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Uncorrelated Asymmetry
In game theory an uncorrelated asymmetry is an arbitrary asymmetry in a game which is otherwise symmetrical. The name 'uncorrelated asymmetry' is due to John Maynard Smith who called payoff relevant asymmetries in games with similar roles for each player 'correlated asymmetries' (note that any game with correlated asymmetries must also have uncorrelated asymmetries). The explanation of an uncorrelated asymmetry usually makes reference to "informational asymmetry". Which may confuse some readers, since, games which may have uncorrelated asymmetries are still games of complete information . What differs between the same game with and without an uncorrelated asymmetry is whether the players know which role they have been assigned. If players in a symmetric game know whether they are Player 1, Player 2, ''etc.'' (or row vs. column player in a bimatrix game) then an uncorrelated asymmetry exists. If the players do not know which player they are then no uncorrelated asymmetry exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Game
In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties. Ordinally symmetric games are games that are symmetric with respect to the ordinal structure of the payoffs. A game is quantitatively symmetric if and only if it is symmetric with respect to the exact payoffs. A partnership game is a symmetric game where both players receive identical payoffs for any strategy set. That is, the payoff for playing strategy ''a'' against strategy ''b'' receives the same payoff as playing strategy ''b'' against strategy ''a''. Symmetry in 2x2 games Only 12 out of the 144 ordinally distinct 2x2 games are symmetric. However, many of the commonly studied 2x2 games are at least ordinally symmetric. The standard represen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics under the well-known biologist J. B. S. Haldane. Maynard Smith was instrumental in the application of game theory to evolution with George R. Price, and theorised on other problems such as the evolution of sex and signalling theory. Biography Early years John Maynard Smith was born in London, the son of the surgeon Sidney Maynard Smith, but following his father's death in 1928, the family moved to Exmoor, where he became interested in natural history. Quite unhappy with the lack of formal science education at Eton College, Maynard Smith took it upon himself to develop an interest in Darwinian evolutionary theory and mathematics, after having read the work of old Etonian J. B. S. Haldane, whose books were in the school's library despite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Information
In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay. Given this information, the players have the ability to plan accordingly based on the information to maximize their own strategies and utility at the end of the game. Inversely, in a game with incomplete information, players do not possess full information about their opponents. Some players possess private information, a fact that the others should take into account when forming expectations about how those players will behave. A typical example is an auction: each player knows his own utility function (valuation for the item), but does not know the utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bimatrix Game
In game theory, a bimatrix game is a simultaneous game for two players in which each player has a finite number of possible actions. The name comes from the fact that the normal form of such a game can be described by two matrices - matrix A describing the payoffs of player 1 and matrix B describing the payoffs of player 2. Player 1 is often called the "row player" and player 2 the "column player". If player 1 has m possible actions and player 2 has n possible actions, then each of the two matrices has m rows by n columns. When the row player selects the i-th action and the column player selects the j-th action, the payoff to the row player is A ,j/math> and the payoff to the column player is B ,j/math>. The players can also play mixed strategies. A mixed strategy for the row player is a non-negative vector x of length m such that: \sum_^m x_i = 1. Similarly, a mixed strategy for the column player is a non-negative vector y of length n such that: \sum_^n y_j = 1. When the players p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Asymmetry
In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. Information asymmetry creates an imbalance of power in transactions, which can sometimes cause the transactions to be inefficient, causing market failure in the worst case. Examples of this problem are adverse selection, moral hazard, and monopolies of knowledge. A common way to visualise information asymmetry is with a scale with one side being the seller and the other the buyer. When the seller has more or better information the transaction will more likely occur in the seller's favour ("the balance of power has shifted to the seller"). An example of this could be when a used car is sold, the seller is likely to have a much better understanding of the car's condition and hence its market value than the buyer, who can only estimate the market value based on the information provided by the seller and their ow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Set (game Theory)
In game theory, an information set is a set that, for a particular player, given what that player has observed shows the decision vertices available to the player which are undistinguishable to them at the current point in the game. For a better idea on decision vertices, refer to Figure 1. If the game has perfect information, every information set contains only one member, namely the point actually reached at that stage of the game, since each player knows the exact mix of chance moves and player strategies up to the current point in the game. Otherwise, it is the case that some players cannot be sure exactly what has taken place so far in the game and what their position is. Information sets are used in extensive form games and are often depicted in game trees. Game trees show the path from the start of a game and the subsequent paths that can be made depending on each player's next move. Information sets can be easily depicted in game trees to display each player's possible mov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensive Form Game
An extensive-form game is a specification of a game in game theory, allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible game outcomes. Extensive-form games also allow for the representation of incomplete information in the form of chance events modeled as " moves by nature". Finite extensive-form games Some authors, particularly in introductory textbooks, initially define the extensive-form game as being just a game tree with payoffs (no imperfect or incomplete information), and add the other elements in subsequent chapters as refinements. Whereas the rest of this article follows this gentle approach with motivating examples, we present upfront the finite extensive-form games as (ultimately) constructed here. Thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionarily Stable Strategies
An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is ''impermeable'' when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy (or set of strategies) which may be novel or initially rare. Introduced by John Maynard Smith and George R. Price in 1972/3, it is an important concept in behavioural ecology, evolutionary psychology, mathematical game theory and economics, with applications in other fields such as anthropology, philosophy and political science. In game-theoretical terms, an ESS is an equilibrium refinement of the Nash equilibrium, being a Nash equilibrium that is also "evolutionarily stable." Thus, once fixed in a population, natural selection alone is sufficient to prevent alternative (mutant) strategies from replacing it (although this does not preclude the possibility that a better strategy, or set of strategies, will emerge in response to selective pressure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Of Chicken
The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if neither yields), the individuals try to avoid it out of pride for not wanting to look like a "chicken". Each player taunts the other to increase the risk of shame in yielding. However, when one player yields, the conflict is avoided, and the game is for the most part over. The name "chicken" has its origins in a game in which two drivers drive toward each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves and the other does not, the one who swerved will be called a "chicken", meaning a coward; this terminology is most prevalent in political science and economics. The name "hawk–dove" refers to a situation in which there is a competition for a shared resource and the contestants can choo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hawk-dove Game
The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if neither yields), the individuals try to avoid it out of pride for not wanting to look like a "chicken". Each player taunts the other to increase the risk of shame in yielding. However, when one player yields, the conflict is avoided, and the game is for the most part over. The name "chicken" has its origins in a game in which two drivers drive toward each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves and the other does not, the one who swerved will be called a "chicken", meaning a coward; this terminology is most prevalent in political science and economics. The name "hawk–dove" refers to a situation in which there is a competition for a shared resource and the contestants can choo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
