Two-Person Game Theory: What Does It Mean?
Game theory is a branch of mathematics which has been explored fairly recently within the century. It is not completely a mathematical science, however. Instead, it dictates what factors comprise strategies. It is to games of strategy what probability is to games of chance. Consequently, a game such as Magic, which relies on both strategy and chance, has both game theory and probability applications.
Most often instead of determining the best possible strategy, game theory only exists to determine the existence of a best possible strategy. Most games are too complex to be charted to the point where a best possible strategy can be determined. That is what makes game theory a mostly theoretical area of study. Nevertheless, the ideas presented in game theory are useful in outlining what the best decision making techniques are in certain situations.
There are several branches and classifications of game theory. A "game" can be one player, two players, or N-players, where N is a positive integer greater than two. There are games of perfect information where all game data is presented to all players, such as in chess, tic-tac-toe, and Monopoly. Then there are games of imperfect information where each player does not get to see all the game data. Magic and poker fall into this category, as there is an element of chance. However, there is not always chance in a game of imperfect information. For instance, take Stratego, a popular board game in which each of the two players arrange forty pieces on their side of an eight-by-eight grid, with each piece's rank facing only himself. Each player does not see the other player's pieces' ranks. Because this information is withheld from the other player, Stratego is a two-player game of imperfect information.
Additionally, a game such as Stratego is classified is a zero-sum game. A zero-sum game is one where all payoffs add up to zero. In this instance, a loss is simply a negative win, which when added together, combine to zero. Poker is also a zero-sum game. Even when not played for money or some stakes, there be one clear winner in poker. When played with N-players a loss can simply be accounted for as a negative fraction of a win (i.e. -1/2 if there are three players, because two losses and one win add up to 0). When played for stakes, the total money a player earns is equal in magnitude and opposite in sign to the money the other players lose. All the money totaled will always equal the same amount, and the total change in money won between all the players combined will always add up to zero. Therefore poker is an N-player zero-sum game of imperfect information.
A non-zero-sum game can be more of a real-life application, where negotiation helps two people both succeed. Remember that the definition of "game" in game theory is quite different than we perceive it. Any situation with two or more people requiring decision making can be classified as a game. Perhaps two people, each independently in business, want to open a chain fast food restaurant in the same town, both of which serve similar items. If they compete, one may strike it rich and the other may go broke. If they work together, they will both do sufficiently but neither will be exceptionally rich. The decisions the two people make can be described in detail by using basic game theory concepts.