Three roommates need to vote on whether they will adopt a new rule and clean their room once a week, or stick to the current once a month rule. Each votes “yes” for the new rule or “no” for the current rule. Imagine that players 1 and2 prefer the new rule while player 3 prefers the old rule. Imagine that the players require a unanimous vote to adopt the new rule. Player 1 votes first, then player 2, and then player 3, each one observing the previous votes. Draw this as an extensive form game and find the Nash equilibria
I've drawn the extensive form game but don't understand why Player 3 would have 16 pure strategies {YYYY,YYYN,YYNY,YYNN,YNYY,YNYN,YNNY, YNNN,NYYY, NYYN, NYNY, NYNN, NNYY, NNYN , NNNY, NNNN} which is says in the solutions.
I understand that Player 1 has 2 pure strategies {Y,N} and Player 2 has 4 {YY,YN,NY,NN} I thought that would mean player 3 would have 8 {YYY,YYN,YNY,YYN,NYY,NYN,NNY,NNN}