Short answers, pulled from the story.
A game is an activity defined by a challenge and a set of rules, typically done for enjoyment, competition, or development. Scholars have long debated the essence of games, and no single definition has achieved universal acceptance.
The Royal Game of Ur and Senet are among the oldest known games, dating back to at least 2600 BCE. The Royal Game of Ur came from ancient Mesopotamia around 2600 BCE, and Senet was played in ancient Egypt with board fragments found from approximately 3100 BCE.
Ludwig Wittgenstein argued in his Philosophical Investigations that elements such as play, rules, and competition all fail to adequately define games. He concluded that people apply the term game to disparate activities that share only what he called family resemblances.
Dungeons and Dragons was the first role-playing game, created by Gary Gygax and Dave Arneson in 1974. Players enact fictional characters while a dungeon master adjudicates situations the rules do not cover.
John Nash proved that games with several players have a stable solution provided that coalitions between players are disallowed. He won the Nobel Prize for economics for this result, which extended von Neumann's theory of zero-sum games and became known as the Nash equilibrium.
Flow is a state of intense concentration and total immersion named by Mihaly Csikszentmihalyi, which boosts life satisfaction. Games help players reach flow by offering clear goals, immediate feedback, and a balance between challenge and skill.