Internet website http://www.foundationwebsite.org, updated 23 October 2020. Books and articles on Planetary Management and other topics from Tucson, Arizona. Copyright © 1999-2020 Joseph George Caldwell. All rights reserved.
Some mathematical theory of global nuclear war. These articles present the basic mathematical theory of global nuclear war and missile defense. (Articles written July-August 2001, summarizing work done mainly in 1967-72.)
The following articles present a mathematical solution to the problem of determining an optimal attack, i.e., an attack (allocation of weapons to targets) that maximizes a specified "payoff" function. The payoff function may be expected damage to a set of targets (e.g., population killed, targets destroyed) or any other target-related characteristic (e.g., commercial energy capacity destroyed, biodiversity threat reduction). If a defense is present (e.g., the attacker uses ballistic missiles and the defender has a national missile defense system in place), the defense is also optimized (to minimize the payoff function).
The complexity of the problem varies, depending on how much detail is considered, and on whether some form of defense is involved. The "no-defense" case applies, for example, to the use of a "suitcase-bomb" attack, or a missile attack against an enemy having no missile defense.
Optimal solutions to the problems are determined using the mathematical theory of games. The optimal solution subject to resource constraints is determined using Hugh Everett's Generalized Lagrange Multipliers (GLM). The GLM method is a very powerful optimization method that can be used to determine solutions to complex constrained-optimization problems, which involve payoff functions that are nonlinear, nonconvex, and discontinuous.
The optimal attacks used in Can America Survive? are special cases of Case 1 below.
Case 1. Optimal Attack in the Case of No Defense (suitcase-bomb attacks, missile attacks against an undefended enemy). This case is a "one-sided" optimization problem.
Case 2. Optimal Attack/Defense in the Case of Terminal Interceptors. This case is a "two-sided" optimization problem, in which the attacking side allocates missiles to targets to maximize damage, and the defending side allocates missile interceptors to each target to minimize damage. This case is an example of a zero-sum game (for which a gain in payoff for one side is a loss in payoff for the other size).
Case 3. Optimal Attack/Defense in the Case of Area Interceptors. This case, like Case 2, is a zero-sum game. It differs in that interceptors can defend more than a single target.
Case 4. General-Sum Game-Theoretic Approach to Warfare. In this case, the two sides (attacker and defender) have their own payoff functions. The situation is called a non-zero-sum game or general-sum game, or bi-matrix game. The solution is determined as the Nash Bargaining Solution, which is such that neither side may change his strategy without decreasing his expected payoff.
A Lagrangian Approach to Customer Relationship Management: Variable-Rate Pricing Strategy. This paper describes an optimization-based approach to customer relationship management (CRM), and illustrates the methodology with an application to the problem of determining a variable-rate pricing model for banking loan products. The methodology employed to solve the problem is Everett's Generalized Lagrange Multiplier (GLM) method. (9 August 2006.)
Election Campaign Strategic Planning Model. This computer-program model determines optimal allocations of campaign budgets corresponding to specified assumptions. It determines the optimal allocation by considering the election process as a two-person mathematical game, and determining the budget allocations (for both sides) that correspond to the optimal strategies for playing the game. The mathematical method for solving the game is Everett's Generalized Lagrange Multiplier method (the same method used in the defense models presented above).
An historical note on Lambda Corporation, Hugh Everett III and John Nash. Some background on the time and place in which the mathematical theory was developed. (6 April 2002, minor changes 28 April 2002)