2 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.