Steven Brams' Theory of Moves is a fascinating publication that supplies qualitative and quantitative mathematical models used to explain the merits and deficiencies in the logic of hypothetical and anecdotal decisions of various types (economic, political, social, etc.).
Brams intermittently isolates two-party conflicts and highlights each conceivable resolution by using a 2x2 matrix that gives a variety of possibilities provided in ordered pair combinations, where the numbers range from a 1, which translates to a worst case scenario for the party concerned, to a 4, which is the best possible outcome. For instance, a (1,4) would be interpreted as a two-party game where the deciding party, who receives a 1, ends up with the theoretically worst possible outcome, leaving the opponent, which receives a 4, with the best. As another case, a (3,2) would be read as a pairing where the 3 represents a next-to-best outcome for the decision making party, whereas the 2, on the other hand, would be the next-to-worst outcome for the opponent.
Brams looks at various situations, comparing and contrasting, for instance, the fictional works of Sir Arthur Conan Doyle, whose most famous character, the detective Sherlock Holmes, always comes out one step ahead of his arch nemesis, with those that display what is referred to as the Minimax Theorem, which espouses that "[i]n a two-person constant-sum game,[it] guarantees that each player can ensure at least a certain expected value, called the value of the game, that does not depend on the strategy choice of the other player". Among the works in this latter category is William Faulkner's Light in August, where a chase scene is partially deconstructed by Brams in such a way that argues that, unlike Doyle, whose protagonist is portrayed as a character with computational abilities that are superior to those of the antagonist, who never, in turn, makes the necessary adjustments to place himself or herself at an unequivocally victorious stage, Faulkner understood the mixed strategies involved in a two-person sum game where, perhaps, a decision made by the inferior might have the silver bullet effect to overcome the superior.
As a relevant case that might be brought forth, sports analysts paid special attention to the selection of players for the 1980 U.S. Olympic hockey team. After the best American players, even at the top of the National Hockey League, had previously been beaten by the Soviets time and again, the hopes of ever defeating Russia, especially in 1980, were dim. What transpired to be the Miracle on Ice was regarded by sports historians as essentially this. Though decision making officials were inclined to put together what were deemed the very best of the best, the U.S. coach used, as I recall, a counterintuitive approach by forming a team that largely consisted of players with, perhaps, less talent than the hockey elite but, nonetheless, an overall determination to win which could not be denied. In other words, the U.S. probably did not have its best team that day, but it had, more importantly, the right team.
Throughout Theory of Moves, Brams portrays various situations where diplomacy and compromise are the appropriate, realistic approaches to dealing with an opponent. For instance, if the outcome is ideologically next-to-best, it might, in reality terms, be the applicable best, especially in cases where the opponent has interests that run counter to those of the decision maker. In those particular scenes, Brams provides further outlets of analyses, expounding upon where it is not worth pursuing the attainment or maintenance of the best possible state; in discussion, Brams introduces us to magnanimity, which is a transfer of moving from what was the best possible state to the next-best possible. Magnanimity, according to Brams, is essential, especially if what was regarded as the best possible situation devolves into a worst case Status Quo, where the opposing party, over time, grows resentful and decides to rise up in hostile action.
What have been provided in these few paragraphs are only a handful of terms that Brams gives in these roughly 215 pages, for there are so many angles for the reader to look upon. In fact, the information and explanations are so thorough and detailed that once a person gains a more refined appreciation or understanding of the decision making powers or adjustments necessary for optimal outcome in game theory, he or she can apply it in life, especially when making personal decisions and effectively dealing with the dilemma that we often put 80% of our energies into what amounts to only 20% of what is really of immediate importance.
Theory of Moves is a definite must have. Quite a bit of the language is technical, but there is enough induction applied where one can draw enough analogies and parallels to what is discussed so as to relate to the points that Brams is getting across.