Investigate which definition of the Pareto order is used in some leading texts, such as Kreps (1990), Mas-Colell et al. (1995), Varian (1992), and Osborne and Rubinstein (1994).
Even if all the constituent orders ≿i are complete, the Pareto order ≿P is only a partial order. Where x ≻i y for some i while x ≻i y for others, x and y are not comparable. This deficiency provides scope for two fertile areas of economic analysis, social choice theory and game theory. Since they also provide good illustrations for the material of this book, we briefly describe each of these areas.