Estate division game is an allocation of an estate between players based on a rule. In this thesis, we consider estate division games and study the necessary and sufficient conditions for division rules under which Nash equilibria induce equal division. Ashlagi, Karag¨ozoˇglu, Klaus (2012) introduce classes of properties for division rules and show that they are sufficient for all Nash equilibria to induce equal division. In this study, we propose a different property, namely conditional full compensation, and prove that it is also a sufficient condition for division rules in order for all Nash equilibria outcomes under these rules to be equal division. We, then, show that under any rule satisfying claims boundedness and conditional equal division lower bound, equal division is a Nash equilibrium outcome. Finally, we prove that letting at least one player get more than the difference between the whole estate and the sum of other players’ claims is a necessary condition for all Nash equilibria to induce equal division.