There are games with perfect information, such as tic-tac-toe or chess, and played on pure strategy. There are also games without perfect information. Based on the mathematical theory of games, there are optimal mixes of strategies and the frequency one can expect to win, such as stone-paper-scissors which is a 2-person zero-sum game. With optimal strategies, there is no win over a long run of plays.
In person competitive situations, there are more players. Also, players can form coalition, and there are infinite number of strategies for such non-zero-sum games.
The equilibrium solution is a set of mixed strategies, with one solution for each player and no one has a reason to deviate from the game plan.
John Nash proved that any many-person, non-cooperative, finite-strategy game has at least one equilibrium solution. Examples are in missile defense, labour negotiations, consumer price wars.
Game theory does not solve problem, but help illuminate the task by offering a different way of interpreting the competitive interactions and possible results.