James Carse wrote a little book in 1987, Finite and Infinite Games. It is an interesting combination of ideas: a loose concept of "game" is applied to the dialectic of the finite and the infinite, and the outcome is a secular theology that can be applied to culture, language, religion, art, and so on. At its core is the idea of internal freedom: Players cannot play if they don't play freely.
See also Wittgenstein's reflections on games, and a talk by James Carse on religious wars.
(Source: Carse, J. P. (1987). Finite and Infinite Games: A Vision of Life as Play and Possibility. Ballantine Books.)
A game is defined by its rules. In a finite game, the rules are designed for the purpose to have a winner, therefore to end the game. In an infinite game, the purpose is to play the game, therefore continue to play.
You know what the game is by knowing the rules. Rules in a finite game are the terms by which the players agree who has won. Rules are valid because the players agree to them. There is no rule that require us to obey the rules. (Saul Kripke on Wittgenstein.)
In a finite game, the players have to agree who won. Since there is a clear end, there must also be a clear beginning. The boundaries for finite games are externally defined.
Players have to play freely, or else it is not a game. Whoever must play, cannot play. This is the only commonality between finite and infinite games.
Infinite games have no boundaries: time is created within the game itself. One cannot say how long an infinite game has been played, because it generates its own time.
Finite games can be played within an infinite game, but an infinite game cannot be played within a finite game.
If the rules change in a finite game, it becomes a different game. In an infinite game, rules protect the continuation of the game. The task is to design rules that allow the continuation of the game even when death is one of the limits. Limits are taken into play, therefore the play cannot be limited. Finite players play within boundaries, infinite players play with boundaries.
Can we acknowledge that we have chosen to face the world through a mask? (p.13)
The finite game is for an audience, therefore theatrical. Infinite players keep the future open, avoid any particular outcome, therefore their play is dramatic. (p.16.)
What one wins in a finite game is a title. (p.19). Death is giving up the attempt to win a title, the triumph of the past over the future.
There is either “death in life” the refusal to compete further, or “life in death”. Your titles supersede your life. This is the maximum gain in finite games.
If live is a finite game, death is always a defeat. The dead are also losers. Life, then, is the prize for winning. Finite players therefore compete for life, and don’t live yet.
Contradiction: All finite play is play against itself.
Infinite players die in the course of play. Infinite games are inherently paradoxical. The players play for others. An infinite game only works when others continue to play.
Culture is an example of an infinite game.