ABSTRACT
From a theoretical point of view, the simplest decision problems are one-person games in which a solitary player tries to obtain as high a payoff as possible or, if the game involves an element of risk, as high an expected (statistically average) payoff as possible. The involvement of a second player whose choices also affect the outcome leads to new and qualitatively different problems. In a two-person game, strategic problems that cannot be reduced to simple payoff maximization arise and, depending on the payoff structure, the players may be motivated to coordinate, to compete, or to strike a suitable balance between coordination and competition. A further quantum leap in strategic complexity arises in games involving three or more players, which are called multi-person or n-person games. Georg Simmel, the turn-of-the-century German sociologist and philosopher, was apparently the first to point out an important phenomenon that emerges when the transition is made from two-person groups (dyads) to three-person or larger groups: “The essential point is that within a dyad, there can be no majority that could outvote the individual. This majority, however, is made possible by the mere addition of a third member” (quoted in Luce and Raiffa, 1957, p. 155).
