Time evolution of strategic and non-strategic 2-party competitions
Shanahan, Linda Lee
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The study of the nature of conflict and competition and its many manifestations—military, social, environmental, biological—has enjoyed a long history and garnered the attention of researchers in many disciplines. It will no doubt continue to do so. That the topic is of interest to some in the physics community has to do with the critical role physicists have shouldered in furthering knowledge in every sphere with reference to behavior observed in nature. The techniques, in the case of this research, have been rooted in statistical physics and the science of probability. Our tools include the use of cellular automata and random number generators in an agent-based modeling approach. In this work, we first examine a type of "conflict" model where two parties vye for the same resources with no apparent strategy or intelligence, their interactions devolving to random encounters. Analytical results for the time evolution of the model are presented with multiple examples. What at first encounter seems a trivial formulation is found to be a model with rich possibilities for adaptation to far more interesting and potentially relevant scenarios. An example of one such possibility—random events punctuated by correlated non-random ones—is included. We then turn our attention to a different conflict scenario, one in which one party acts with no strategy and in a random manner while the other receives intelligence, makes decisions, and acts with a specific purpose. We develop a set of parameters and examine several examples for insight into the model behavior in different regions of the parameter space, finding both intuitive and non-intuitive results. Of particular interest is the role of the so-called "intelligence" in determining the outcome of a conflict. We consider two applications for which specific conditions are imposed on the parameters. First, can an invader beginning in a single cell or site and utilizing a search and deploy strategy gain territory in an environment defined by constant exposure to random attacks? What magnitude of defense is sufficient to eliminate or contain such growth, and what role does the quantity and quality of available information play? Second, we build on the idea of a single intruder to include a look at a scenario where a single intruder or a small group of intruders invades or attacks a space which may have significant restrictions (such as walls or other inaccessible spaces). The importance of information and strategy emerges in keeping with intuitive expectations. Additional derivations are provided in the appendix, along with the MATLAB codes for the models. References are relegated to the end of the thesis.