Player 1 writes an integer between 1 and 20 on a slip ofpaper. Without showing this slip of paper to player 2, player1 tells player 2 what he has written. Player 1 may lie or tellthe truth. Player 2 must then guess whether or not player 1has told the truth. If caught in a lie, player 1 must pay player2 $10; if falsely accused of lying, player 1 collects $5 fromplayer 2. If player 1 tells the truth and player 2 guesses thatplayer 1 has told the truth, then player 1 must pay $1 toplayer 2. If player 1 lies and player 2 does not guess thatplayer 1 has lied, player 1 wins $5 from player 2. Determinethe value of this game and each player’s optimal strategy.
Player 1 writes an integer between 1 and 20 on a slip ofpaper. Without showing this slip of paper to player 2, player1 tells player 2 what he has written. Player 1 may lie or tellthe truth. Player 2 must then guess whether or not player 1has told the truth. If caught in a lie, player 1 must pay player2 $10; if falsely accused of lying, player 1 collects $5 fromplayer 2. If player 1 tells the truth and player 2 guesses thatplayer 1 has told the truth, then player 1 must pay $1 toplayer 2. If player 1 lies and player 2 does not guess thatplayer 1 has lied, player 1 wins $5 from player 2. Determinethe value of this game and each player’s optimal strategy.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Player 1 writes an integer between 1 and 20 on a slip of
paper. Without showing this slip of paper to player 2, player
1 tells player 2 what he has written. Player 1 may lie or tell
the truth. Player 2 must then guess whether or not player 1
has told the truth. If caught in a lie, player 1 must pay player
2 $10; if falsely accused of lying, player 1 collects $5 from
player 2. If player 1 tells the truth and player 2 guesses that
player 1 has told the truth, then player 1 must pay $1 to
player 2. If player 1 lies and player 2 does not guess that
player 1 has lied, player 1 wins $5 from player 2. Determine
the value of this game and each player’s optimal strategy.
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