All of life is a game, and evolution by natural selection is no exception. The evolutionary game theory developed in this 2005 book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.

This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters are an outgrowth of presentations from the 11th International Symposium on Dynamic Games and Applications.

Key topics covered include:

* stochastic and differential games

* dynamic games and their applications in various areas, such as ecology and economics

* numerical methods and algorithms in dynamic games

* zero- and nonzero-sum games

* pursuit-evasion games

* evolutionary game theory and applications

The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.

This volume contains the proceedings of the US-Australia workshop on Control and Chaos held in Honolulu, Hawaii from 29 June to 1 July, 1995. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Industry, Science and Technology (Australia) under the US-Australia agreement. Control and Chaos-it brings back memories of the endless reruns of "Get Smart" where the good guys worked for Control and the bad guys were associated with Chaos. In keeping with current events, Control and Chaos are no longer adversaries but are now working together. In fact, bringing together workers in the two areas was the focus of the workshop. The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. This involves finding and using orbits in nonlinear systems which can take a system from one region of state space to other regions where we wish to stabilize the system. Control is used to generate useful chaotic trajectories where they do not exist, and to identify and take advantage of useful ones where they do exist. A controller must be able to nudge a system into a proper chaotic orbit and know when to come off that orbit. Also, it must be able to identify regions of state space where feedback control will be effective.

This vol ume contains the proceedings of the second U. S. -Austral ia workshop on Renewable Resource Management held at the East-West Center, Honolulu, Hawaii, December 9-12, 1985. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Science and Technology (Austral ia) under the U. S. -Austral ia Cooperative Science Program. The objective of the workshop was to focus on problems associated with the management of renewable resource systems. A particular emphasis was given to methods for handling uncertain elements whieh are present in any real system. Toward this end, the partiei pants were chosen so that the collective expertise included mathematical modeling, dynamical control/game theory, ecology, and practical management of real systems. Each participant was invited to give an informal presentation in his field of expertise as related to the overall theme. The formal papers (contained in this vo 1 ume) were written after the workshop so that the authors coul d util ize the workshop experience in relating their own work to others. To further encourage this exchange, each paper contained in this volume was reviewed by two other participants who then wrote formal comments. These comments (with author's reply in some cases) are attached to the end of each paper.

As society becomes stressed by economic and population pressures, in turn, nature's renewable resources become stressed by harvesting pressures. For our own survival and euphoria, it is paramount that such resources remain as their name implies and not be driven to extinction through short term programs of over exploitation. Consideration of the harvesting of renewable resources leads to a simple question that was the theme of the workshop and is the focus of these proceedings: SUPPoRe you are assigned the role of manager for a specific renewable resource eco system. How would you decide on harvesting policies so that the system can be exploited economically yet at the same time maintain the integrity of the system? This, of course, is a loaded question. First of all, it is not clear that there is ever anyone single decision maker who is able to set the rules for all of the harvesters in an exploited ecosystem. The political process is complicated and to some extent unpredictable. This aspect of the question is recognized to be important, but could not be addressed here. Assuming then that someone really is in charge, what would be involved in the * decision making process? As Clark points out, "there is no alternative but first to model the system. " We agree. However, if the original question was loaded, modeling is the adulterate."

All of life is a game, and evolution by natural selection is no exception. The evolutionary game theory developed in this 2005 book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.