Optimal control for competitive-cooperative systems: Modeling flexible coalitions in tomorrow's competitive world

摘要

The last years have witnessed a dramatic shift of the world's military, political, and economic paradigm from a bi-polar competitive gridlock to a more fluid, multi-player environment. This change has necessarily been followed by a re-evaluation of the strategic thinking and by a reassessment of mutual positions, options, and decisions. The essential attributes of the new situation are modeled by a system of nonlinear evolution equations with competitive/cooperative interactions. The mathematical setting is quite general to accommodate models related to military confrontation, arms control, economic competition, political negotiations, etc. Irrespective of the specific details, all these situations share a common denominator, namely the presence of various players with different and often changing interests and goals. The interests, ranging from conflicting to consensual, are defined in a context of interactions between the players that vary from competitive to cooperative. Players with converging interests tend to build up cooperative coalitions while coalitions with diverging interests usually compete among themselves, but this is not an absolute requirement (namely, one may have groups with converging interests and competitive interactions, and vice-versa). Appurtenance to a coalition may change in time according to the shift in one's perceptions, interests, or obligations. During the time evolution, the players try to modify their strategies as to best achieve their respective goals. An objective functional quantifying the rate of success (payoff) vs. effort (cost) measures the degree of goal attainment for all players involved, thus selecting an optimal strategy based on optimal controls. While the technical details may vary from problem to problem, the general approach described here establishes a standard framework for a host of concrete situations that may arise from tomorrow's next competition.