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- 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.GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
- The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofConsider 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. ElektGAME 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.
- Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.Consider the two-player game depicted below w А 1,5 2,2 0,4 3,11 В 13,0 4,1 2,5 4,2 с 1,3 2,6 5,2 2,0] a. What is Player 2's best response if Player 1 plays B? b. What is Player l's best response if Player 2 plays z? c. What are the pure strategy Nash Equilibria? సా
- 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.1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?5. Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first payoff in each entry is for A and the second for B.(8 points) B Right Left 3,3 5,1 Down 2,2 4,4 a. Find the Nash equilibrium or equilibria. b. Which player, if any, has a dominant strategy? A Up