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"To become a player, one must voluntarily accept the rules and constraints of a game." 
Players in competition
In most games, one player (or team) is declared the winner, the player who performed the best. Some multiplayer games can have multiple winners, but in Western societies, one player (or team) is normally considered to be the "1st place", or best, among them, and tie-breaking structures are commonly used to ensure a singular "1st place". This is not true universally, however; for example, in Japan, ties are considered to be wins for both sides. Some games use multiple means of scoring or determining the conditions of victory; in these games, it may be possible for two or more players or teams to simultaneously win, which, depending on the game, may be counted as wins for both or simply a tie.
Among the players on a team, the one who plays the best in a given contest may be deemed the player or over the course of a series or season may be deemed the most valuable player for that period. They may also be identified as a player of the Match, player of the week, player of the month, player of the year, or even player of the century.
Player Interaction Patterns
Single Player vs the Game
In this type of pattern the player competes against a game system. Examples of this are Solitaire and Pac-Man. To get a feeling of challenge and entertainment usually there are puzzles or play structures to create conflict such as AI enemies.
Multiple Individual Players vs the Game
Multiple players compete against the game system, but there is no need for the players to interact with each others. An example of this is the game Bingo, in which a player do not interat with the rest, but all compete against the game. The players in Bingo do not need to compete against other players.
Player vs Player
It is a competitive structure in which two players compete against each other. By the nature of the structure, it is also a personal contest and it is usually related to strategy games. Chess is a perfect example of this structure.
In this structure, two or more players compete against a single player. Some examples are Tag, Hide and seek, Marco Polo, among others.
It is a direct competition between three or more players. This structure is also known as "multiplayer". Examples range from card games like Poker, up to video games like Age of Mythology.
This is a structure in which the players join forces in order to beat the game system.
In this structure, two or more teams compete against each other. Sports like American Football, Basketball, Baseball, Soccer, among others.
- Fullerton (2008). Game Design Workshop: A Playcentric Approach To Creating Innovative Games (PDF). Elsevier.