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The paper attempts to combine the traditional learning model with the recent theory of economic growth using Maddison's long-run real GDP per capita data of the three fastest growing countries in East Asia: Korea, Taiwan, and Japan. The authors first explain games of catching-up among nations, and then explain the learning coefficients of Taiwan and Korea with Japan and the United States through periods before and after World War II. The model of leaning leads to the logistic model of economic growth of convergence between two countries. Using time-series data, the coefficients of a logistic model are estimated to confirm that the real GDP per capita of Taiwan and Korea are converging to that of Japan and the United States, respectively. Similarly, Japan's GDP per capita converges to that of the United States. The time required for finite convergence for these countries is also estimated. [ABSTRACT FROM AUTHOR]