Assignment games, chromatic number, and exchange theory

The exchange networks that social psychologists have studied can usefully be represented as game theoretic 2‐sided assignment games. Conceiving of these networks as 2‐sided assignment games opens up the possibility of studying N‐sided assignment games and games without cores. 2‐sided assignment games are special in that they always have cores, stable solutions in which every individual and subgroup behave rationally.

The implicit assignment of positions to categories of an N‐sided assignment game is related to coloring a graph. The color classes form sets of positions with potentially related interests. Color equivalence is compared to structural, regular, automorphic, and ecological positional equivalence.