Roxanne, Sara and Ted all love to eat cookies, but there is only one left in the package. No one wants to split the cookie, so Sara proposes to use the game "Evens or Odds" to determine who gets to eat it. On the count of three, each of them will show one or two fingers, they will add them up, and then divide the sum by 3. If the reminder is 0, Roxanne gets the cookie, if the reminder is 1, Sara gets it, and if it is 2, Ted gets it. Each of them receives a payoff of 1 for winning and eating the cookie, and 0 otherwise.

Provide the game table for this three-player game. Roxanne the Row player, Sara the Column player, and Tedthe Page player. (List the payoff in orders of Roxanne, Sara and Ted.)

Find all the pure-strategy Nash Equilibria in this game. Is this a game a fair mechanism for allocating this cookie? Explain why.