Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann.Von Neumann's original proof used Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players.
This theory was developed extensively in the 1950s by many scholars.
Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s.
Game theory has been widely recognized as an important tool in many fields.
With the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole in 2014, eleven game-theorists have now won the economics Nobel Prize.
John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.
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.
Des Hague, the former CEO who was caught on video kicking a puppy in a Vancouver hotel elevator, has been fined ,000 and banned from owning or controlling an animal for three years. Hague pleaded guilty to animal cruelty in February. A veterinarian found the Doberman pup was not injured, according to Hague's lawyer.