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- FOOP 6. (a) For the following extensive-form game: i. Identify the pure and mixed strategy Nash Equilibria. ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in part (a)? Explain (a couple of sentences should suffice). (3,1) A D B C (-2,-2) (2,5) D (0,7)Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 10) Firm 1 A B F2 • this strategy profile is F2 Fight Don't fight Fight Don't fight [Select] (20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses don't fight if A, and fight if B. (-10, 30) (25, 15) • this strategy profile i✓ [Select ] (b) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses don't fight if A, and don't fight if B. • this strategy profile is [Select ] (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A and fight if B. not a Nash equilibrium a Nash equilibrium, but not a subgame perfect Nash equilibrium a subgame perfect Nash equilibrium none of the aboveProblem 2. (SPNE 2). Consider the following extensive form game between two players. (1,10) .. D 2 1 B X Y (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)
- Consider the following normal form game Player 2 L C R Player 1 5,4 4, 5 3,8 8,3 8,0 8,8 5,5 6,3 0,8 UMDQuestion 36 Consider the following normal form of a game. A D. (-3,-4) (-2,-5) (-1,0) (-4,-3) What is the maximin strategy of the row player? A O BProblem 1. (SPNE 1). Consider the following extensive form game between two players. (1,1) u D (a) List all pure strategies of player 1. (b) List all pure strategies of player 2. (c) Find all SPNE (in pure strategies) of this game. A B W X (5,1) (10,1) (4,2) (0, 1)
- 3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 8760а.) Your Crush Love Friendship You Love (100, 60) (30, 120) Friendship (60, 50) (40, 40) i. What is(are) the Nash equilibrium (equilibria), if any, under pure strategies in the above simultaneous game? i. What is the Nash equilibrium under mixed strategy? ii. What is the expected payoff for you and your crash respectively from the game under the mixed strategy in (ii.)?rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
- What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)4. EncryptCo is a Canadian company considering an international contract with a firm in the nation of Iceberg. The contract will last 5 years. It will involve the construction of an electrical generator for a residential area in Iceberg's largest city, Snowville. Iceberg's national currency is the blizzar. The table below contains data for the project. Complete this question using Excel. Include the output onto your solution and please ensure that it fits onto a page. First Cost (Blizzars) Net Revenue 2022 to 2027 (Blizzars) Expected Iceberg Inflation Rate Value of the Blizzar VS Canadian dollar in 2022 ($) Expected annual rate of decline of the value of the Blizzar VS the Canadian dollar Expected Inflation in Canada EncryptCo's Real MARR 1,800,000 550,000 10% $1.25 5% 6.5% 15% (a) Find the present worth of the project assuming no inflation. (b) Find the present worth of the contract using the above inflation rates. (c) Should EncryptCo pursue the project given the above inflation…Y A BA B (PERFECT-INFO GAME) Consider the game shown at the right. -1 a. What is the number of pure strategies of Player 1? Player 2? 2 -2 4 b. How many subgames are in this game? c. Find all subgame perfect equilibria (SPE)? -2 d. Find all other NE which is not SPE. -3