Game theory Game theory In mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different players who need runways of different lengths. The problem was introduced by S. C. Littlechild and G. Owen in 1973. ...more on Wikipedia about "Airport problem"
The Angel problem is a question in game theory proposed by John Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2D lattice). The angel has power (a natural number 1 or greater). The chessboard starts empty with the angel at the origin. On each turn, the angel jumps to a different empty square at most squares away, that is, a square which could be reached by at most moves of a chess king. (The distance from the starting square is at most in the infinity norm). The devil, on his turn, may add a block on any square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is unable to move. The angel wins by surviving indefinitely. ...more on Wikipedia about "Angel problem"
Assured destruction is a concept sometimes used in game theory and similar discussions to describe a condition where certain behaviors or choices are deterred because they will lead to the imposition by others of overwhelming punitive consequences. ...more on Wikipedia about "Assured destruction"
In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. ...more on Wikipedia about "Axiom of projective determinacy"
In game theory, backward induction is one of dynamic programming algorithms used to compute subgame perfect equilibria in sequential games. The process proceeds by first looking at the last possible action, determine what the last player will do in each situation (i.e. information set). Using this information, one can then determine what the second to last player will do. This process continues until one determines all possible actions. ...more on Wikipedia about "Backward induction"
In mathematics, in particular in general topology and set theory, a Banach- Mazur game is a game played between two players, trying to pin down elements in a set (space). The concept of a Banach-Mazur game is closely related to the concept of Baire spaces. ...more on Wikipedia about "Banach-Mazur game"
In mathematical sociology, and especially game theory, the bankruptcy problem is a distribution problem involving the allocation of a given amount of a perfectly divisible good among a group of agents. The focus is on the case where the amount is insufficient to satisfy all their demands. ...more on Wikipedia about "Bankruptcy problem"
The Battle of the Sexes is a two player game used in game theory. Imagine a couple, Kelly and Chris. Kelly would most of all like to go to the football game. Chris would like to go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate where should they go? ...more on Wikipedia about "Battle of the sexes (game theory)"
In game theory, a Bayesian game is one in which information about characteristics of the other players (i.e. payoffs) is incomplete. Following John C. Harsanyi's framework, a Bayesian game can be modelled by introducing Nature as a player in a game. Nature assigns a random variable to each player which could take values of types for each player and associating probabilities or a probability density function with those types (in the course of the game, nature randomly chooses a type for each player according to the probability distribution across each player's type space). Harsanyi's approach to modelling a Bayesian game in such a way allows game of incomplete information to become games of imperfect information (in which the history of the game is not available to all players). The type of a player determines that player's payoff function and the probability associated with the type is the probability that the player for whom the type is specified is that type. In a Bayesian game, the incompleteness of information means that at least one player is unsure of the type (and so the payoff function) of another player. ...more on Wikipedia about "Bayesian game"
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822-1900). Specifically, it is a model of price competition between duopoly firms which results in each charging the price that would be charged under perfect competition, known as marginal cost pricing. ...more on Wikipedia about "Bertrand competition"
In economics, the Bertrand paradox describes a situation in which two players reaching a state of Nash equilibrium find themselves with no profits. ...more on Wikipedia about "Bertrand paradox (economics)"
In game theory, the best response is the strategy (or strategies) in a single period that creates the most favorable immediate outcome for the current player, taking other players' strategies as given. The concept of a best response is central to John Nash's most well-known theory, the Nash equilibrium which is dependent on each player selecting the best response during each period. ...more on Wikipedia about "Best response"
In game theory, the Bishop-Cannings theorem proves that all members of a mixed evolutionarily stable strategy have the same payoff, and that none of these can also be a pure evolutionarily stable strategy. ...more on Wikipedia about "Bishop-Cannings theorem"
(Bounded rationality) Many economics models assume that people are hyperrational, and would never do anything to violate their preferences. ...more on Wikipedia about "Bounded rationality"
In computing, tree data structures, and game theory, the branching factor is the number of children of each node. If this value is not uniform, an average branching factor can be calculated. ...more on Wikipedia about "Branching factor"
In mathematics and game theory, Bulgarian solitaire is a random card game. ...more on Wikipedia about "Bulgarian solitaire"
In game theory, the centipede game is an extensive form game in which two players take turns choosing either to take a slightly larger share of a slowly increasing pot, or to pass the pot to the other player. The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes the pot, one receives slightly less than if one had taken the pot. Although the original centipede game had a limit of 100 rounds (hence the name), any game with this structure but a different number of rounds is called a centipede game. The unique Nash equilibrium of these games is for the first player to take the pot on the very first round of the game; however in empirical tests relatively few players do so. ...more on Wikipedia about "Centipede game"
Cheap talk is a term used in game theory for pre-play communication which carries no cost. For example, in the Prisoner's Dilemma one might add a round of pre-play communication where each player announces the action they intend to take (or alternatively the action they would like the other to take). In the Prisoner's dilemma cheap talk is not expected to have any effect (for an exception see Robson 1990). In other games Cheap Talk does have a demonstrated effect on play. ...more on Wikipedia about "Cheap talk"
In the study of economics, collusion takes place within an industry when rival companies cooperate for their mutual benefit. Collusion most often takes place within the market form of oligopoly, where the decision of a few firms to collude can significantly impact the market as a whole. Cartels are a special case of explicit collusion. Overt collusion, on the other hand, also known as tacit collusion. ...more on Wikipedia about "Collusion"
Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. ...more on Wikipedia about "Common knowledge"
Complete information is a term used in economics and game theory to describe an economic situation or game in which knowledge about other market participants or players is available to all participants. Every player knows the payoffs and strategies available to other players. ...more on Wikipedia about "Complete information"
In evolutionary game theory, complete mixing refers to an assumption about the type of interactions that occur between individual organisms. Interactions between individuals in a population attains complete mixing if and only if the probably individual x interacts with individual y is equal for all y. ...more on Wikipedia about "Complete mixing"
A contingent cooperator is a person or agent who is willing to act in the collective interest, rather than his short-term selfish interest, if he observes a majority of the other agents in the collective doing the same. The apparent contradiction in this stance is resolved by game theory, which shows that in the right circumstances, cooperation with a sufficient number of other participants will have a better outcome for cooperators than pursuing short-term selfish interests. ...more on Wikipedia about "Contingent cooperator"
A cooperative game is a game where groups of players ("coalitions") may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. ...more on Wikipedia about "Cooperative game"
The coordination game is a classic (symmetric) two player, two strategy game, with payoff matrix as follows: ...more on Wikipedia about "Coordination game"
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