Game theory is a fairly modern branch of mathematics, originally developed by the Hungarian-born American mathematician John Von Neumann (1903-1957) and the German-born American economist Oskar Morgenstern (1902-1977) to solve problems in economics.Such that p 1,p 2, q 1,q 2 are all nonnegative and p 1 +p 2 =1 and q 1 +q 2 =1. In mixed strategies, each play picks a probability profile P1 =(p 1,p 2)=p and P2=(q 1,q 2)=q.
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