A Mathematical Treatment of Economic Cooperation and Competition Among Nations: With Nigeria, USA, UK, China and Middle East Examples

The book presents a careful mathematical study of Economic Cooperation and Competition among Nations. It appropriates the principles of Supply and Demand and of Rational Expectations to build the dynamic model of the Gross Domestic Products of two groups of nations which are linked up together. The first group consists of Nigeria, the US, the UK and China. The second group is made up of Egypt, the US, Jordan and Israel. The link connecting the four nations of each group is mirrored in the net export function which is broadened to include trade, debts and the inflow or the outflow of wealth from the competing and cooperating nations. This realistic models of the four interacting GDP's, a hereditary differential game of pursuit are validated with historical data from International Financial Statistic Year Book. The Mathematical model is then studied for controllability: from a current initial GDPs a better state can be attained using government and private strategies which are carefully identified. We use regression and differential equation methods to test whether the four countries are competing or cooperating. The consequences of competition or cooperation are explored. Cooperation can be realized and the growth of wealth assured because the system is controllable and we can increase the growth of GDP and then increase the coefficient of cooperation. The outcome may be unbounded growth of wealth for all concerned - the triumph of cooperation. With analogous simple examples the book shows that sufficiently cooperating systems grow unbounded and competing ones are either bounded at best, or become extinct in finite time. If competition is small, i.e. limited, or regulated the GDP's need not be extinct even after a long time. This results are in contrast with popular opinion which advocate competition over cooperation. The detailed policy implication of the cooperation analysis at one time or the other were