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- Mark and Bevis play a static game. Mark chooses x and Bevis chooses y. Mark's payoff is 16 - (x- y)2, and Bevis' payoff is 16 - (x-0.5)2 - (y-0.5)2. Then O a. both Mark and Bevis have dominant strategies O b. Mark has a dominant strategy, but Bevis does not O c. Bevis has a dominant strategy, but Mark does not O d. neither Mark or Bevis have dominant strategiesYou 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 moveConsider the following simultaneous game: Player 1 U D Player 2 L 30,10 -10, 20 R 10, 20 5,-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.
- GAME 5 Player B B1 B2 Player A A1 7,3 | 5, 10 A2 3, 8| 9, 6 In Game 5 above, O Neither player has a dominant strategy. O Player B has a dominant strategy. O Player A has a dominant strategy. O Both players have dominant strategies.Why is a solution that we find through backward induction always a subgame perfect Nash equilibrium? O The results of backward induction are the only possible Nash equilibria. O The backward induction solution maximizes the combined payoffs of all players. O At each decision node, backward induction chooses the best option going forward for the player who moves at that point. O When we use backward induction, we only consider dominant strategies. Show your steps please.Consider this as a simultaneous-move (static) game: Player A Top Bottom Player B Left Right ETEL UU 1.b) Does any player have a dominant strategy in this game? Explain. 1.a) Write down the Best Response Correspondence for each of the two players. Molimonsbestich Quinit 1.c) Find all Nash Equilibria in pure strategies of this game. 1.d) Is there any Nash Equilibria in mixed strategies? If so, find it. Elekt
- GAME 5 Player B B2 B1 Player A A1 7, 3 5, 10 A2 3, 8 9, 6 In Game 5 above, O there are no Nash equilibria in pure strategies. Player A choosing A1 and Player B choosing B2 is a Nash equilibrium. O Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. O Player A choosing A2 and Player B choosing B1 is a Nash equilibrium.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 equilibriumAnashequilibriumisastrategyprofilesuchthat: a)Both players are playing a best response strategy b)Both players must be playing a dominant strategyc)Both players achieve their highest possible payoff d)a) and c) e)b) and c)
- 1. What are the advantages and disadvantages of collusion? Define Collusion 2. In a Stackelberg game, what is the best response that follower firm 2 can make to the choice y1 already made by the leader, firm 1? Defining the game and provide an example of the best response.Refer to the accompanying game. Firm A Which of the following is true? Multiple Choice O O O Low Price High Price O None of the answers is correct. Firm B Low Price (10,9) (-10,7) A dominant strategy for firm A is "high price." 19 There does not exist a dominant strategy for firm A. A dominant strategy for firm B is "low price." High Price (15,8) (11,11)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.