“Zero-player games are essentially ‘physics’ or any of the hard sciences – nature abides by its own axioms, not those Axioms we define as ‘economic rationality’.
One-player games can be thought of as optimization programs, where a single player is tuning a process to a goal he controls, with parameters he defines.
Two or more players form a game we restrict with the Axioms of Rationality. We require more than the “natural order” because we seek to describe movements through state-spaces defined by mathematical rules. Those state-space descriptions are given in the language of payouts weighted by probabilities – so-called “expectations” – as well as number of rounds and players.”