Overview

The theory of moves (TOM) brings a dynamic dimension to the classical theory of games, which its founders characterized as “thoroughly static” (von Neumann and Morgenstern, 1944; 3rd edn, 1953, p. 44). I illustrate this dimension with two games in section 2 of this Introduction, which distinguish TOM not only from classical game theory but also from modern approaches to the study of game dynamics that use the past to explain or predict the unfolding of the future.

By postulating that players think ahead not just to the immediate consequences of making moves but also to the consequences of counter-moves to these moves, counter–countermoves, and so on, TOM extends strategic thinking into the more distant future than most other dynamic theories do. By elucidating the rational flow of moves over time, it facilitates the dynamic analysis of conflicts in which thoughtful and intelligent (but not superintelligent!) players, with at least some degree of foresight, might find themselves engaged. The theory has a number of features worth noting at the outset.

Tractability

To keep the analysis tractable, I concentrate on two-person games in which each player has only two strategies and can strictly rank the resulting four outcomes from best to worst. There are exactly 78 such “strict ordinal” 2 × 2 games – so called because the players order the outcomes but do not attach cardinal utilities to them – but I focus on the 57 “conflict games” in which there is no mutually best outcome.