the winner of a westinghouse scholarship, he attended the carnegie institute of technology, where he received both his bachelor's degree and his master's degree in 1948. from pittsburgh he went to princeton university where he worked on his equilibrium theory. he received a ph.d. in 1950 with a dissertation on non-cooperative games. the thesis, which was written under the supervision of albert w. tucker, contained the definition and properties of what would later be called the nash equilibrium. his studies on this subject led to three articles: