Altruistic Agents in Dynamic Games

This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to “the game” solve the original design problem? Using the fundamentals of game theory, the book explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, the book examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.

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Quantity Precommitment and Bertrand Competition: A Dynamic Games Approach

SSRN Electronic Journal ◽

10.2139/ssrn.2560641 ◽

2014 ◽

Author(s):

Philipp Renner

Keyword(s):

Dynamic Games ◽

Bertrand Competition

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Characterization of Optimal Strategies in Dynamic Games

Journal of the Operational Research Society ◽

10.1057/jors.1982.106 ◽

1982 ◽

Vol 33 (5) ◽

pp. 496-497

Author(s):

Lyn Thomas

Keyword(s):

Dynamic Games ◽

Optimal Strategies

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Dynamic Quantum Games

Dynamic Games and Applications ◽

10.1007/s13235-021-00389-w ◽

2021 ◽

Author(s):

Vassili N. Kolokoltsov

Keyword(s):

Real Time ◽

Repeated Games ◽

Dynamic Games ◽

Quantum Control ◽

Diffusion Processes ◽

Natural Class ◽

Quantum Games ◽

Technical Problems ◽

Modern Development ◽

Starting Point

AbstractQuantum games represent the really twenty-first century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated games. In this paper, we aim at initiating the truly dynamic theory with strategies chosen by players in real time. Since direct continuous observations are known to destroy quantum evolutions (so-called quantum Zeno paradox), the necessary new ingredient for quantum dynamic games must be the theory of non-direct observations and the corresponding quantum filtering. Apart from the technical problems in organizing feedback quantum control in real time, the difficulty in applying this theory for obtaining mathematically amenable control systems is due partially to the fact that it leads usually to rather non-trivial jump-type Markov processes and/or degenerate diffusions on manifolds, for which the corresponding control is very difficult to handle. The starting point for the present research is the remarkable discovery (quite unexpected, at least to the author) that there exists a very natural class of homodyne detections such that the diffusion processes on projective spaces resulting by filtering under such arrangements coincide exactly with the standard Brownian motions (BM) on these spaces. In some cases, one can even reduce the process to the plain BM on Euclidean spaces or tori. The theory of such motions is well studied making it possible to develop a tractable theory of related control and games, which can be at the same time practically implemented on quantum optical devices.

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