Mutual Knowledge

	Mutual Knowledge Mutual knowledge in game theory is information known by all participatory agents. However, unlike common knowledge, a related topic, mutual knowledge does not require that all agents are aware that this knowledge is mutual. All common knowledge is mutual knowledge, but not all mutual knowledge is common knowledge. Mutual knowledge can arise accidentally, due to a failure to design the game properly, so all players independently discover this mutual knowledge, or deliberately, due to the expected course of the game. The difference between mutual knowledge and common knowledge The difference is crucial in a co-operation game. For example, in the game depicted below, with a random event determining the payoff matrix, both players, being fully rational Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Game Theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi 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 balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. 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 mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Common Knowledge (logic) Common knowledge is a special kind of knowledge for a group of agents. There is ''common knowledge'' of ''p'' in a group of agents ''G'' when all the agents in ''G'' know ''p'', they all know that they know ''p'', they all know that they all know that they know ''p'', and so on ''ad infinitum''.Osborne, Martin J., and Ariel Rubinstein. ''A Course in Game Theory''. Cambridge, MA: MIT, 1994. Print. It can be denoted as C_G p. The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study ''Convention'' (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject of epistemic logic in general – and of common knowledge in particular – starting in the 1980s. There are numerous puzzles based upon the concept which have been extensively investigated by mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Rational Agent A rational agent or rational being is a person or entity that always aims to perform optimal actions based on given premises and information. A rational agent can be anything that makes decisions, typically a person, firm, machine, or software. The concept of rational agents can be found in various disciplines such as artificial intelligence, cognitive science, decision theory, economics, ethics, game theory, and the study of practical reason. Economics In reference to economics, rational agent refers to hypothetical consumers and how they make decisions in a free market. This concept is one of the assumptions made in neoclassical economic theory. The concept of economic rationality arises from a tradition of marginal analysis used in neoclassical economics. The idea of a rational agent is important to the philosophy of utilitarianism, as detailed by philosopher Jeremy Bentham's theory of the felicific calculus, also known as the hedonistic calculus. The action a rational age ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]