Game theory

"Since the graph is closed and since the image of each point under the mapping is convex, we infer from Kakutani's theorem that the mapping has a fixed point (i.e., point contained in its image). Hence there is an equilibrium point. In the two-person zero-sum case the "main theorem" and the existence of an equilibrium point are equivalent. In this case any two equilibrium points lead to the same expectations for the players, but this need not occur in general."

"The two-person iterated Prisoner’s Dilemma is the E. coli of the social sciences, allowing a very large variety of studies to be undertaken in a common framework."

"I will argue that group selection is important, contrary to the prevailing dogma among biologists. If group selection is important, Prisoner's Dilemma is not a good model for evolution. It is still an amusing toy for mathematicians and game-theorists to play with."

"I do not believe the fashionable dogma. Here is my argument to show that group selection is important. Imagine Alice and Bob to be two dodoes on the island of Mauritius before the arrival of human predators. Alice has superior individual fitness and has produced many grandchildren. Bob is individually unfit and unfertile. Then the predators arrive with their guns and massacre the progeny indiscriminately. The fitness of Alice and Bob is reduced to zero because their species made a bad choice long ago, putting on weight and forgetting how to fly. I do not take the Prisoner’s Dilemma seriously as a model of evolution of cooperation, because I consider it likely that groups lacking cooperation are like dodoes, losing the battle for survival collectively rather than individually."

"Evolutionary game theory originated as an application of the mathematical theory of games to biological contexts, arising from the realization that frequency dependent fitness introduces a strategic aspect to evolution. Recently, however, evolutionary game theory has become of increased interest to economists, sociologists, and anthropologists--and social scientists in general--as well as philosophers."

"Traditionally, game theory has been seen as a theory of how rational actors behave. Ironically, game theory... has shown... the limited capacity of the concept of rationality alone to predict human behavior. ...Evolutionary game theory deploys the Darwinian notion that good strategies diffuse across populations of players rather than being learned by rational agents. ...[A]gents choose best responses, and otherwise behave as good citizens of game theory society. But they may be pigs, dung beetles, birds, spiders, or even... s and s. How do they accomplish these feats with their small minds and alien mentalities? ...the agent is displaced by the strategy as the dynamic game-theoretic unit. ...[W]e provide agent-based computer simulations of games, showing that really stupid critters can evolve toward the solution of games previously thought to require "rationality" and high-level information processing capacity."

"Ever since Darwin read Malthus, the theory of evolution has benefited from the interaction of ecology with economics. Evolutionary game theory belongs to this tradition: it merges population ecology with game theory."

"Evolutionary game theory is one of the most active and rapidly growing areas of research in economics. Unlike traditional game theory models, which assume that all players are fully rational and have complete knowledge of details of the game, evolutionary models assume that people choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. In games that are repeated many times, low-payoff strategies tend to be weeded out, and an equilibrium may emerge."

"Evolutionary game theory is a way of thinking about evolution at the phenotypic level when the fitnesses of particular phenotypes depend on their frequencies in the population."

"Current evolutionary game theory — where ideas from evolutionary biology and rationalistic economics meet — emphasizing the links between static and dynamic approaches and noncooperative game theory."