MAS Combat Simulation
H. Van Dyke Parunak
2. Combat Modeling
The roots of combat modeling go back well before the computer era, and follow two distinct lines, one mathematical and the other behavioral.
2.1. Mathematical Models
Mathematical models of combat are of two main types: Lanchester theory and game theory.
Lanchester Theory. In 1916, F.W. Lanchester published a set of differential equations that expressed how the change in strength of each side in a conflict varies with the current strength of the other side [11]. In their simplest form, his equations define the evolution through time of the strength of the two sides,R(t) andB(t), as a function of the effective firing ratesαR andαB of the two sides,dR/dt=−αBB(t);dB/dt=−αRR(t). His system is a version of the Lotka-Voltera equations for predatorprey populations [35]. An early application of computers to military modeling was integrating the Lanch- ester equations, and many of the militarys leading models today are still based on refinements of this model, for example, the Bonder-Farrell Attrition Algorithm equations [2].
Game Theory. Game theory was originally developed in context of economic analysis [31, 32], but after WWII, it became a central tool for military plan- ning at the DoD-sponsored RAND Institute and elsewhere. Game theory focuses on the rationality of the parties in conflict, and assumes that each seeks to maximize its own utility while recognizing that the other party is seeking to do the same.
Game theory and Lanchester theory differ in two important ways.
1. Lanchester theory models combatants as physical forces with no rationality.
Game theory assumes that players are rational and seek to maximize a utility function.
2. Lanchester theory describes the evolution of combat through time. Game theory in its simplest form is concerned with the final outcome.
In spite of these differences, the two mathematical theories treat the opposing sides as aggregates, and do not consider the detailed interactions of individual soldiers and their weapons.
2.2. Behavioral Models
Behavioral models are exemplified by wargames, either with real troops or on sand tables on which experimenters alternatively move playing pieces to explore tactics (Fig. 1). Inexpensive computers and multi-agent techniques permit models of combat in which each entity is represented by an individual computer agent.
Such models are superior to traditional mathematical models because they can capture the individual evolution of interacting entities, rather than modeling them as averages over the population. Combat interactions are strongly nonlinear, and population averages often miss important divergences in individual trajectories [27, 36]. As a result, entity-based models can often yield more realistic results than do Lanchester or game-theoretic models.
Figure 1. A physical combat simulation using a “sand table”.
A disadvantage of agent-based models is that they can require more com- putation than classical mathematical models. Fortunately, relatively simple entity models, embedded in an environment based on cellular automata, are often suffi- cient to capture much of the complexity of warfare [9]. One explanation for this outcome is the phenomenon of universality [21], which recognizes that the struc- ture of interactions may overwhelm differences in the processing carried out by individual agents.
For instance, EINSTein [9] represents an agents personality as a set of six weights, each in [-1, 1], describing the agents response to six kinds of information.
Four of these describe the number of living friendly, living enemy, injured friendly, and injured enemy troops within the agents sensor range. The other two weights relate to the models use of a childhood game, capture the flag, as a prototype of combat. Each team has a flag, and seeks to protect it from the other team while simultaneously capturing the other teams flag. The fifth and sixth weights describe how far the agent is from its own flag and its adversarys flag. A positive weight indicates that the agent is attracted to the entity described by the weight, while a negative weight indicates that it is repelled.
MANA [12] extends the concepts in EINSTein. Friendly and enemy flags are replaced by the waypoints being pursued by each side. MANA includes four additional components: low, medium, and high threat enemies. In addition, it defines a set of triggers (e.g., reaching a waypoint, being shot at, making contact with the enemy, being injured) that shift the agent from one personality vector to another. A default state defines the personality vector when no trigger state is active. In spite of their simplicity, EINSTein and MANA yield highly realistic aggregate battle dynamics.
2.3. Unmet Challenges
Entity-based models, of which multi-agent models are an instance, offer significant benefits over mathematical models. But as implemented in current simulation technology (such as Combat XXI [1] and OOS [30]), they still face significant challenges. Four merit our attention.
Fitting. Having a separate agent for each unit or soldier allows the model to capture the effects of nonlinear interactions, but requires the modeler to con- struct a model for each entity. This process, analogous to the knowledge acquisition task in the early days of expert systems, is expensive and time- consuming. Use of simple numerical reasoning as in EINSTein and MANA simplifies the problem, but the modeler still must define the correct person- ality vector for each fighter.
Closure. While agent-based models are useful tools, they are not the only meth- ods available for predicting a conflict. For example, one might want to in- corporate estimates from a Bayesian reasoner or other statistical techniques.
Because of the cost of fitting individual units, one might want to approximate the larger context for a conflict with a game-theoretic or Lanchester model, and use agent-based modeling only for a specific engagement.
Dynamism. Models have traditionally been used as a planning tool, in prepara- tion for an engagement. They show how the world might unfold, but once it actually begins to unfold, their detailed results quickly become out of date.
One would like to couple model execution to a stream of information from the developing battle and use the model as a real-time monitoring tool, along the lines of model-based control techniques in industrial applications [3].
Singularity. The strength of agent-based models (capturing individual interac- tions) is also a weakness. A single run of a model captures only one possible evolution of the world. If the number of entities is n and the model is run for t time steps, the number of possible trajectories can be on the order of nt, far too large to be sampled adequately even by many repeated runs, each yielding a single trajectory [17].
A new modeling structure, the polyagent, offers solutions to these challenges.