DALL Problems 1. Th e travelers\' dilemma: Consider a simultaneous game where pl
ID: 1134580 • Letter: D
Question
DALL Problems 1. Th e travelers' dilemma: Consider a simultaneous game where player I writes down x, and player 2 writes down x2. Players can choose any xi and x2 in the interval [0,100). Payoffs are as follows Ifx,-X2, then player l receives $X1 and player 2 receives SX2. But if X1 then both players receive an amount equal to whichever is lower, with the player who wrote down the lower number receiving an additional $2 bonus. What are the Nash Equilibrium values of x1 and x2? (Hard) If be any additional Nash Equilibria? a. b. xi and x2 were restricted to be integers in the interval [0,100] would thereExplanation / Answer
a.
In order to receive the bonus of $2 both would try to choose an amount lower than the other player but in a simultaneous game both players do not know the actions of the other players hence both would choose the lowest option .i.e. zero and receive nothing. It is Nash equilibrium because no player would want to deviate from this strategy as deviating would mean the other player would get the bonus.
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