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Epsilon Equilibrium
In game theory, an epsilon-equilibrium, or near-Nash equilibrium, is a strategy profile that approximately satisfies the condition of Nash equilibrium. In a Nash equilibrium, no player has an incentive to change his behavior. In an approximate Nash equilibrium, this requirement is weakened to allow the possibility that a player may have a small incentive to do something different. This may still be considered an adequate solution concept, assuming for example status quo bias. This solution concept may be preferred to Nash equilibrium due to being easier to compute, or alternatively due to the possibility that in games of more than 2 players, the probabilities involved in an exact Nash equilibrium need not be rational numbers. Definition There is more than one alternative definition. The standard definition Given a game and a real non-negative parameter \varepsilon, a strategy profile is said to be an \varepsilon-equilibrium if it is not possible for any player to gain more t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly. 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 theirs 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 Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmica
''Algorithmica'' is a monthly peer-reviewed scientific journal focusing on research and the application of computer science algorithms. The journal was established in 1986 and is published by Springer Science+Business Media. The editor in chief is Mohammad Hajiaghayi. Subject coverage includes sorting, searching, data structures, computational geometry, and linear programming, VLSI, distributed computing, parallel processing, computer aided design, robotics, graphics, data base design, and software tool A programming tool or software development tool is a computer program that is used to software development, develop another computer program, usually by helping the developer manage computer files. For example, a programmer may use a tool called ...s. Springer Science+Business Media. 2013 Abstract ...
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Roy Radner
Roy Radner (June 29, 1927 – October 6, 2022) was Leonard N. Stern School Professor of Business at New York University. He was a micro-economic theorist. Radner's research interests included strategic analysis of climate change, bounded rationality, game-theoretic models of corruption, pricing of information goods and statistical theory of data mining. Previously he was a faculty member at the University of California, Berkeley, and a Distinguished Member of Technical Staff at AT&T Bell Laboratories. Life and career Roy Radner received his Ph.B. in the liberal arts from the University of Chicago in 1945. Continuing his education at the University of Chicago, Radner went on to receive a B.S. in mathematics in 1950, an M.S. in mathematics in 1951, and his Ph.D. in mathematical statistics in 1956. He died on October 6, 2022, at Pennswood Village in Newtown, Bucks County, Pennsylvania, aged 95. Radner equilibrium Among Radner's various contributions, the one that bears his n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huw Dixon
Huw David Dixon (/hju: devəd dɪksən/; born 1958) is a British economist. He has been a professor at Cardiff Business School since 2006, having previously been Head of Economics at the University of York (2003–2006) after being a professor of economics there (1992–2003), and the University of Swansea (1991–1992), a Reader at Essex University (1987–1991) and a lecturer at Birkbeck College (University of London) 1983–1987. Education Dixon graduated from his first degree in Philosophy and Economics from Balliol College, University of Oxford in 1980, and he went on to do his PhD at Nuffield College, University of Oxford under the supervision of Nobel Laureate Sir James Mirrlees graduating in 1984. Career Dixon was a fellow of the CEPR from 1991 to 2001, a member of the Royal Economic Society council (1996–2001), and a fellow of the Ces-ifo institute since 2000. He has been on the editorial board of the '' Review of Economic Studies'' (1986–1993), the ''Journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand–Edgeworth Model
In microeconomics, the Bertrand–Edgeworth model of price-setting oligopoly explores what happens when firms compete to sell a homogeneous product (a good for which consumers buy only from the cheapest available seller) but face limits on how much they can supply. Unlike in the standard Bertrand competition model, where firms are assumed to meet all demand at their chosen price, the Bertrand–Edgeworth model assumes each firm has a capacity constraint: a fixed maximum output it can sell, regardless of price. This constraint may be physical (as in Edgeworth’s formulation) or may depend on price or other conditions. A key result of the model is that pure-strategy price equilibria may fail to exist, even with just two firms, because firms have an incentive to undercut competitors' prices until they hit their capacity constraints. As a result, the model can lead to price cycles or the emergence of mixed-strategy equilibria, where firms randomize over prices. History Joseph Lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Strategy
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 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 authors treat strate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grim Trigger
In game theory, grim trigger (also called the grim strategy or just grim) is a trigger strategy for a repeated game. Initially, a player using grim trigger will cooperate, but as soon as the opponent defects (thus satisfying the trigger condition), the player using grim trigger will defect for the remainder of the iterated game. Since a single defect by the opponent triggers defection forever, grim trigger is the most strictly unforgiving of strategies in an iterated game. In Robert Axelrod's book '' The Evolution of Cooperation'', grim trigger is called "Friedman", for a 1971 paper by James W. Friedman, which uses the concept. The infinitely repeated prisoners' dilemma The infinitely repeated prisoners’ dilemma is a well-known example for the grim trigger strategy. The normal game for two prisoners is as follows: In the prisoners' dilemma, each player has two choices in each stage: # Cooperate # Defect for an immediate gain If a player defects, he will be punished for t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tit-for-tat
Tit for tat is an English saying meaning "equivalent retaliation". It is an alternation (linguistics), alternation of ''wikt:tip#Noun 3, tip for wikt:tap#Verb 2, tap'' "blow for blow", first recorded in 1558. It is also a highly effective strategy in game theory. An intelligent agent, agent using this strategy will first cooperate, then subsequently replicate an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is similar to reciprocal altruism in biology. Game theory Tit-for-tat has been very successfully used as a strategy for the iterated prisoner's dilemma. The strategy was first introduced by Anatol Rapoport in Robert Axelrod (political scientist), Robert Axelrod's two tournaments, held around 1980. Notably, it was (on both occasions) both the simplest strategy and the most successful in direct competition. Few have extended the game theoretical approach to other applications such as finance. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeated Game
In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of their current action on the future actions of other players; this impact is sometimes called their reputation. Single stage game or single shot game are names for non-repeated games. Example Consider two gas stations that are adjacent to one another. They compete by publicly posting pricing, and have the same and constant marginal cost ''c'' (the wholesale price of gasoline). Assume that when they both charge , their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, either can steal all of their competitors' customers, nearly doub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching Pennies
Matching pennies is a non-cooperative game studied 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 wins and keeps both pennies. If the pennies do not match (one heads and one tails), then Odd wins and keeps both pennies. 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 is used primarily to illustrate the concept of mixed strategies and a mixed str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SICOMP
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References External linksSIAM Journal on Computing on |
Stochastic Game
In game theory, a stochastic game (or Markov game) is a repeated game with probabilistic transitions played by one or more players. The game is played in a sequence of stages. At the beginning of each stage the game is in some state. The players select actions and each player receives a payoff that depends on the current state and the chosen actions. The game then moves to a new random state whose distribution depends on the previous state and the actions chosen by the players. The procedure is repeated at the new state and play continues for a finite or infinite number of stages. The total payoff to a player is often taken to be the discounted sum of the stage payoffs or the limit inferior of the averages of the stage payoffs. Stochastic games were introduced by Lloyd Shapley in the early 1950s. They generalize Markov decision processes to multiple interacting decision makers, as well as strategic-form games to dynamic situations in which the environment changes in response to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
