Saul I. Gass
Professor emeritus at the University of Maryland
After learning how to play the game tick-tack-toe, players typically discover a strategy of play that enables them to achieve at least a draw and potentially a win if the opponent makes a mistake. Sticking to that strategy ensures that the player will not lose. This illustrates the essential aspects of game theory.
Games with perfect information, such as tick-tack-toe, allow for the development of a pure strategy, an overall plan specifying moves to be taken in all eventualities that can arise. Games without perfect information (e.g. poker), however, offer a challenge because there is no pure strategy that ensures a win.
Players of games with imperfect information must then reconcile the questions: What is the optimal mix of strategies to play? How much do I expect to win?
Players must seek an equilibrium solution or a mixed set of strategies for each player, so that each player has no reason to deviate from that strategy, assuming all other players stick to their equilibrium strategy. This then creates the important generalization of a solution for game theory. All many-person non-cooperative finite strategy games have at least one equilibrium solution.
It is important to note, however, that for many competitive situations, game theory does not really solve the problem. Rather, game theory helps to illuminate the problem and offers players a different way of interpreting the competitive interactions and possible results. Game theory is a standard tool of analysis for professionals working the fields of operations research, economics, regulation, military, retail marketing, politics, conflict analysis, and many more.
Specific real-world situations include missile defense, sale price wars, NASCAR racing, military conflicts, conflict resolution, the stock market, telecommunications, elections and voting, and arbitration to name a few.