TABLE OF CONTENTS Introduction 1 1. Basi c definitions an d preliminar y result s 2 2. Uppe r an d lowe r value o f game s of fixe d duratio n 9 3. Existenc e o f valu e fo r game s of fixe d duratio n 13 4. Existenc e o f saddl e points fo r game s of fixe d duration . Exampl e 2 6 5. Existenc e theorem s fo r generalize d pursuit-evasio n game s 2 9 6. Existenc e theorem s fo r game s of surviva l 3 7 7. Compariso n theorems the Hamilton-Jacob i equatio n 3 9 8. Game s with restricte d phas e coordinate s 4 6 9. Capturabilit y theorem s 5 2 10. TV-perso n differential game s 5 4 11. Differentia l game s with partia l differentia l equation s 5 8 12. Stochasti c differentia l game s 6 0 Bibliography 6 2 Supplementary Bibliograph y 6 5
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