Consider a simultaneous$-$move integer game between two players: Marilyn and Noah. Each of the player is required to announce a positive integer between $1$ to $4.$ In other words, a player can announce $1,2,3,$ or $4.$ Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: $(1)$ when the two announced integers are different, whoever reports the lower number pays $$1$ to the other player, so that the loser of the game has payoff $-1$ and the winner of the game has payoff $1$; $(2)$ when the two players announce the same integer, their payoffs are both $0.$ Does Marilyn have a dominant strategy?Group of answer choicesYesNo