3 (25 ) Consider a strategic form game with 3 players i 1,2,3 whose actions Xi are numbers from the set (1,2,3,4) If any two or all players select the same number x, then each player i (including the player with a possibly different number) receives the payoff equal to this number, U x In all other cases, that is, if all numbers are different, then each player receives the payoff 2 (a) Find any (just one) Nash equilibrium (x1 ,x2 ,x3 ) in which the payoff of each player i 1,2,3 is Uf(x2 ,x2 ,x3 ) 3 and verify it (b) Is there a Nash equilibrium in which all player's numbers are different If yes, then find any such an equilibrium and verify it If no, then show that for any action profile with all different numbers there is a player and a profitable deviation for that player 3 (25 ) Consider a strategic form game with 3 players i 1,2,3 whose actions Xi are numbers from the set (1,2,3,4) If any two or all players select the same number x, then each player i (including the player with a possibly different number) receives the payoff equal to this number, U x In all other cases, that is, if all numbers are different, then each player receives the payoff 2 (a) Find any (just one) Nash equilibrium (x1 ,x2 ,x3 ) in which the payoff of each player i 1,2,3 is Uf(x2 ,x2 ,x3 ) 3 and verify it (b) Is there a Nash equilibrium in which all player's numbers are different If yes, then find any such an equilibrium and verify it If no, then show that for any action profile with all different numbers there is a player and a profitable deviation for that player

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3  (25 ) Consider a strategic form game with 3 players i   1,2,3 whose actions Xi are numbers from the set (1,2,3,4)  If any two or all players select the same number x, then each player i (including the player with a possibly different number) receives the payoff equal to this number, U   x  In all other cases, that is, if all numbers are different, then each player receives the payoff 2  (a) Find any (just one) Nash equilibrium (x1 ,x2 ,x3 ) in which the payoff of each player i   1,2,3 is Uf(x2 ,x2 ,x3 )   3 and verify it  (b) Is there a Nash equilibrium in which all player's numbers are different  If yes, then find any such an equilibrium and verify it  If no, then show that for any action profile with all different numbers there is a player and a profitable deviation for that player  3  (25 ) Consider a strategic form game with 3 players i   1,2,3 whose actions Xi are numbers from the set (1,2,3,4)  If any two or all players select the same number x, then each player i (including the player with a possibly different number) receives the payoff equal to this number, U   x  In all other cases, that is, if all numbers are different, then each player receives the payoff 2  (a) Find any (just one) Nash equilibrium (x1 ,x2 ,x3 ) in which the payoff of each player i   1,2,3 is Uf(x2 ,x2 ,x3 )   3 and verify it  (b) Is there a Nash equilibrium in which all player's numbers are different  If yes, then find any such an equilibrium and verify it  If no, then show that for any action profile with all different numbers there is a player and a profitable deviation for that player

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3. (25%) Consider a strategic-form game with 3 players i = 1,2,3 whose actions Xi are numbers from the set (1,2,3,4). If any two or

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