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Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in all fields of social science, as well as in logic, systems science and computer science. The concepts of game theory are used extensively in economics as well. The traditional methods of game theory addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by the losses and gains of other participants. In the 21st century, the advanced game theories apply to a wider range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers.
In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase.
The RGB color model is an additive color model in which the red, green and blue primary colors of light are added together in various ways to reproduce a broad array of colors. The name of the model comes from the initials of the three additive primary colors, red, green, and blue.
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.
The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws were widely recognized.
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, 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.
In game theory, cheap talk is communication between players that does not directly affect the payoffs of the game. Providing and receiving information is free. This is in contrast to signaling in which sending certain messages may be costly for the sender depending on the state of the world.
In game theory, a signaling game is a simple type of a dynamic Bayesian game.
Column chromatography in chemistry is a chromatography method used to isolate a single chemical compound from a mixture. Chromatography is able to separate substances based on differential adsorption of compounds to the adsorbent; compounds move through the column at different rates, allowing them to be separated into fractions. The technique is widely applicable, as many different adsorbents can be used with a wide range of solvents. The technique can be used on scales from micrograms up to kilograms. The main advantage of column chromatography is the relatively low cost and disposability of the stationary phase used in the process. The latter prevents cross-contamination and stationary phase degradation due to recycling. Column chromatography can be done using gravity to move the solvent, or using compressed gas to push the solvent through the column.
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
In game theory, a Perfect Bayesian Equilibrium (PBE) is an equilibrium concept relevant for dynamic games with incomplete information. It is a refinement of Bayesian Nash equilibrium (BNE). A perfect Bayesian equilibrium has two components -- strategies and beliefs:
In contract theory, signalling is the idea that one party credibly conveys some information about itself to another party.
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games. The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept: subgame-perfect Nash equilibria rather than Nash equilibria.
In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base 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 his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. Single stage game or single shot game are names for non-repeated games.
Quantal response equilibrium (QRE) is a solution concept in game theory. First introduced by Richard McKelvey and Thomas Palfrey, it provides an equilibrium notion with bounded rationality. QRE is not an equilibrium refinement, and it can give significantly different results from Nash equilibrium. QRE is only defined for games with discrete strategies, although there are continuous-strategy analogues.
In game theory, the traveler's dilemma 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.
In economics and game theory, global games are games of incomplete information where players receive possibly-correlated signals of the underlying state of the world. Global games were originally defined by Carlsson and van Damme (1993).
The intuitive criterion is a technique for equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by restricting the possible sender types to types who could obtain higher utility levels by deviating to off-the-equilibrium messages, and to types for which the off-the-equilibrium message is not equilibrium dominated.
A Markov perfect equilibrium is an equilibrium concept in game theory. It has been used in analyses of industrial organization, macroeconomics, and political economy. It is a refinement of the concept of subgame perfect equilibrium to extensive form games for which a pay-off relevant state space can be identified. The term appeared in publications starting about 1988 in the work of economists Jean Tirole and Eric Maskin.
Jean-François Mertens was a Belgian game theorist and mathematical economist.
References
- ↑ "separating equilibrium". Oxford Reference. Retrieved 3 January 2022.
- ↑ Lada, Akos. (PDF) https://scholar.harvard.edu/files/alada/files/section12_1.pdf.
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