Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Research and Training School (RTS)


Rao, C. Radhakrishna (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

It was John von-leumann who laid the foundationa of a miathematical theory of games of strategy . The climax of the pioneering period of de velopment oame in 1944 with the publication of The Theory of Gamea And Economic Behaviour by John von-Neumann and Oscar Morgenstern. Tha field of game theory ja now well established and widely diffused through the mathematical world- thanke to the auccese of thẻ volumes entitled Contributione to the theory of games and Advances in game theory . These volumes conprise a collection of contributions to the theory of games and answer some questions raised explicitly or implicitly by von-Neumann.My interest in the theory of gsmea received great stimuluo from the inspiring articles of Dr. L.s.Shapley and a number of others. Thege papera arc listed at the and of this thesis.Detailed introduction and sumhary will be given at the beginninK of each chapter., I shall now desoribe in an outline the contents of thie thesis.In chapter I, various nufficient conditiona are givera tander which an infint te game with unbounded Kernel K(x, y) posscsees a nolution, In some cases thene aufficient conditiona have been supplemented by effective necesoary Finally an application to a minimax theorem, in probability thaory is given. In chapter II, we consider the bounded pay-off QK(x,y) defined on the unit square and whone discontinuities lie on a finite number of curves of the forn y - O(x); K = 1, 2,..., n. In general such games need not ponse3s the but it is ahown that such grmes have mi value provided the sccond player a mixed atrategies are restricted to abaolutely continuous dtstributtons on the unit interval.In the last chapter a ne class of product solutiona is obtained for the product game J X) K where J a M3 X) B4 ; M3being 1-person majority game and B4being 1 - person pure bargaining game and K ia an arbitrary simple game, These solutioną need not have the property of full monotonicity in the sense of Shapley and the orem 5 or 6 of Shapley fSolutions of compound nimple games By L. S. Shapley - in Advances in game theory ] oannot prediot thege nolutions.


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