6. Consider the following game. There is a class with 10 students. Every student must simulataneously choose an integer number between 0 and 10. If a player chooses a number equal to the average of the other players, then she receives $1, otherwise she receives nothing. (a) Are there any (b) Suppose now players get a payoff $1 if their number equals the average of other players and a payoff of $2 if it is greater than the average but by no more than one unit. In any other case they get zero. i. Are there any strictly dominated strategies? Is there any strategy that is unreasonable in the sense that there are others that weakly dominates it? ii. Analyze the game by sequential elimination of these unreasonable strate- gies. What is or are the possible outcomes