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Peace War Game
Peace war game is an iterated game originally played in academic groups and by computer simulation for years to study possible strategies of cooperation and aggression. As peace makers became richer over time it became clear that making war had greater costs than initially anticipated. The only strategy that acquired wealth more rapidly was a " Genghis Khan", a constant aggressor making war continually to gain resources. This led to the development of the "provokable nice guy" strategy, a peace-maker until attacked.N.R. Miller"Nice Strategies Finish First: A Review of ''The Evolution of Cooperation''" ''Politics and the Life Sciences'', Association for Politics and the Life Sciences, 1985. Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor. The Hanseatic League for trade and mutual defense appears to have originated from just such concerns about seaborne raiders. The peace war game is a variation of the iterated prisoner ...
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Mongol Empire Map
The Mongols ( mn, Монголчууд, , , ; ; russian: Монголы) are an East Asian ethnic group native to Mongolia, Inner Mongolia in China and the Buryatia Republic of the Russian Federation. The Mongols are the principal member of the large family of Mongolic peoples. The Oirats in Western Mongolia as well as the Buryats and Kalmyks of Russia are classified either as distinct ethno-linguistic groups or subgroups of Mongols. The Mongols are bound together by a common heritage and ethnic identity. Their indigenous dialects are collectively known as the Mongolian language. The ancestors of the modern-day Mongols are referred to as Proto-Mongols. Definition Broadly defined, the term includes the Mongols proper (also known as the Khalkha Mongols), Buryats, Oirats, the Kalmyk people and the Southern Mongols. The latter comprises the Abaga Mongols, Abaganar, Aohans, Baarins, Chahars, Eastern Dorbets, Gorlos Mongols, Jalaids, Jaruud, Kharchins, Khishigten, Khorchins ...
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Deterministic Algorithm
In computer science, a deterministic algorithm is an algorithm that, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. Formally, a deterministic algorithm computes a mathematical function; a function has a unique value for any input in its domain, and the algorithm is a process that produces this particular value as output. Formal definition Deterministic algorithms can be defined in terms of a state machine: a ''state'' describes what a machine is doing at a particular instant in time. State machines pass in a discrete manner from one state to another. Just after we enter the input, the machine is in its ''initial state'' or ''start state''. If the machine is deterministic, this means that from this point onwards, ...
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Sun Tzu
Sun Tzu ( ; zh, t=孫子, s=孙子, first= t, p=Sūnzǐ) was a Chinese military general, strategist, philosopher, and writer who lived during the Eastern Zhou period of 771 to 256 BCE. Sun Tzu is traditionally credited as the author of ''The Art of War'', an influential work of military strategy that has affected both Western and East Asian philosophy and military thinking. Sun Tzu is revered in Chinese and East Asian culture as a legendary historical and military figure. His birth name was Sun Wu ( zh, t=孫武, s=孙武, first=t) and he was known outside of his family by his courtesy name Changqing ( zh, t=長卿). The name ''Sun Tzu'' by which he is more popularly known is an honorific which means "Master Sun". Sun Tzu's historicity is uncertain. The Han dynasty historian Sima Qian and other traditional Chinese historians placed him as a minister to King Helü of Wu and dated his lifetime to 544–496 BCE. Modern scholars accepting his historicity place the extant text of ...
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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing to it ...
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Herbert Gintis
Herbert Gintis (February 11, 1940 – January 5, 2023) was an American economist, behavioral scientist, and educator known for his theoretical contributions to sociobiology, especially altruism, cooperation, epistemic game theory, gene-culture coevolution, efficiency wages, strong reciprocity, and human capital theory. Throughout his career, he worked extensively with economist Samuel Bowles. Their landmark book, ''Schooling in Capitalist America'', had multiple editions in five languages since it was first published in 1976. Their book, ''A Cooperative Species: Human Reciprocity and its Evolution'' was published by Princeton University Press in 2011. Life and career Gintis was born in Philadelphia, Pennsylvania, where his father had a retail furniture business. He grew up there and later in Bala Cynwyd (just outside Philadelphia). Gintis completed his undergraduate degree at the University of Pennsylvania in three years, one of which was spent at the University of Paris, and ...
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Subgame Perfect
In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players' behavior from that point onward should represent a Nash equilibrium of the continuation game (i.e. of the subgame), no matter what happened before. Every finite extensive game with perfect recall has a subgame perfect equilibrium. Perfect recall is a term introduced by Harold W. Kuhn in 1953 and ''"equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves"''. A common method for determining subgame perfect equilibria in the case of a finite game is backward induction. Here one first considers the last actions of the game and determines w ...
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Game
A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching a World Chess Championship, chess championship. On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who is a player. A toy and a game are not the same. Toys generally allow for unrestr ...
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Economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on glossary of economics, these elements. Other broad distinctions within economics include those between positive economics, desc ...
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Probabilities
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ...
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Optimization (mathematics)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ...
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Nash Equilibrium
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. 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 their's 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 ...
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Payoff Matrix
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 that ...
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