Abstract:Future conflict between armed forces will occur both in the physical domain as well as the information domain. The linkage of these domains is not yet fully understood. We study the dynamics of a force subject to kinetic effects as well as a specific network effect-spreading malware. In the course of our study, we unify two well-studied models: the Lanchester model of armed conflict and deterministic models of epidemiology. We develop basic results, including a rule for determining when explicit modeling of network propagation is required. We then generalize the model to a force subdivided by both physical and network topology, and demonstrate the specific case where the force is divided between front-and rear-echelons.

W e consider an extension of Lanchester's models of conflict by studying the effect of instantaneous, global reductions in effectiveness to include changes in the underlying process. We apply this extension to a hypothetical scenario based on the battle of Iwo Jima and discuss implications for networked forces.

Harrison Schramm, Isaac Rubin and Norah Schramm investigate the impact distance learning may have had on the grades of students at a California high school

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S)12. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited 13. SUPPLEMENTARY NOTES ABSTRACTWe study cyber conflict as a two-person, zero-sum game in discrete time, where each player discovers new exploits according to an independent random process. Upon discovery, the player must decide if and when to exercise a munition based on that exploit. The payoff from using the munition is a function of time that is (generally) increasing. These factors create a basic tension: the longer a player waits to exercise a munition, the greater his payoff because the munition is more mature, but also the greater the chance that the opponent will also discover the exploit and nullify the munition. Assuming perfect knowledge, and under mild restrictions on the time-dependent payoff function for a munition, we derive optimal exercise strategies and quantify the value of engaging in cyber conflict. Our analysis also leads to high-level insights on cyber conflict strategy. SUBJECT TERMS ABSTRACTWe study cyber conflict as a two-person, zero-sum game in discrete time, where each player discovers new exploits according to an independent random process. Upon discovery, the player must decide if and when to exercise a munition based on that exploit. The payoff from using the munition is a function of time that is (generally) increasing. These factors create a basic tension: the longer a player waits to exercise a munition, the greater his payoff because the munition is more mature, but also the greater the chance that the opponent will also discover the exploit and nullify the munition. Assuming perfect knowledge, and under mild restrictions on the time-dependent payoff function for a munition, we derive optimal exercise strategies and quantify the value of engaging in cyber conflict. Our analysis also leads to high-level insights on cyber conflict strategy. vi THIS PAGE INTENTIONALLY LEFT BLANK vii

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