In particular, the simple scenario of zero-sum games is extended to cover a large variety of non-zero-sum games
, and concepts of algorithmic game theory are generalised to infinite-duration games.
He describes the history of probability theory, the basic laws of probability, the definition and applications of mathematical expectation/expected value, and unexpected results related to mathematical expectation, such as the roles of aversion and risk in rational decision making in areas like gambling, purchasing insurance, and airline overbooking; envelope problems; Parrondo's paradox (how negative expectations can be combined to give a winning result); problems associated with imperfect recall; non-zero-sum games
like the prisoner's dilemma and the game of chicken; Newcomb's paradox relating to free will; and Benford's law and its use in computer design and fraud detection.
Evolution has steered us in a direction whereby we are naturally inclined to be cooperative to capture the riches of non-zero-sum games
There is also new material on sensitivity analysis for the two-variable problem, and Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games
To study such behavior, that is, to capture the competitive and cooperative elements that are observed when people interact, non-zero-sum games are required.
Nash used the term "noncooperative" to describe his approach: Although in non-zero-sum games there may be gains from cooperation, Nash assumed it is "impossible for players to communicate or collaborate in any way.
In this way, Nash's result extended and generalized von Neumann's result to non-zero-sum games with potentially many players.
Just as natural selection favors certain genes over others, leading to the triumph of our large-brained species, its equivalent in history favors non-zero-sum games
that lead to greater prosperity and social interdependence.
What quickly emerges from a study of these kinds of games is that winning a non-zero-sum game
really translates into getting the best outcome rather than defeating all opponents.