies in a single time period without regard to possible interactions in subsequent time periods 10 11 A game that occurs more than once Instructions: Enter a numeric response corresponding to the number of the definition listed above. a. Collusion: b. Zero-sum…Company A both 100 100 200 200 Above is the payoff matrix for company A and company B as they choose thek advertising strategies. The payoffs of company A are indicated with color red, for company B in O Both players have a dominant strategy of Advertise O Nolther player has a dominant strategy. O For company A, dominant strategy is Advertise, Company B does not have a dominant strategy O For company B, dominant strategy is Advertise, Company A does not have a dominant strategy
- 10:04 PM cb = Chegg Economics Vo LTE expert.chegg.com/expertqna Time remaining: 00:09:49 Consider the following payoff matrix for two oligopolists that are deciding what quantity to produce: Firm 2 High Quantity Low Quantity $70k; $70k $130k; $20k High Quantity Firm 1 $20k; $130k $100k; $100k Low Quantity In the Nash equilibrium of this game, what are the payoffs to each firm? O a. Firm 1 receives $130k and Firm 2 receives $20k. O b. Firm 1 receives $20k and Firm 2 receives $130k. O c. Firm 1 receives $100k and Firm 2 receives $100k. O d. Firm 1 receives $70k and Firm 2 receives $70k. Answer Skip 4G Exit 2 ¹20%You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next move5. 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…
- Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.Please look at the payoff matrix below which shows the benefits that would accrue to each player in a 2-player.non-sequential, non-repeated game. a) Identify the collusive (cooperative) equilibrium. b) Identify the secure strategy (maximin) equilibrium c) Identify the maximax equilibrium d) Identify the Nash equilibrium Apple Inc. Strategy 1 Strategy 2 Strategy 3 20 40 60 60 1000 200 Strategy A 70 50 90 Banana Inc. 400 70 300 Strategy B 40 80 100 90 150 80 Strategy CUofC Aggressive Restrained Aggressive 18, 26 29,47 MRU Restrained 45, 59 32, 23 Consider the case of a Sequential-Move game. Uofc moves First Part 1. Is UofC 's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) 1 Part 2. Is MRU's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) Number: Part 3. How much profit does UofC make under the Sub-game perfect Nash-Equilibrium? Number Part 4. How much profit does MRU make under the Sub-game perfect Nash-Equilibrium? Number
- Two farmers, Ali and Hasan, graze their animals on a common land. They canchoose to use the common resource lightly or heavily and the resulting strategic interactionmay be described as a strategic form game. The payoff matrix is the following: (The table is attached on iamges part) Suppose that the game is repeated infinitely. If both players play a Grim-Trigger strategy, findthe discount factor δ such that (Light,Light) be a Nash equilibriumConsider the following simultaneous game. a. b. C. d. Player 1 U Player 2 L 8,8 3,0 R 3,3 8,3 What are the pure-strategy Nash equilibria? Identify. Find whether there are any mixed-strategy equilibria. Assume now the game above is being modified as a sequential game where player 1 would move first and player 2 second. Find all Nash and subgame perfect equilibria for the game. Would a Nash equilibrium always be Pareto efficient? Use your answer in (a) to explain.Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.