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List Of Games In Game Theory
Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games Explanation of features Games can have several features, a few of the most common are listed here. *Number of players: Each person who makes a choice in a game or who receives a payoff from the outcome of those choices is a player. *Strategies per player: In a game each player chooses from a set of possible actions, known as pure strategies. If the number is the same for all players, it is listed here. *Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the other strategies. In other words, if every player is playing their part of a Nash equilibrium, no player has an incentive to unilaterally change their strategy. Considering only situations where players play a single strategy without randomizing (a pure strategy) a ... [...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 mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordination Game
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibria in which players choose matching strategies. Figure 1 shows a 2-player example. Both (Up, Left) and (Down, Right) are Nash equilibria. If the players expect (Up, Left) to be played, then player 1 thinks their payoff would fall from 2 to 1 if they deviated to Down, and player 2 thinks their payoff would fall from 4 to 3 if they chose Right. If the players expect (Down, Right), player 1 thinks their payoff would fall from 2 to 1 if they deviated to Up, and player 2 thinks their payoff would fall from 4 to 3 if they chose Left. A player's optimal move depends on what they expect the other player to do, and they both do better if they coordinate than if they played an off-equilibrium combinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Induction Puzzles
Induction puzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction. A puzzle's scenario always involves multiple players with the same reasoning capability, who go through the same reasoning steps. According to the principle of induction, a solution to the simplest case makes the solution of the next complicated case obvious. Once the simplest case of the induction puzzle is solved, the whole puzzle is solved subsequently. Typical tell-tale features of these puzzles include any puzzle in which each participant has a given piece of information (usually as common knowledge) about all other participants but not themselves. Also, usually, some kind of hint is given to suggest that the participants can trust each other's intelligence — they are capable of theory of mind (that "every participant knows modus ponens" is common knowledge). Also, the inaction of a participant is a non-verbal communication of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Effort Game Aka Weak-Link Game
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching Pennies
Matching pennies is the name for a simple game used in game theory. It is played between two players, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then Even keeps both pennies, so wins one from Odd (+1 for Even, −1 for Odd). If the pennies do not match (one heads and one tails) Odd keeps both pennies, so receives one from Even (−1 for Even, +1 for Odd). Theory Matching Pennies is a zero-sum game because each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the participants' total gains are added up and their total losses subtracted, the sum will be zero. The game can be written in a payoff matrix (pictured right - from Even's point of view). Each cell of the matrix shows the two players' payoffs, with Even's payoffs listed first. Matching pennies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuhn Poker
Kuhn poker is an extremely simplified form of poker developed by Harold W. Kuhn as a simple model zero-sum two-player imperfect-information game, amenable to a complete game-theoretic analysis. In Kuhn poker, the deck includes only three playing cards, for example a King, Queen, and Jack. One card is dealt to each player, which may place bets similarly to a standard poker. If both players bet or both players pass, the player with the higher card wins, otherwise, the betting player wins. Game description In conventional poker terms, a game of Kuhn poker proceeds as follows: *Each player antes 1. *Each player is dealt one of the three cards, and the third is put aside unseen. *Player one can check or bet 1. **If player one checks then player two can check or bet 1. ***If player two checks there is a showdown for the pot of 2 (i.e. the higher card wins 1 from the other player). ***If player two bets then player one can fold or call. ****If player one folds then player two takes th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guess 2/3 Of The Average
In game theory, "guess of the average" is a game that explores how a player’s strategic reasoning process takes into account the mental process of others in the game. In this game, 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 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." In his influential book, Keynes compared the determination of prices in a stock market to that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gift-exchange Game
The gift-exchange game is a game that was introduced by George Akerlof and Janet Yellen to model labor relations. The simplest form of the game involves two players – an employee and an employer. The employer first decides whether to award a higher salary to the employee. The employee then decides whether they will work harder or not due to the salary change. Like trust games, gift-exchange games are used to study reciprocity for human subject research in social psychology and economics. If the employer pays extra salary and the employee puts extra effort, then both players are better off than otherwise. The relationship between an investor and an investee has been investigated as the same type of a game. Equilibrium analysis The extra effort in gift-exchange games is modeled to be a negative payoff if not compensated by salary. The IKEA effect of own extra work is not considered in the payoff structure of this game. Therefore, this model rather fits labor conditions, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Example Of A Game Without A Value
In the mathematical theory of games, in particular the study of zero-sum continuous games, not every game has a minimax value. This is the expected value to one of the players when both play a perfect strategy (which is to choose from a particular PDF). This article gives an example of a zero-sum game that has no value. It is due to Sion and Wolfe. Zero-sum games with a finite number of pure strategies are known to have a minimax value (originally proved by John von Neumann) but this is not necessarily the case if the game has an infinite set of strategies. There follows a simple example of a game with no minimax value. The existence of such zero-sum games is interesting because many of the results of game theory become inapplicable if there is no minimax value. The game Players I and II choose numbers x and y respectively, between 0 and 1. The payoff to player I is K(x,y)= \begin -1 & \text x [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
El Farol Bar Problem
The El Farol bar problem is a problem in game theory. Every Thursday night, a fixed population want to go have fun at the El Farol Bar, unless it's too crowded. * If less than 60% of the population go to the bar, they'll all have more fun than if they stayed home. * If more than 60% of the population go to the bar, they'll all have less fun than if they stayed home. Everyone must decide ''at the same time'' whether to go or not, with no knowledge of others' choices. Paradoxically, if everyone uses a deterministic pure strategy which is symmetric (same strategy for all players), it is guaranteed to fail no matter what it is. If the strategy suggests it will not be crowded, everyone will go, and thus it ''will'' be crowded; but if the strategy suggests it will be crowded, nobody will go, and thus it will ''not'' be crowded, but again no one will have fun. Better success is possible with a probabilistic mixed strategy. For the single-stage El Farol Bar problem, there exists a unique ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dollar Auction
The dollar auction is a non-zero sum sequential game explored by economist Martin Shubik to illustrate a paradox brought about by traditional rational choice theory in which players are compelled to make an ultimately irrational decision based completely on a sequence of apparently rational choices made throughout the game. Shubik: 1971. Page 109 Play The setup involves an auctioneer who volunteers to auction off a dollar bill with the following rule: the bill goes to the winner; however, the second-highest bidder also loses the amount that they bid, making them the biggest loser in the auction. The winner can get a dollar for a mere 5 cents (the minimum bid), but only if no one else enters into the bidding war. However, entering the auction with a low bid may result in a problematic outcome. For instance, a player might begin by bidding 5 cents, hoping to make a 95-cent profit. They can be outbid by another player bidding 10 cents, as a 90-cent profit is still desirable. Similar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diner's Dilemma
In game theory, the unscrupulous diner's dilemma (or just diner's dilemma) is an ''n''-player prisoner's dilemma. The situation imagined is that several people go out to eat, and before ordering, they agree to split the cost equally between them. Each diner must now choose whether to order the costly or cheap dish. It is presupposed that the costlier dish is better than the cheaper, but not by enough to warrant paying the difference when eating alone. Each diner reasons that, by ordering the costlier dish, the extra cost to their own bill will be small, and thus the better dinner is worth the money. However, all diners having reasoned thus, they each end up paying for the costlier dish, which by assumption, is worse than had they each ordered the cheaper. Formal definition and equilibrium analysis Let ''a'' represent the joy of eating the expensive meal, ''b'' the joy of eating the cheap meal, ''k'' is the cost of the expensive meal, ''l'' the cost of the cheap meal, and ''n'' the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
