Games

Computer science and logic Game theory has come to play an increasingly important role in logic and in computer science. Several logical theories have a basis in game semantics. In addition, computer scientists have used games to model interactive computations. Also, game theory provides a theoretical basis to the field of multi-agent systems. Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms, especially online algorithms. The emergence of the internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets....

General and applied uses As a method of applied mathematics, game theory has been used to study a wide variety of human and animal behaviors. It was initially developed in economics to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The first use of game-theoretic analysis was by Antoine Augustin Cournot in 1838 with his solution of the Cournot duopoly. The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well. Although pre-twentieth century naturalists such as Charles Darwin made game-theoretic kinds of statements, the use of game-theoretic analysis in biology began with Ronald Fisher's studies of animal behavior during the 1930s. This work predates the name "game theory", but it shares many important features with this field. The developments in economics were later ...

Representation of games The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome. (Eric Rasmusen refers to these four "essential elements" by the acronym "PAPI".) A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability. Most cooperative games are presented in the characteristic function form, while the extensive and the n...

Cooperative / Non-cooperative A game is cooperative if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is non-cooperative if players cannot form alliances or if all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory ,  which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structre, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs withi...

Cooperative / Non-cooperative A game is cooperative if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is non-cooperative if players cannot form alliances or if all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory ,  which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structre, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within ea...

Game classification Game classification is the classification of games, forming a game taxonomy. Many different methods of classifying games exist. Physical education There are four basic approaches to classifying the games used in physical education: Game categories This is a classification scheme proposed by Nicols, who classifies games according to three major categories: the game's physical requirements (i.e. what the game requires in addition to the players — equipment, size and nature of playing field, and so forth), the structure of the game (i.e. number of players, groupings of players, strategies, and so forth), and the game's personal requirements (i.e. what the game requires of the player — motor skills, fitness levels, numeracy, social skills, and so forth). Games for understanding This is a classification scheme proposed by Werner and Alomond that classifies games according to their strategies. It divides games into target games (e.g. archery); net ...

History of Games The first writer of history was Herodotus, an ancient Greek. He wrote a book called “The History” around 440 [four hundred and forty] BC, and that is more than 2,450 [two thousand four hundred and fifty] years ago. Herodotus tells us about king Atys; he ruled about 5,500 [five thousand five hundred] years ago in a country called Lydia. Today we call the country of king Atys Turkey, the western half closest to Greece. Atys had a serious problem; his lands had very little food because the climate was not good for agriculture. The people of Lydia demonstrated patience and hoped that the good times of plenty would return. But when things failed to get better, the people of Lydia thought up a strange solution for their problem. The path they took to fight their natural need to eat – the hungry times caused by the unusually hard climate - was to play games for one entire day so that they would not think about food. On the next day they would eat, so eat...