Answers to the odd-numbered problems and teaching notes for theclassroom games can be found via the Miscellaneous page.Varioussupplementary teaching materials are there too. If you would like the latex andpdf overheads I used in my class in Fall 2006, email me.
Games And Information: An Introduction To Game ...
A Game is a structured form of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool.[1] Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games).
Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching a chess championship. On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who is a player. A toy and a game are not the same. Toys generally allow for unrestricted play whereas games present rules for the player to follow.
Key components of games are goals, rules, challenge, and interaction. Games generally involve mental or physical stimulation, and often both. Many games help develop practical skills, serve as a form of exercise, or otherwise perform an educational, simulational, or psychological role.
Ludwig Wittgenstein was probably the first academic philosopher to address the definition of the word game. In his Philosophical Investigations,[5] Wittgenstein argued that the elements of games, such as play, rules, and competition, all fail to adequately define what games are. From this, Wittgenstein concluded that people apply the term game to a range of disparate human activities that bear to one another only what one might call family resemblances. As the following game definitions show, this conclusion was not a final one and today many philosophers, like Thomas Hurka, think that Wittgenstein was wrong and that Bernard Suits' definition is a good answer to the problem.[6]
Games are often classified by the components required to play them (e.g. miniatures, a ball, cards, a board and pieces, or a computer). In places where the use of leather is well-established, the ball has been a popular game piece throughout recorded history, resulting in a worldwide popularity of ball games such as rugby, basketball, soccer (football), cricket, tennis, and volleyball. Other tools are more idiosyncratic to a certain region. Many countries in Europe, for instance, have unique standard decks of playing cards. Other games such as chess may be traced primarily through the development and evolution of its game pieces.
Games are often characterized by their tools and rules. While rules are subject to variations and changes, enough change in the rules usually results in a "new" game. For instance, baseball can be played with "real" baseballs or with wiffleballs. However, if the players decide to play with only three bases, they are arguably playing a different game. There are exceptions to this in that some games deliberately involve the changing of their own rules, but even then there are often immutable meta-rules.
The rules of a game may be distinguished from its aims.[16][17] For most competitive games, the ultimate aim is winning: in this sense, checkmate is the aim of chess.[18] Common win conditions are being first to amass a certain quota of points or tokens (as in Settlers of Catan), having the greatest number of tokens at the end of the game (as in Monopoly), or some relationship of one's game tokens to those of one's opponent (as in chess's checkmate). There may also be intermediate aims, which are tasks that move a player toward winning. For instance, an intermediate aim in football is to score goals, because scoring goals will increase one's likelihood of winning the game, but isn't alone sufficient to win the game.
Games of skill include games of physical skill, such as wrestling, tug of war, hopscotch, target shooting, and stake, and games of mental skill such as checkers and chess. Games of strategy include checkers, chess, Go, arimaa, and tic-tac-toe, and often require special equipment to play them. Games of chance include gambling games (blackjack, Mahjong, roulette, etc.), as well as snakes and ladders and rock, paper, scissors; most require equipment such as cards or dice. However, most games contain two or all three of these elements. For example, American football and baseball involve both physical skill and strategy while tiddlywinks, poker, and Monopoly combine strategy and chance. Many card and board games combine all three; most trick-taking games involve mental skill, strategy, and an element of chance, as do many strategic board games such as Risk, Settlers of Catan, and Carcassonne.
Most games require multiple players. However, single-player games are unique in respect to the type of challenges a player faces. Unlike a game with multiple players competing with or against each other to reach the game's goal, a one-player game is a battle solely against an element of the environment (an artificial opponent), against one's own skills, against time, or against chance. Playing with a yo-yo or playing tennis against a wall is not generally recognized as playing a game due to the lack of any formidable opposition. Many games described as "single-player" may be termed actually puzzles or recreations.
John Nash proved that games with several players have a stable solution provided that coalitions between players are disallowed. Nash won the Nobel prize for economics for this important result which extended von Neumann's theory of zero-sum games. Nash's stable solution is known as the Nash equilibrium.[20]
If cooperation between players is allowed, then the game becomes more complex; many concepts have been developed to analyze such games. While these have had some partial success in the fields of economics, politics and conflict, no good general theory has yet been developed.[20]
In quantum game theory, it has been found that the introduction of quantum information into multiplayer games allows a new type of equilibrium strategy not found in traditional games. The entanglement of player's choices can have the effect of a contract by preventing players from profiting from what is known as betrayal.[21]
Popular sports may have spectators who are entertained just by watching games. A community will often align itself with a local sports team that supposedly represents it (even if the team or most of its players only recently moved in); they often align themselves against their opponents or have traditional rivalries. The concept of fandom began with sports fans.
Lawn games are outdoor games that can be played on a lawn; an area of mowed grass (or alternately, on graded soil) generally smaller than a sports field (pitch). Variations of many games that are traditionally played on a sports field are marketed as "lawn games" for home use in a front or back yard. Common lawn games include horseshoes, sholf, croquet, bocce, and lawn bowls.
A tabletop game is a game where the elements of play are confined to a small area and require little physical exertion, usually simply placing, picking up and moving game pieces. Most of these games are played at a table around which the players are seated and on which the game's elements are located. However, many games falling into this category, particularly party games, are more free-form in their play and can involve physical activity such as mime. Still, these games do not require a large area in which to play them, large amounts of strength or stamina, or specialized equipment other than what comes in a box.
This class of games includes any game in which the skill element involved relates to manual dexterity or hand-eye coordination, but excludes the class of video games (see below). Games such as jacks, paper football, and Jenga require only very portable or improvised equipment and can be played on any flat level surface, while other examples, such as pinball, billiards, air hockey, foosball, and table hockey require specialized tables or other self-contained modules on which the game is played. The advent of home video game systems largely replaced some of these, such as table hockey, however air hockey, billiards, pinball and foosball remain popular fixtures in private and public game rooms. These games and others, as they require reflexes and coordination, are generally performed more poorly by intoxicated persons but are unlikely to result in injury because of this; as such the games are popular as drinking games. In addition, dedicated drinking games such as quarters and beer pong also involve physical coordination and are popular for similar reasons.
Board games use as a central tool a board on which the players' status, resources, and progress are tracked using physical tokens. Many also involve dice or cards. Most games that simulate war are board games (though a large number of video games have been created to simulate strategic combat), and the board may be a map on which the players' tokens move. Virtually all board games involve "turn-based" play; one player contemplates and then makes a move, then the next player does the same, and a player can only act on their turn. This is opposed to "real-time" play as is found in some card games, most sports and most video games.
Some games, such as chess and Go, are entirely deterministic, relying only on the strategy element for their interest. Such games are usually described as having "perfect information"; the only unknown is the exact thought processes of one's opponent, not the outcome of any unknown event inherent in the game (such as a card draw or die roll). Children's games, on the other hand, tend to be very luck-based, with games such as Candy Land and Chutes and Ladders having virtually no decisions to be made. By some definitions, such as that by Greg Costikyan, they are not games since there are no decisions to make which affect the outcome.[22] Many other games involving a high degree of luck do not allow direct attacks between opponents; the random event simply determines a gain or loss in the standing of the current player within the game, which is independent of any other player; the "game" then is actually a "race" by definitions such as Crawford's.
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