Review of Steven J. Brams : Game Theory and the Humanities. (2011). The MIT
Press. 336 pages
Let’s have a game of 2 players of which both have 2 strategies. While it is almost
impossible to imagine a situation which would seem more simple than such a game with
2x2=4 possible outcomes, the whole thing gets much more complex when one realizes that
even under assumption that both players do not attribute to diverse outcomes some absolute
cardinal utilities but only four simple mutually relative ordinal ranks (i.e. 1: worst outcome,
2: next-worst, 3:next-best and 4: best outcome), there exist a variety of 78 diverse 2x2
« games » for players with different preferences.
Steven J. Brams’ « Game Theory and the Humanities – Bridging Two Worlds» offers
concrete historical or fictious examples of more than a dozen of such games. Starting with
interpretation of Abrahams’ son-sacrifying dilemma as a possibly intrapsychic game which
the old shepherd played with a somewhat sadic god character; continuing through intricacies
of Pascal’s wager towards more mundane games played between Nixon and Supreme Court
after the Watergate crisis or the game played between Khomeini & Carter during 1979 Iran
hostage crisis ; and ending with the famous Catch-22 case between Yossarian and the war
machinery – almost everywhere in his book Brams makes a non-negligeable step in
direction of unification of law, history, politology, litterary critics or even theology under the
mathematically sound clef de voute offered by the game theory.
Such an act in itself would be worthy of praise but luckily for science, Brams goes much
further. Introduction of a Theory of Moves framework allows him to extend the classical
notion of Nash equilibrium into a notion of a « nonmyopic equilibrium » which takes into
account the players’ faculty of «anticipating all possible rational moves and countermoves
from the initial state ». Structural similarities among Shakespeare’s MacBeth or
Aristophanes’ Λυσιστράτη are subsumed into a generic category of (Self-)Frustration games
while other concrete instances of 2x2 conflicts (e.g. the American Civil War) are presented
in order to illustrate other generic categories like « Magnanimity games » or « King-on-themountain games ».
Topics like deception, games where some players have incomplete or false information,
rationality of emotions or the « paradox of omniscience » demonstrating that « in certain
games it is more advantageous not to know everything than the contrary » are introduced
with erudition of a scholar with almost half-century of practice in the field. To summarize:
the interdisciplinary paradigm presented in the glossary, appendix, 11 chapters, and 35
figures of Brams’ book is not only intellectually pleasing but could also furnish practically
exploitable insights for experts in domains as distant as comparative mythology,
evolutionary psychology, roboethics, or - if the Turing Test can be collapsed into a 2x2
game – even in the domain of hard-core AI.
Written in 2013 for the quarterly of Artificial Intelligence and Simulated Behaviour Society (AISB).
Daniel Devatman Hromada is a double PhD candidate of Slovak Technical University (dpt. of
cybernetics) and Université Paris 8 (dpt. of cognitive psychology).