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22,800 | In his 2018 book "The Polymath", British author Waqas Ahmed defines polymaths as those who have made significant contributions to at least three different fields. Rather than seeing polymaths as exceptionally gifted, he argues that every human being has the potential to become one: that people naturally have multiple i... | https://en.wikipedia.org/wiki?curid=25121 |
22,801 | For individuals, Ahmed says, specialisation is dehumanising and stifles their full range of expression whereas polymathy "is a powerful means to social and intellectual emancipation" which enables a more fulfilling life. In terms of social progress, he argues that answers to specific problems often come from combining ... | https://en.wikipedia.org/wiki?curid=25121 |
22,802 | Ahmed examines evidence suggesting that developing multiple talents and perspectives is helpful for success in a highly specialised field. He cites a study of Nobel Prize-winning scientists which found them 25 times more likely to sing, dance, or act than average scientists. Another study found that children scored hig... | https://en.wikipedia.org/wiki?curid=25121 |
22,803 | Ahmed cites many historical claims for the advantages of polymathy. Some of these are about general intellectual abilities that polymaths apply across multiple domains. For example, Aristotle wrote that full understanding of a topic requires, in addition to subject knowledge, a general critical thinking ability that ca... | https://en.wikipedia.org/wiki?curid=25121 |
22,804 | Aside from "Renaissance man", similar terms in use are (Latin) and (Italian), which translate to "universal man". The related term "generalist"—contrasted with a "specialist"—is used to describe a person with a general approach to knowledge. | https://en.wikipedia.org/wiki?curid=25121 |
22,805 | The term "universal genius" or "versatile genius" is also used, with Leonardo da Vinci as the prime example again. The term is used especially for people who made lasting contributions in at least one of the fields in which they were actively involved and when they took a universality of approach. | https://en.wikipedia.org/wiki?curid=25121 |
22,806 | When a person is described as having encyclopedic knowledge, they exhibit a vast scope of knowledge. However, this designation may be anachronistic in the case of persons such as Eratosthenes, whose reputation for having encyclopedic knowledge predates the existence of any encyclopedic object. | https://en.wikipedia.org/wiki?curid=25121 |
22,807 | In Greek mythology, Icarus (; , ) was the son of the master craftsman Daedalus, the architect of the labyrinth of Crete. After Theseus, king of Athens and enemy of Minos, escaped from the labyrinth, King Minos suspected that Icarus and Daedalus had revealed the labyrinth's secrets and imprisoned them--either in a large... | https://en.wikipedia.org/wiki?curid=82721 |
22,808 | Icarus's father Daedalus, a very talented Athenian craftsman, built a labyrinth for King Minos of Crete near his palace at Knossos to imprison the Minotaur, a half-man, half-bull monster born of his wife and the Cretan bull. Minos imprisoned Daedalus himself in the labyrinth because he gave Minos's daughter, Ariadne, a... | https://en.wikipedia.org/wiki?curid=82721 |
22,809 | Daedalus fashioned two pairs of wings out of beeswax and feathers for himself and his son. Before trying to escape the island, he warned his son not to fly too close to the sun, nor too close to the sea, but to follow his path of flight. Overcome by giddiness while flying, Icarus disobeyed his father and soared into th... | https://en.wikipedia.org/wiki?curid=82721 |
22,810 | Hellenistic writers give euhemerising variants in which the escape from Crete was actually by boat, provided by Pasiphaë, for which Daedalus invented the first sails, to outstrip Minos' pursuing galleys, that Icarus fell overboard en route to Sicily and drowned, and that Heracles erected a tomb for him. | https://en.wikipedia.org/wiki?curid=82721 |
22,811 | Icarus' flight was often alluded to by Greek poets in passing and was told briefly in Pseudo-Apollodorus. Augustan writers who wrote about it in Latin include Hyginus, who tells in "Fabula" of the bovine love affair of Pasiphaë, daughter of the Sun, that resulted in the birth of the Minotaur, as well as Ovid, who tells... | https://en.wikipedia.org/wiki?curid=82721 |
22,812 | Ovid's version of the Icarus myth and its connection to Phaethon influenced the mythological tradition in English literature reflected in the writings of Chaucer, Marlowe, Shakespeare, Milton, and Joyce. | https://en.wikipedia.org/wiki?curid=82721 |
22,813 | In Renaissance iconography, the significance of Icarus depends on context: in the Orion Fountain at Messina, he is one of many figures associated with water; but he is also shown on the Bankruptcy Court of the Amsterdam Town Hall – where he symbolizes high-flying ambition. The 16th-century painting "Landscape with the ... | https://en.wikipedia.org/wiki?curid=82721 |
22,814 | Literary interpretation has considered the myth of Icarus as a consequence of excessive ambition. An Icarus-related study of the Daedalus myth was published by the French hellenist . In psychology, there have been synthetic studies of the "Icarus complex" with respect to the alleged relationship between fascination for... | https://en.wikipedia.org/wiki?curid=82721 |
22,815 | 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. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly bal... | https://en.wikipedia.org/wiki?curid=11924 |
22,816 | 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 mathematical economics. ... | https://en.wikipedia.org/wiki?curid=11924 |
22,817 | Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to evolution in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. , with the Nobel Memorial Prize in Economic Sciences g... | https://en.wikipedia.org/wiki?curid=11924 |
22,818 | Discussions on the mathematics of games began long before the rise of modern mathematical game theory. Cardano's work on games of chance in "Liber de ludo aleae" ("Book on Games of Chance"), which was written around 1564 but published posthumously in 1663, formulated some of the field's basic ideas. In the 1650s, Pasca... | https://en.wikipedia.org/wiki?curid=11924 |
22,819 | In 1713, a letter attributed to Charles Waldegrave analyzed a game called "le Her". He was an active Jacobite and uncle to James Waldegrave, a British diplomat. In this letter, Waldegrave provided a minimax mixed strategy solution to a two-person version of the card game le Her, and the problem is now known as Waldegra... | https://en.wikipedia.org/wiki?curid=11924 |
22,820 | In 1913, Ernst Zermelo published "Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels" ("On an Application of Set Theory to the Theory of the Game of Chess"), which proved that the optimal chess strategy is strictly determined. This paved the way for more general theorems. | https://en.wikipedia.org/wiki?curid=11924 |
22,821 | In 1938, the Danish mathematical economist Frederik Zeuthen proved that the mathematical model had a winning strategy by using Brouwer's fixed point theorem. In his 1938 book "Applications aux Jeux de Hasard" and earlier notes, Émile Borel proved a minimax theorem for two-person zero-sum matrix games only when the pay-... | https://en.wikipedia.org/wiki?curid=11924 |
22,822 | Game theory did not exist as a unique field until John von Neumann published the paper "On the Theory of Games of Strategy" in 1928. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. ... | https://en.wikipedia.org/wiki?curid=11924 |
22,823 | In 1950, the first mathematical discussion of the prisoner's dilemma appeared, and an experiment was undertaken by notable mathematicians Merrill M. Flood and Melvin Dresher, as part of the RAND Corporation's investigations into game theory. RAND pursued the studies because of possible applications to global nuclear st... | https://en.wikipedia.org/wiki?curid=11924 |
22,824 | Game theory experienced a flurry of activity in the 1950s, during which the concepts of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed. The 1950s also saw the first applications of game theory to philosophy and political science. | https://en.wikipedia.org/wiki?curid=11924 |
22,825 | In 1965, Reinhard Selten introduced his solution concept of subgame perfect equilibria, which further refined the Nash equilibrium. Later he would introduce trembling hand perfection as well. In 1994 Nash, Selten and Harsanyi became Economics Nobel Laureates for their contributions to economic game theory. | https://en.wikipedia.org/wiki?curid=11924 |
22,826 | In the 1970s, game theory was extensively applied in biology, largely as a result of the work of John Maynard Smith and his evolutionarily stable strategy. In addition, the concepts of correlated equilibrium, trembling hand perfection, and common knowledge were introduced and analyzed. | https://en.wikipedia.org/wiki?curid=11924 |
22,827 | In 2005, game theorists Thomas Schelling and Robert Aumann followed Nash, Selten, and Harsanyi as Nobel Laureates. Schelling worked on dynamic models, early examples of evolutionary game theory. Aumann contributed more to the equilibrium school, introducing equilibrium coarsening and correlated equilibria, and developi... | https://en.wikipedia.org/wiki?curid=11924 |
22,828 | In 2007, Leonid Hurwicz, Eric Maskin, and Roger Myerson were awarded the Nobel Prize in Economics "for having laid the foundations of mechanism design theory". Myerson's contributions include the notion of proper equilibrium, and an important graduate text: "Game Theory, Analysis of Conflict". Hurwicz introduced and fo... | https://en.wikipedia.org/wiki?curid=11924 |
22,829 | In 2012, Alvin E. Roth and Lloyd S. Shapley were awarded the Nobel Prize in Economics "for the theory of stable allocations and the practice of market design". In 2014, the Nobel went to game theorist Jean Tirole. | https://en.wikipedia.org/wiki?curid=11924 |
22,830 | A game is "cooperative" if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is "non-cooperative" if players cannot form alliances or if all agreements need to be self-enforcing (e.g. through credible threats). | https://en.wikipedia.org/wiki?curid=11924 |
22,831 | Cooperative games are often analyzed through the framework of "cooperative game theory", which focuses on predicting which coalitions will form, the joint actions that groups take, and the resulting collective payoffs. It is opposed to the traditional "non-cooperative game theory" which focuses on predicting individual... | https://en.wikipedia.org/wiki?curid=11924 |
22,832 | Cooperative game theory provides a high-level approach as it describes only the structure, strategies, and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, coo... | https://en.wikipedia.org/wiki?curid=11924 |
22,833 | 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. That is, if the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the commonly studied 2×2 game... | https://en.wikipedia.org/wiki?curid=11924 |
22,834 | The most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the ultimatum game and similarly the dictator game have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmet... | https://en.wikipedia.org/wiki?curid=11924 |
22,835 | Zero-sum games (more generally, constant-sum games) are games in which choices by players can neither increase nor decrease the available resources. In zero-sum games, the total benefit goes to all players in a game, for every combination of strategies, always adds to zero (more informally, a player benefits only at th... | https://en.wikipedia.org/wiki?curid=11924 |
22,836 | Many games studied by game theorists (including the famed prisoner's dilemma) are non-zero-sum games, because the outcome has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another. | https://en.wikipedia.org/wiki?curid=11924 |
22,837 | Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential gains from trade. It is possible to transform any constant-sum game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called "the board") whose losses ... | https://en.wikipedia.org/wiki?curid=11924 |
22,838 | Simultaneous games are games where both players move simultaneously, or instead the later players are unaware of the earlier players' actions (making them "effectively" simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be perfect in... | https://en.wikipedia.org/wiki?curid=11924 |
22,839 | The difference between simultaneous and sequential games is captured in the different representations discussed above. Often, normal form is used to represent simultaneous games, while extensive form is used to represent sequential ones. The transformation of extensive to normal form is one way, meaning that multiple e... | https://en.wikipedia.org/wiki?curid=11924 |
22,840 | The Cournot competition model involves players choosing quantity of a homogenous product to produce independently and simultaneously, where marginal cost can be different for each firm and the firm's payoff is profit. The production costs are public information and the firm aims to find their profit-maximising quantity... | https://en.wikipedia.org/wiki?curid=11924 |
22,841 | The Bertrand competition, assumes homogenous products and a constant marginal cost and players choose the prices. The equilibrium of price competition is where the price is equal to marginal costs, assuming complete information about the competitors' costs. Therefore, the firms have an incentive to deviate from the equ... | https://en.wikipedia.org/wiki?curid=11924 |
22,842 | An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players, at every move in the game, know the moves previously made by all other players. In reality, this can be applied to firms and consumers having information about price and quality of all ... | https://en.wikipedia.org/wiki?curid=11924 |
22,843 | Many card games are games of imperfect information, such as poker and bridge. Perfect information is often confused with complete information, which is a similar concept. Complete information requires that every player know the strategies and payoffs available to the other players but not necessarily the actions taken,... | https://en.wikipedia.org/wiki?curid=11924 |
22,844 | One of the assumptions of the Nash equilibrium is that every player has correct beliefs about the actions of the other players. However, there are many situations in game theory where participants do not fully understand the characteristics of their opponents. Negotiators may be unaware of their opponent's valuation of... | https://en.wikipedia.org/wiki?curid=11924 |
22,845 | Bayesian game means a strategic game with incomplete information. For a strategic game, decision makers are players, and every player has a group of actions. A core part of the imperfect information specification is the set of states. Every state completely describes a collection of characteristics relevant to the play... | https://en.wikipedia.org/wiki?curid=11924 |
22,846 | For example, where Player 1 is unsure whether Player 2 would rather date her or get away from her, while Player 2 understands Player 1's preferences as before. To be specific, supposing that Player 1 believes that Player 2 wants to date her under a probability of 1/2 and get away from her under a probability of 1/2 (th... | https://en.wikipedia.org/wiki?curid=11924 |
22,847 | Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games. Examples include chess and Go. Games that involve imperfect information may also have a strong combinatorial character, for instance backgammon. There is no unified theory addressin... | https://en.wikipedia.org/wiki?curid=11924 |
22,848 | Games of perfect information have been studied in combinatorial game theory, which has developed novel representations, e.g. surreal numbers, as well as combinatorial and algebraic (and sometimes non-constructive) proof methods to solve games of certain types, including "loopy" games that may result in infinitely long ... | https://en.wikipedia.org/wiki?curid=11924 |
22,849 | Research in artificial intelligence has addressed both perfect and imperfect information games that have very complex combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational heuristics, like alpha–beta pruning or us... | https://en.wikipedia.org/wiki?curid=11924 |
22,850 | Games, as studied by economists and real-world game players, are generally finished in finitely many moves. Pure mathematicians are not so constrained, and set theorists in particular study games that last for infinitely many moves, with the winner (or other payoff) not known until "after" all those moves are completed... | https://en.wikipedia.org/wiki?curid=11924 |
22,851 | The focus of attention is usually not so much on the best way to play such a game, but whether one player has a winning strategy. (It can be proven, using the axiom of choice, that there are gameseven with perfect information and where the only outcomes are "win" or "lose"for which "neither" player has a winning strate... | https://en.wikipedia.org/wiki?curid=11924 |
22,852 | Much of game theory is concerned with finite, discrete games that have a finite number of players, moves, events, outcomes, etc. Many concepts can be extended, however. Continuous games allow players to choose a strategy from a continuous strategy set. For instance, Cournot competition is typically modeled with players... | https://en.wikipedia.org/wiki?curid=11924 |
22,853 | Differential games such as the continuous pursuit and evasion game are continuous games where the evolution of the players' state variables is governed by differential equations. The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory. In particular, there are ... | https://en.wikipedia.org/wiki?curid=11924 |
22,854 | A particular case of differential games are the games with a random time horizon. In such games, the terminal time is a random variable with a given probability distribution function. Therefore, the players maximize the mathematical expectation of the cost function. It was shown that the modified optimization problem c... | https://en.wikipedia.org/wiki?curid=11924 |
22,855 | Evolutionary game theory studies players who adjust their strategies over time according to rules that are not necessarily rational or farsighted. In general, the evolution of strategies over time according to such rules is modeled as a Markov chain with a state variable such as the current strategy profile or how the ... | https://en.wikipedia.org/wiki?curid=11924 |
22,856 | In biology, such models can represent evolution, in which offspring adopt their parents' strategies and parents who play more successful strategies (i.e. corresponding to higher payoffs) have a greater number of offspring. In the social sciences, such models typically represent strategic adjustment by players who play ... | https://en.wikipedia.org/wiki?curid=11924 |
22,857 | Individual decision problems with stochastic outcomes are sometimes considered "one-player games". They may be modeled using similar tools within the related disciplines of decision theory, operations research, and areas of artificial intelligence, particularly AI planning (with uncertainty) and multi-agent system. Alt... | https://en.wikipedia.org/wiki?curid=11924 |
22,858 | Stochastic outcomes can also be modeled in terms of game theory by adding a randomly acting player who makes "chance moves" ("moves by nature"). This player is not typically considered a third player in what is otherwise a two-player game, but merely serves to provide a roll of the dice where required by the game. | https://en.wikipedia.org/wiki?curid=11924 |
22,859 | For some problems, different approaches to modeling stochastic outcomes may lead to different solutions. For example, the difference in approach between MDPs and the minimax solution is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given... | https://en.wikipedia.org/wiki?curid=11924 |
22,860 | General models that include all elements of stochastic outcomes, adversaries, and partial or noisy observability (of moves by other players) have also been studied. The "gold standard" is considered to be partially observable stochastic game (POSG), but few realistic problems are computationally feasible in POSG repres... | https://en.wikipedia.org/wiki?curid=11924 |
22,861 | These are games the play of which is the development of the rules for another game, the target or subject game. Metagames seek to maximize the utility value of the rule set developed. The theory of metagames is related to mechanism design theory. | https://en.wikipedia.org/wiki?curid=11924 |
22,862 | The term metagame analysis is also used to refer to a practical approach developed by Nigel Howard, whereby a situation is framed as a strategic game in which stakeholders try to realize their objectives by means of the options available to them. Subsequent developments have led to the formulation of confrontation anal... | https://en.wikipedia.org/wiki?curid=11924 |
22,863 | These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path, and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling game theory emerges to formally recognize the int... | https://en.wikipedia.org/wiki?curid=11924 |
22,864 | Mean field game theory is the study of strategic decision making in very large populations of small interacting agents. This class of problems was considered in the economics literature by Boyan Jovanovic and Robert W. Rosenthal, in the engineering literature by Peter E. Caines, and by mathematicians Pierre-Louis Lions... | https://en.wikipedia.org/wiki?curid=11924 |
22,865 | The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the "players" of the game, the "information" and "actions" available to each player at each decision point, and the "payoffs" for each outcome. (Eric Rasmusen refers to these four "es... | https://en.wikipedia.org/wiki?curid=11924 |
22,866 | Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. | https://en.wikipedia.org/wiki?curid=11924 |
22,867 | The extensive form can be used to formalize games with a time sequencing of moves. Games here are played on trees (as pictured here). Here each vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action fo... | https://en.wikipedia.org/wiki?curid=11924 |
22,868 | The game pictured consists of two players. The way this particular game is structured (i.e., with sequential decision making and perfect information), "Player 1" "moves" first by choosing either or (fair or unfair). Next in the sequence, "Player 2", who has now seen "Player 1"s move, chooses to play either or . Once "P... | https://en.wikipedia.org/wiki?curid=11924 |
22,869 | The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set (i.e. the players do not know at which point they are), or a closed line is drawn around them. (... | https://en.wikipedia.org/wiki?curid=11924 |
22,870 | The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions. In the accompanying example th... | https://en.wikipedia.org/wiki?curid=11924 |
22,871 | When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form. | https://en.wikipedia.org/wiki?curid=11924 |
22,872 | Every extensive-form game has an equivalent normal-form game, however, the transformation to normal form may result in an exponential blowup in the size of the representation, making it computationally impractical. | https://en.wikipedia.org/wiki?curid=11924 |
22,873 | In games that possess removable utility, separate rewards are not given; rather, the characteristic function decides the payoff of each unity. The idea is that the unity that is 'empty', so to speak, does not receive a reward at all. | https://en.wikipedia.org/wiki?curid=11924 |
22,874 | The origin of this form is to be found in John von Neumann and Oskar Morgenstern's book; when looking at these instances, they guessed that when a union formula_1 appears, it works against the fraction | https://en.wikipedia.org/wiki?curid=11924 |
22,875 | as if two individuals were playing a normal game. The balanced payoff of C is a basic function. Although there are differing examples that help determine coalitional amounts from normal games, not all appear that in their function form can be derived from such. | https://en.wikipedia.org/wiki?curid=11924 |
22,876 | Formally, a characteristic function is seen as: (N,v), where N represents the group of people and formula_3 is a normal utility. | https://en.wikipedia.org/wiki?curid=11924 |
22,877 | Alternative game representation forms are used for some subclasses of games or adjusted to the needs of interdisciplinary research. In addition to classical game representations, some of the alternative representations also encode time related aspects. | https://en.wikipedia.org/wiki?curid=11924 |
22,878 | As a method of applied mathematics, game theory has been used to study a wide variety of human and animal behaviors. It was initially developed in economics to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The first use of game-theoretic analysis was by Antoi... | https://en.wikipedia.org/wiki?curid=11924 |
22,879 | Although pre-twentieth-century naturalists such as Charles Darwin made game-theoretic kinds of statements, the use of game-theoretic analysis in biology began with Ronald Fisher's studies of animal behavior during the 1930s. This work predates the name "game theory", but it shares many important features with this fiel... | https://en.wikipedia.org/wiki?curid=11924 |
22,880 | In addition to being used to describe, predict, and explain behavior, game theory has also been used to develop theories of ethical or normative behavior and to prescribe such behavior. In economics and philosophy, scholars have applied game theory to help in the understanding of good or proper behavior. Game-theoretic... | https://en.wikipedia.org/wiki?curid=11924 |
22,881 | The primary use of game theory is to describe and model how human populations behave. Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has been ... | https://en.wikipedia.org/wiki?curid=11924 |
22,882 | Some game theorists, following the work of John Maynard Smith and George R. Price, have turned to evolutionary game theory in order to resolve these issues. These models presume either no rationality or bounded rationality on the part of players. Despite the name, evolutionary game theory does not necessarily presume n... | https://en.wikipedia.org/wiki?curid=11924 |
22,883 | Some scholars see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave. Since a strategy, corresponding to a Nash equilibrium of a game constitutes one's best response to the actions of the other players – provided they are in (the same) Nash equilibr... | https://en.wikipedia.org/wiki?curid=11924 |
22,884 | Game theory is a major method used in mathematical economics and business for modeling competing behaviors of interacting agents. Applications include a wide array of economic phenomena and approaches, such as auctions, bargaining, mergers and acquisitions pricing, fair division, duopolies, oligopolies, social network ... | https://en.wikipedia.org/wiki?curid=11924 |
22,885 | This research usually focuses on particular sets of strategies known as "solution concepts" or "equilibria". A common assumption is that players act rationally. In non-cooperative games, the most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a best response to the... | https://en.wikipedia.org/wiki?curid=11924 |
22,886 | A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type. Economists and business professo... | https://en.wikipedia.org/wiki?curid=11924 |
22,887 | The Chartered Institute of Procurement & Supply (CIPS) promotes knowledge and use of game theory within the context of business procurement. CIPS and TWS Partners have conducted a series of surveys designed to explore the understanding, awareness and application of game theory among procurement professionals. Some of t... | https://en.wikipedia.org/wiki?curid=11924 |
22,888 | Sensible decision-making is critical for the success of projects. In project management, game theory is used to model the decision-making process of players, such as investors, project managers, contractors, sub-contractors, governments and customers. Quite often, these players have competing interests, and sometimes t... | https://en.wikipedia.org/wiki?curid=11924 |
22,889 | Piraveenan (2019) in his review provides several examples where game theory is used to model project management scenarios. For instance, an investor typically has several investment options, and each option will likely result in a different project, and thus one of the investment options has to be chosen before the pro... | https://en.wikipedia.org/wiki?curid=11924 |
22,890 | Piraveenan summarises that two-player games are predominantly used to model project management scenarios, and based on the identity of these players, five distinct types of games are used in project management. | https://en.wikipedia.org/wiki?curid=11924 |
22,891 | In terms of types of games, both cooperative as well as non-cooperative, normal-form as well as extensive-form, and zero-sum as well as non-zero-sum are used to model various project management scenarios. | https://en.wikipedia.org/wiki?curid=11924 |
22,892 | The application of game theory to political science is focused in the overlapping areas of fair division, political economy, public choice, war bargaining, positive political theory, and social choice theory. In each of these areas, researchers have developed game-theoretic models in which the players are often voters,... | https://en.wikipedia.org/wiki?curid=11924 |
22,893 | Early examples of game theory applied to political science are provided by Anthony Downs. In his 1957 book "An Economic Theory of Democracy", he applies the Hotelling firm location model to the political process. In the Downsian model, political candidates commit to ideologies on a one-dimensional policy space. Downs f... | https://en.wikipedia.org/wiki?curid=11924 |
22,894 | It has also been proposed that game theory explains the stability of any form of political government. Taking the simplest case of a monarchy, for example, the king, being only one person, does not and cannot maintain his authority by personally exercising physical control over all or even any significant number of his... | https://en.wikipedia.org/wiki?curid=11924 |
22,895 | A game-theoretic explanation for democratic peace is that public and open debate in democracies sends clear and reliable information regarding their intentions to other states. In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept. ... | https://en.wikipedia.org/wiki?curid=11924 |
22,896 | However, game theory predicts that two countries may still go to war even if their leaders are cognizant of the costs of fighting. War may result from asymmetric information; two countries may have incentives to mis-represent the amount of military resources they have on hand, rendering them unable to settle disputes a... | https://en.wikipedia.org/wiki?curid=11924 |
22,897 | Game theory could also help predict a nation's responses when there is a new rule or law to be applied to that nation. One example is Peter John Wood's (2013) research looking into what nations could do to help reduce climate change. Wood thought this could be accomplished by making treaties with other nations to reduc... | https://en.wikipedia.org/wiki?curid=11924 |
22,898 | Unlike those in economics, the payoffs for games in biology are often interpreted as corresponding to fitness. In addition, the focus has been less on equilibria that correspond to a notion of rationality and more on ones that would be maintained by evolutionary forces. The best-known equilibrium in biology is known as... | https://en.wikipedia.org/wiki?curid=11924 |
22,899 | In biology, game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution (and stability) of the approximate 1:1 sex ratios. suggested that the 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their... | https://en.wikipedia.org/wiki?curid=11924 |
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