A great deal of thought by many clever people has gone into answering this question. Since I disagree with most of the contents of the answers, I am going to attempt my own definition, foolhardy though the attempt may be.
A game is an activity performed within a closed formal system arising from at least one rule and performed by at least one player-character.
Player-characters are semantically distinct from players. For instance, chess is a game that requires two player-characters; that is, two distinct powers that compete with one another. A single player may play a game of chess by controlling both player-characters. Similarly, two players may cooperate to control a single player-character in a game, if they so choose.
Rules structure games. There are many ways to talk abut rules and many ways to divide them. I will be dividing them rather a lot in this article, as I believe that various divisions can teach us different things about the nature of rules. For instance, all rules fall into at least one of these three categories: descriptive, elective and prescriptive.
- Descriptive rules offer no choices to the players, nor indicate who is winning. Rather, they do everything else: structure turns and rounds, describe what various game objects do, trigger the orders of events that occur when player-characters take actions, etc.
- Elective rules offer choices to players, where the results of each choice is accounted for in the closed formal system.
- Prescriptive rules determine what actions and/or events confer value upon a player-character, be that a win condition, victory points, drinks to give out, etc.
A number of previous definitions of games have included win and/or lose conditions. I believe that this is not only misguided (Minecraft has no win or lose condition, for instance), but redundant, since the inclusion of rules in a definition already allows for the possibility of win and lose conditions.
Although my definition does not include materials, the vast majority of games do require them. Depending on how materials is defined, it is arguable that materials are also essential to game playing. For instance, if hands are counted as a material object, Rock Paper Scissors requires materials to be played. However, even with the strictest definition of materials in place, the game known as The Game can still be played with only one rule and one player. The rule is ‘if you think about the game, you lose the game’. Arguing that a material- a mind- is required to play The Game, involves including players as materials. In this case, the only requirements for games are rules and materials. I prefer to distinguish players from materials.
Now that we’ve talked about what games and rules are, lets look at some more ways of dividing rules into types. I have categorized rules by function and employed established terms to do so. I’ve further categorized these functions temporally and meta-structurally.
I’ll now briefly elaborate on each rule category and provide an example from Uwe Rosenberg’s rules for Agricola.
Material: defines the types and numbers of materials that are required to play the game. Descriptive.
Example: Agricola requires a large flat surface and all of its board game components, including its board, cards and various cardboard and wood chits.
Player Capacity: describes the number of player-characters the game is intended to support. Descriptive.
Example: Agricola supports 2-5 player characters
Pre/Post-Round: describes all board preparations and material arrangements which occur between turns.Descriptive and/or prescriptive.
Example: Pre-round, Agricola requires certain board spaces to receive goods turns and for a new round card to be revealed. Post-round, players are to remove their meeples from the board, and when a harvest phase is occurring, exchange goods in a prescribed fashion.
Round: sets the bounds for turn structures within a round. Within each round, any elective rules will be contained within a turn structure. Any descriptive rules will be part of the Pre/Post-Round and/or Structural rules. It should be noted that, while I am drawing on frequently used game terminology, these definitions may be and often are distinct from in-game terminological uses. Descriptive, prescriptive and/or elective.
Example: In Agricola, rounds consist of players taking their turns in a circular order starting with the person in possession of the starting player marker until all players may no longer take a turn.
Player-Bounding: sets the bounds for what players can and cannot do (usually, but not always) during their turn.Elective and/or prescriptive.
Example: During a Agricola player’s turn they must place one of their workers on a revealed and non-occupied gameboard space.
Object-Bounding: sets the bounds for each non-player object in the game. Descriptive and/or prescriptive.
Example: A fireplace, if possessed by a player, may convert goods to food at a specified rate at any time when activated by said player.
End Condition: describes all in-game conditions that will end a game. Descriptive.
Example: Agricola ends after the 14th round.
Victory/Draw/Defeat Condition: assigns a victory/draw/defeat condition to all players for each possible end condition. End conditions may trigger victory/draw/defeat conditions, or vice versa. Prescriptive.
Example: At the end of the game, the winner of Agricola is the player with the most victory points.
Clarifying: resolve ambiguous situations that arise due to implications of other rules. Descriptive, prescriptive and/or elective.
Example: Agricola clarifies that animals can never exceed the pasture limit, but that animals may be immediately converted to food rather than discarded when the pasture limit is exceeded, if food conversion is possible.
Implied: rules that are not stated outright, yet heavily implied by the structure and materials of a game. Descriptive, prescriptive and/or elective.
Example: It is implied in Agricola but not stated that players cannot build on other player’s farm boards.
Adjunct: alters and/or adds rules to any of the previous rule categories not stated in the basic game rules.Descriptive, prescriptive and/or elective.
Example: Agricola’s Farmers of the Moor expansion adds a number of adjunct rules, as well as materials, to the basic game.
Structural: governs changes to larger scale events. Examples: alterations in materials, round structures, etc.Descriptive and/or prescriptive.
Example: The timing and rules governing Agricola’s Harvests, which trigger sporadically between rounds.
Temporal categorization parameters:
Establishing: define the basic parameters required to initiate a game.
Central: define the parameters through which a game is defined and played.
Concluding: define the descriptive and/or prescriptive rules associated with the end of the game.
Meta-structural categorization parameters:
Rules: govern interactions between the players and/or objects.
Meta-Rules: govern interactions between rules.
Did I miss something or does something not make sense? Let me know! If you want to read more, my game design analysis blog is here- http://www.zamagame.com)