Ex. 5- - Agenda Setting An agenda-setting game is described as follows. The "issue space" (set of feasible poli- cies) is an interval X = [0,5]. An agenda setter (player 1) proposes an alternative x = X against the status quo q = 4. After player 1 proposes x, the legislator (player 2) ob- serves the proposal and selects between the proposal x and the status quo q. Player 1's most-preferred policy is 1, and for any final policy y = X his payoff is given by v1(y) = 10|y — 1|, - where |y1| denotes the absolute value of (y-1). Player 2's most preferred policy is 3, any final policy y Є X he payoff is given by and for v2(y) = 10|y3|. That is, each player prefers policies that are closer to his/her most-preferred policy. (1) Write down the strategic-form representation of the dynamic game. (2) Find a subgame perfect Nash equilibrium. Is it unique?

Table 9-03. Suppose you are a general in the army. Your country is at war. You are trying to invade the enemy. You can attack on the enemys east coast or the west coast. The enemy has only enough troops to defend one coast. The payoff matrix below represents whether you or the enemy wins (represented by 1) or loses (represented by 0). Enemy Defend east coast Defend west coast Enemy: 1 Enemy: 0 Attack east coast You: 0 You: 1 You Enemy: 0 Enemy: 1 Attack west coast You: 1 You: 0 Refer to Table 9-03. To win the war, O a. you must attack the west coast, only if you have credible information that the enemy is defending the east coast. O b. you must attack the west coast, and information about whether the enemy is defending the east or the west coast is irrelevant to you. c. you must attack the west coast, only if you have credible information that the enemy is defending the west coast. d. you must never attack the west coast, and information about whether the enemy is defending the east or…

Question 2. Two students are working together to submit their Microeconomics mid-semester group coursework. Each student i can put in the effort x; that costs c(x;), in which x; E [0, 1]. This gives each student the utility of u(x1, x2). Formu- late this situation as a strategic game.

Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column.     Up   Down Left   1, -1   -1, 1 Right   -1, 1   1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up

Write the game below in normal form and find all Nash equilibria. C 2. Write the game below in normal form and find all Nash equilibria. जल P = 1/1535 Nature ताल P = 1/3 P1 A (3,6) P1 B P2 B C2 P2 Pz Pz (0,3) ✓ (9,0) (3,3) ✓ (0, 6) (-3,3) ✓ (9,6) Х (3,0) (-3, 12)