|
Traveler's Dilemma
In game theory, the traveler's dilemma (sometimes abbreviated TD) is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surprisingly, the Nash equilibrium is for both players to aggressively lowball. The traveler's dilemma is notable in that naive play appears to outperform the Nash equilibrium; this apparent paradox also appears in the centipede game and the finitely-iterated prisoner's dilemma. Formulation The original game scenario was formulated in 1994 by Kaushik Basu and goes as follows: "An airline loses two suitcases belonging to two different travelers. Both suitcases happen to be identical and contain identical antiques. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of $100 per suitcase—he is unable to find o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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 mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guess 2/3 Of The Average
In game theory, "guess of the average" is a game where players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to of the average of numbers chosen by all players. History Alain Ledoux is the founding father of the "guess of the average" game. In 1981, Ledoux used this game as a tie breaker in his French magazine :fr:Jeux et Stratégie, Jeux et Stratégie. He asked about 4,000 readers, who reached the same number of points in previous puzzles, to state an integer between 1 and 1,000,000,000. The winner was the one who guessed closest to of the average guess. Rosemarie Nagel (1995) revealed the potential of guessing games of that kind: They are able to disclose participants' "depth of reasoning." Equilibrium analysis In this game, there is no dominance (game theory), strictly dominant strategy, but there are strongly dominated strategies. There is a unique pure strategy Nash equilibrium. Th ... [...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 represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal-form Game
In game theory, normal form is a description of a ''game''. Unlike extensive form, normal-form representations are not graphical ''per se'', but rather represent the game by way of a matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as compared to extensive-form representations. The normal-form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, for each player. In static games of complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of all strategies available to that player, whereas a strategy is a complete plan of action for every stage of the game, regardless of whether that stage actually arises in play. A payoff function for a player is a mapping from the cross-product of players' strategy spaces to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategy (game Theory)
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or conflated with that of a move or action, because of the correspondence between moves and pure strategies in normal-form game, most games: for any move ''X'', "always play move ''X''" is an example of a valid strategy, and as a result every move can also be considered to be a strategy. Other autho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Payoff Matrix
In game theory, normal form is a description of a ''game''. Unlike extensive-form game, extensive form, normal-form representations are not Graph (discrete mathematics), graphical ''per se'', but rather represent the game by way of a matrix (mathematics), matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibrium, Nash equilibria, some information is lost as compared to extensive-form representations. The normal-form representation of a game includes all perceptible and conceivable Strategy (game theory), strategies, and their corresponding payoffs, for each player. In static games of complete information, complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of all strategies available to that player, whereas a strategy is a complete plan of action for every stage of the game, regardless of whether th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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 mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategic Dominance
In game theory, a strategy ''A'' dominates another strategy ''B'' if ''A'' will always produce a better result than ''B'', regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance. Terminology A player can compare two strategies, A and B, to determine which one is better. The result of the comparison is one of: * B strictly dominates (>) A: choosing B always gives a better outcome than choosing A, no matter what the other players do. * B weakly dominates (≥) A: choosing B always gives at least as good an outcome as choosing A, no matter what the other players do, and there is at least one set of opponents' actions for which B gives a better outcome than A. (Notice that if B strictly dominates A, then B weakly dominates A. Therefore, we can say "B dominates A" to mean "B weakly dominates A".) * B is weakly dominated by A: there is at least one set of opponents' actions for which B gives a worse outcome than A, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keynesian Beauty Contest
A Keynesian beauty contest is a beauty contest in which judges are rewarded for selecting the ''most popular'' faces among all judges, rather than those they may personally find the most attractive. This idea is often applied in financial markets, whereby investors could profit more by buying whichever stocks they think other investors will buy, rather than the stocks that have fundamentally the best value, because when other people buy a stock, they bid up the price, allowing an earlier investor to cash out with a profit, regardless of whether the price increases are supported by its fundamentals and theoretical arguments. The concept was developed by John Maynard Keynes and introduced in Chapter 12 of his work ''The General Theory of Employment, Interest and Money'' (1936) to explain price fluctuations in equity markets. Overview Keynes described the action of rational agents in a market using an analogy based on a fictional newspaper contest, in which entrants are asked to ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-sum
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero. If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, sport and bridge where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Nash Equilibrium
In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players may hold private information relevant to the game, meaning that the payoffs are not common knowledge. Bayesian games model the outcome of player interactions using aspects of Bayesian probability. They are notable because they allowed the specification of the solutions to games with incomplete information for the first time in game theory. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Memorial Prize in Economic Sciences for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned a set of characteristics by nature at the start of the game. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Focal Point (game Theory)
In game theory, a focal point (or Schelling point) is a solution that people tend to choose by default in the absence of communication in order to avoid Coordination game#Experimental results, coordination failure. The concept was introduced by the American economist Thomas Schelling in his book ''The Strategy of Conflict'' (1960). Schelling states that "[p]eople ''can'' often concert their intentions or expectations with others if each knows that the other is trying to do the same" in a cooperative situation (p. 57), so their action would converge on a focal point which has some kind of prominence compared with the environment. However, the conspicuousness of the focal point depends on time, place and people themselves. It may not be a definite solution. Existence The existence of the focal point is first demonstrated by Schelling with a series of questions. Here is one example: to determine the time and place to meet a stranger in New York City, but without being able to communi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
