ABSTRACT

It was noted before that there are far reaching implications for the structure of social interaction as the number of players increases from n = 2 to n = 3. There are also changes in the form of social interaction associated with a further increase in the number of players from n = 3 to n ≥ 4. When n = 3, the only way to disrupt a 2-person coalition is to entice one of its members into another 2-person coalition. But when n ≥ 4, the alternative coalitions to a 2-person or 3-person coalition may vary in size, and may not even require the cooperation of any of the original coalition members. With the increase in n, coordination among the players becomes an issue worth investigation, and coalition size becomes a variable that may play a role in theory. A major consequence of the shift from n = 3 to n ≥ 4, which has interesting implications for experimental design and theory, concerns the number of multiperson coalitions within some coalition structure. When n = 3, each coalition structure may include at most one multiperson coalition. But when n ≥ 4, a coalition structure may include two or more multiperson coalitions, e.g., {AC,BD}, and the process of forming these coalitions–whether simultaneously or sequentially–must be addressed by experimentalists and theoreticians.