## Paradoxes of Rationality

## Overview

Since the theory of metagames is a thoroughly new development, built up from "classical" game theory, the author has taken great care to assess the soundness of its structural parts, proving all assertions and evoking a high degree of mathematical rigor and generality akin to that found in abstract set theory in pure mathematics. However, the aim of his work is to produce a technique that can be used to resolve real-life, real-time conflict situations and to investigate political and social interactions between decision makers. Such applications have in fact already been made, and the book contains, for example, an analysis of the Vietnam conflict.

The most primitive ideas of game theory—the extensive and normal forms, and the equilibrium point—are developed in such a way as to create a theory that is not purely formal and is in no way normative but rather is realistic, empirical, and experimental. Moreover, the approach is "nonquantitative." One reason is that numerical utilities usually cannot be estimated in a reliable manner in the real world. Another is that some of the most powerful methods developed by twentieth-century mathematics (those, for example, in topology, modern algebra, and set theory) are nonquantitative, and their application to social science, with its many "unmeasurables," is clearly appropriate and potentially of enormous value.

Other features of the approach are that it embraces both cooperative and noncooperative games simultaneously; it embraces both pure-strategy and mixed-strategy games; and it engages generally in *n*-person, variable-sum games, of which the common two-person, zero-sum game is only a special case.

Metagames are those "derived from a given game by allowing one of the players to choose his strategy (in the given game) after the others in knowledge of their choices." The theory has important comsequences regarding the nature of rational behavior, which is defined here as choosing alternatives that are most likely to achieve a given end. Indeed, the author proves several theorems that assert that in some cases to be rational is to be wrong, that irrationality is sometimes more effective, and, even, "that to be rational in two-person games is usually to be a sucker." He identifies three separate breakdowns of rationality. A consideration of "metarationality" leads to similar conclusions at that higher level of decision making.

Of special interest are the sections on the existentialist axiom, the free will argument, and the axiom of choice, and the paradoxes implicit in the use of these concepts.

Models based on metagame theory have been tentatively developed elsewhere to deal with urban transportation priorities, the New York school strike, and the Arab-Israeli conflict, as well as the Vietnam struggle.