ECON Game Theory

Jack, Jill, Mike and Molly are deciding whether or not to attend their high school reunion. However, not all four of them get along well and they would prefer to stay at home rather than meeting someone they do not like at the reunion. In particular, Jack prefers not to attend the reunion if Molly is attending the reunion, otherwise he prefers to attend. Molly prefers not to attend if Jack and/or Jill attends otherwise she prefers to attend. Mike prefers not to attend if Jack attends otherwise he prefers to attend. Finally, Jill prefers not to attend if Molly and/or Mike attends otherwise she prefers to attend. Assuming that all of them make their decision simultaneously find all of the pure strategy Nash equilibria of this game. You need to argue who will end up attending the reunion and who will stay at home in Nash equilibrium. Clearly explain your reasoning.