John Forbes Nash Jr. (1928-2015), was an American mathematician who made fundamental contributions to, among other fields, game theory, where he introduced the Nash equilibrium concept.
Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing their strategy. In a Nash equilibrium, the strategy of each player is a best response to the strategies of all other players. The contribution of Nash in his 1951 article Non-Cooperative Games was to define a mixed-strategy Nash equilibrium for any game with a finite set of actions and prove that at least one (mixed-strategy) Nash equilibrium must exist in such a game.
The New York Times explain the concept of Nash Equilibrium
Obituary in the New York Times