1 Social Interactions Steven

In these notes I define and explore some implications of complementarities between choices and complementarities between characteristics for a group of individuals. Complementarity is a fundamental concept in the social interactions literature because it characterizes how the attributes of one individual affect others. An important distinction will turn out to involve the way that one person is affected by the choices of others versus the way that one person is affected by the characteristics of others. The difference between choices and characteristics is that the latter are treated as predetermined when considering the equilibrium of a given environment. Consider a group of I individuals. Each individual is associated with vector of attributes i x . The attributes are assumed to common across agents; this is without loss of generality since one can take the union of a set of attributes and define this as the common attribute set. At this stage, the attributes may be choices, characteristics, or some combination of each; ia x denotes an element of i x . Each vector of attributes produces a payoff