A solved game is a game whose outcome can be correctly predicted from any position, assuming that both players play perfectly.
This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance;
solving such a game may use combinatorial game theory and/or computer assistance.
The game of Connect Four has been solved
Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science. Traditional game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 21st century, game theory applies to a wider range of behavioral relations, and it is now an umbrella term for the science of rational decision making in humans, animals, as well as computers.
John Nash
Example of a Bayesian game