Let\'s now go back to the first simultaneous game, and consider instead the case
ID: 1141428 • Letter: L
Question
Let's now go back to the first simultaneous game, and consider instead the case in which the players nd independently announce an integer number between 0 and 100. As before, each player's payoff is the product of the two numbers announced. First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced (c) Describe the best responses of this game. How many Nastilbria does the game have? Explain (d) As before, first, Player 1 can choose either to "Stop or "Continue. If she chooses Stop then the game ends with the pair of payoffs (1, 1). If she chooses "Cantinue" then the game described above is played. Would Player 1 choose "Continue"? Justify your anwer.Explanation / Answer
Playesr announce an integer between 0 and 100.
Each player's pay off is the product of two numbers announced.
Let us assunme that the numbers are a &b, hence the pay off for each player would be "ab".
Nash Equilibrium is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players.
Here, two numbers are announced by two players. They know that the consequence is unconditional on the pay off which will be multiplied of the two selected numbers and both of them will be selecting the highest number i.e. 100 to maximise the pay off for self and this would result in maximising the pay off for the other. Hence with no consequential condition applied, one nash equilibrium exists i.e. (100,100)
d) Player 1 will definitely choose Continue as the gain of player1 is dependent on the selection of the pay off for herself. She will not choose STOP that may result in a meagre payout of (1,1).
She will be opting to CONTINUE to maximise her gain
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