Zero-sum game in the context of "Peace studies"

A conflict continuum is a model or concept various social science researchers use when modeling conflict on a continuum from low to high-intensity, such as from aggression to irritation to explosiveness.

The mathematical model of game theory originally posited only a winner and a loser (a zero-sum game) in a conflict, but was extended to cooperation (a win-win situation and a non-zero sum game), and lets users specify any point on a scale between cooperation, peace, rivalry, contest, crisis, and conflict among stakeholders.

Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, individuals, economic and social groups, etc. The rivalry can be over attainment of any exclusive goal, including recognition.

Competition occurs in nature, between living organisms which co-exist in the same environment. Animals compete over water supplies, food, mates, and other biological resources. Humans usually compete for food and mates, though when these needs are met deep rivalries often arise over the pursuit of wealth, power, prestige, and fame when in a static, repetitive, or unchanging environment. Competition is a major tenet of market economies and business, often associated with business competition as companies are in competition with at least one other firm over the same group of customers. Competition inside a company is usually stimulated with the larger purpose of meeting and reaching higher quality of services or improved products that the company may produce or develop.

Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of behavioral relations. It is now an umbrella term for the science of rational decision making in humans, animals, and computers.

Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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. His paper was followed by Theory of Games and Economic Behavior (1944), co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

Air supremacy (as well as air superiority) is the degree to which a side in a conflict holds control of air power over opposing forces. There are levels of control of the air in aerial warfare. Control of the air is the aerial equivalent of command of the sea.

Air power has increasingly become a powerful element of military campaigns; military planners view having an environment of at least air superiority as a necessity. Air supremacy allows increased bombing efforts, tactical air support for ground forces, paratroop assaults, airdrops and simple cargo plane transfers, which can move ground forces and supplies. Air power is a function of the degree of air superiority and numbers or types of aircraft, but it represents a situation that defies black-and-white characterization. The degree of a force's air control is a zero-sum game with its opponent's; increasing control by one corresponds to decreasing control by the other. Air forces unable to contest for air superiority or air parity can strive for air denial, where they maintain an operations level conceding air superiority to the other side, but preventing it from achieving air supremacy.