The field of game theory came into being with Émile Borel's researches in his 1938 book ‘Applications aux Jeux des Hazard’, and was followed by the 1944 book ‘Theory of Games and Economic Behaviour’ by John von Neumann and Oskar Morgenstern. This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s.
Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology. It is also used in engineering, political science, international relations, computer science, and philosophy. Game theory attempts to mathematically capture behaviour in strategic situations, or games, in which an individual's success in making choices depends on the choices of others. While initially developed to analyse competitions in which one individual does better at another's expense such as in zero sum games, it has been expanded to treat a wide class of interactions, which are classified according to several criteria. Today, "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players (computers, animals, plants)" (Aumann 1987).
2.0 CONCEPTUAL CLARIFICATION
Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter. There are theories in many and varied fields of study, including the arts and sciences. A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content. Theories may be expressed mathematically, symbolically, or in common language, but are generally expected to follow principles of rational thought or logic (Curry, Haskel 1986).
A game is a structured activity, usually undertaken for enjoyment and sometimes used as an educational tool. Ludwig Wittgenstein was probably the first academic philosopher to address the definition of the word game. In his Philosophical Investigations, Wittgenstein demonstrated that the elements of games, such as play, rules, and competition, all fail to adequately define what games are. Wittgenstein concluded that people apply the term game to a range of disparate human activities that bear to one another only what one might call family resemblances (Wittgenstein and Ludwig 1953/2002).
Shubik observes “the essence of the Game is that it involves decision-makers with goals and objectives whose fates are intertwined. They have some control but the control is partial. Each group or individual faces a cross-purpose optimization problem. His plans must be adjusted not only to his own desires and abilities but also to those of others (In Adedeji 1989). Schelling sees it as the formal study of the rational, consistent expectations that participants can have about each other’s choices (Asobie 1987).
The game theory is based essentially upon an abstract form of reasoning, arising from a combination of logic and mathematics. Proponents of the Game Theory share the assumption that actors in the International arena are rational with respect to the goals they seek to advance. Although there may be fundamental disagreements about what these goals are, the game theoretic analyst does not assume events transpire on their own and uncontrolled. Rather, he is predisposed to assume that most foreign policy decisions are made by decision makers who carefully weigh the advantages and disadvantages likely to follow from alternative policies. This is true particularly if the stakes are high as they tend to be in international politics (Akinboye and Ottoh 2005/2007). The crux of the theory is that it is impossible for any one player to make a choice because whatever choice made by him depends largely on the...