Differential Games of Multiple Agents and Geometric Structures

Panos M. Pardalos (), Vitaliy A. Yatsenko (), Altannar Chinchuluun () and Artyom G. Nahapetyan ()
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Panos M. Pardalos: University of Florida
Vitaliy A. Yatsenko: University of Florida
Altannar Chinchuluun: University of Florida
Artyom G. Nahapetyan: University of Florida

A chapter in Pareto Optimality, Game Theory And Equilibria, 2008, pp 267-306 from Springer

Abstract: This chapter deals with problems of differential games of multiple agents moving in a region. We describe such a game by a hierarchical structure, which can be simplified using a fiber bundle. Then, using geometric techniques, we study controllability, observability, and optimality problems. In addition, we also consider a cooperative problem when the agent's motions must satisfy a separation constraint throughout the encounter to be conflict-free. A classification of maneuvers based on different commutative diagrams is introduced using their fiber bundles representation. In the case of two agents, these optimality conditions allow us to construct the optimal maneuvers geometrically.

Keywords: cooperative game; differential games; multiple agents; hierarchical structure; Yang–Mills field; controllability; observability (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-77247-9_11

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DOI: 10.1007/978-0-387-77247-9_11

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