Game of Deception: Applying Game Theory to Battlefield Tactics

Introduction to Game Theory

Game theory is the theory of independent and interdependent decision making. It is concerned with organizational decision making wherein the outcome involves the types of decisions made by two or more autonomous players — one of which may be nature itself — and in which no single decision-maker has complete control over the outcomes (Kelly, 2003). As Kelly points out, "Obviously, games like chess and bridge fall within the ambit of game theory, but so do many other social situations which are not commonly regarded as games in the everyday sense of the word" (p. 1). Although game theory has been extended into a number of human endeavors in an effort to model real-world behaviors, its origins were focused on identifying theoretical solutions to the problems posed by uncertainty in games of chance (Schmidt, 2002).

According to Edling (2002), the term "game theory" may be misleading for some observers because the techniques involved are essentially the same as those used to develop other decision-making scenarios. Edling reports that, "Strictly speaking, game theory and decision theory are not that distinct; a decision is also said to be a game against nature, i.e., against an unintentional actor" (p. 197). Although game theory has been used for a wide range of industrial, sociological, and environmental applications, historically it has also been used to model specific military situations in order to identify superior alternatives (Schofield, 1999). Game theory therefore provides researchers with a framework that allows the modeling of various decision-making scenarios to identify the superior course of action for each player — which can consist of an outright "win" or, alternatively, the minimization of potential negative outcomes.

Statement of the Problem

Following the collapse of the Soviet Union in the early 1990s and the terrorist attacks of September 11, 2001, some observers lamented the passing of the "good old days of Communism," when the enemy was well-known and all of the actors were states with known geographic coordinates (Kelemen & Kostera, 2002). As one analyst team points out, "The abrupt ending of the Cold War has left a vacuum in our strategic thinking. Neither our institutions nor our ways of thinking about national strategy have kept pace with the stunning changes of recent history" (Summers & Morin, 1995, p. 343). By sharp contrast, today's threats are much more nebulous and uncertain, and adversaries continually seek to develop low-cost countermeasures to the high-cost technology being deployed by the United States in its ongoing war on terrorism as well as to prosecute conventional warfare. One such low-cost tactic that can diminish the effectiveness of high-technology weapons systems is persistent area denial. According to Davis and Shapiro (2003), "During the past several years, all of the [military] services have worried about the challenges of antiaccess and area denial, widely regarded as key ways in which future adversaries will seek to undermine U.S. conventional military dominance" (p. 42).

Moreover, terrorist organizations and other non-state actors have become increasingly sophisticated in their use of such low-cost countermeasures because their very survival depends on it. Davis and Shapiro add that, "Understanding that they are now at much greater risk for attack, the groups have a powerful incentive to use their own forms of antiaccess and area-denial strategies to greatly complicate U.S. military operations against them, even if found" (p. 42). In this regard, Shen, Chen, Cruz, Kwan, and Kruger (2007) note that, "In an adversarial military environment, it is important to efficiently and promptly predict the enemy's tactical intent from lower level spatial and temporal information" (p. 1). Fortunately, technological innovations have created a dynamic modern battlefield that is amenable to analysis using game theory. According to a study by Castanon, Pachter, and Chandler (2004), "The problem of persistent area denial arises in military operations, where an aircraft in a patrol area is trying to prevent ground vehicles from moving into position and launching a missile. Ground vehicles are detected as they move, and the aircraft can choose to pursue the vehicle, and destroy it if it is determined to carry a missile" (p. 3364).

Enemy ground vehicle operators will, of course, seek to avoid detection at all costs in order to fulfill their launch missions. Castanon and colleagues add that, "In order to increase the chance of successful attack, the ground vehicle may use diversionary tactics, such as sending decoy vehicles to force the aircraft to move away and examine the decoys, thus opening a safe launch window for the missile vehicle" (p. 3364). These researchers conceptualize the respective combatants' strategic decisions — concerning when to use a decoy versus a missile vehicle, and when the aircraft should leave its patrol station or pursue a vehicle — by using a two-person zero-sum Markov game framework. According to Edling (2002), "The main tool for describing stochastic processes is the stationary Markov process, of which the Poisson process and Brownian motion are variants" (p. 197). The use of game theory for such military applications is certainly not new; it dates back to at least World War II, when concepts of zero-sum two-person games were used to evaluate weapons systems (Weintraub, 1992).

The approach advocated by Castanon et al. is also congruent with Shen and colleagues (2007), who advise that "A Markov decision process (MDP) can effectively model the uncertainties in the noisy military environment" (p. 2). Likewise, a study by Blasch, Chen, and Pham (2008) uses Markov game theory to outline an approach capable of enhancing threat detection, validation, and mitigation for future situational awareness operations in outer space. The results of Castanon and associates' study determined that the use of decoys provided a distinct advantage to the adversary when the actions of the aircraft are observed; however, this advantage is removed if the aircraft can prevent the observation of its own movements. These findings also represent the basis of the present study.

Purpose, Scope, and Methodology

The purpose of this study is to provide the background and overview needed to confirm or refute the efficacy of a two-person zero-sum game approach for addressing the persistent area denial tactics described above, using the methodological approach described below.

To accomplish the above-stated research purpose, the study uses a mixed methodology consisting of a review of the relevant peer-reviewed, scholarly, and governmental literature concerning game theory in general and its battlefield applications in particular, together with a series of sample vignettes illustrating its application in real-world settings. This mixed approach is congruent with the recommendations of a number of social researchers who emphasize the need to review existing publications to determine what is already known. Fraenkel and Wallen (2001) report that, "Researchers usually dig into the literature to find out what has already been written about the topic they are interested in investigating. Both the opinions of experts in the field and other research studies are of interest. Such reading is referred to as a review of the literature" (p. 48).

Gratton and Jones (2003) likewise emphasize that a review of the literature represents an essential starting point for almost all types of research projects: "No matter how original you think the research question may be," they advise, "it is almost certain that your work will be building on the work of others. It is here that the review of such existing work is important" (p. 51). A well-conducted literature review will also succeed in identifying existing gaps in the body of knowledge. Gratton and Jones add that, "A literature review is the background to the research, where it is important to demonstrate a clear understanding of the relevant theories and concepts, the results of past research into the area, the types of methodologies and research designs employed in such research, and areas where the literature is deficient" (p. 51). Therefore, a review of the literature followed by a series of vignettes that illustrate the use of game theory to help decision-makers identify superior alternatives in a dynamic battlefield setting represents a viable and timely research approach.

The scope of the study extends to an analysis of relevant resources published within the past ten years (except for historical references) and in the English language.

Review of the Literature

Although game theory has received an increasing amount of attention in recent years, the concept actually originated in the 17th century when mathematicians sought to solve gambling problems associated with French nobility (Kelly, 2004). Originally, game theory was primarily concerned with two-person zero-sum interactions based on its origins in parlor games such as chess and cards (Kelly). According to Flanagan (1998), more recently, "Game theory emerged as a distinct intellectual enterprise in 1944 with the publication of The Theory of Games and Economic Behavior, by John von Neumann and Oskar Morgenstern. Its maturity was signaled fifty years later by the award of the 1994 Nobel Prize for economics to three eminent scholars in the field" (p. 122).

The fundamental stages of development of game theory were as follows:

1928: Von Neumann demonstrates his minimax theory within the framework of two-person zero-sum games in which chance plays no explicit part and results depend solely upon the reason of the players, not upon their ability. Such "strategic games" lend themselves naturally to an economic interpretation.

1937: Pursuing his topological work on the fixed-point theorem, Von Neumann discovers a connection between the minimax problem in game theory and the saddle point problem as an equilibrium in economic theory.

1940: Von Neumann enlists the economist Oskar Morgenstern to assist in composing what would become the first treatise of game theory. The title of their work makes the intent explicit: the theoretical understanding of games is presented as directly relevant to the analysis of economic behavior (Schmidt, 2002, p. 2).

Today, game theory is a popular analytical tool in economics and political science, and to a lesser degree in psychology, sociology, and the other social sciences (Flanagan). In sum, "Game theory is a branch of mathematics involving the creation and study of models of situations in which outcomes are interdependent on choices made by two or more actors" (Flanagan, p. 121). According to Read (2004), typical game theory scenarios present each player with a decision that he or she might or might not make, along with their preferences for the possible combinations of decisions. The first player in a game has two strategies (option 1 or option 2); likewise, the opposing player has four strategies: (a) execute their option 1 regardless of what the first player does; (b) execute their option 2 regardless of what the first player does; (c) execute their option 1 if the first player chooses option 1, and their option 2 if the first player chooses option 2 (tit-for-tat); or (d) execute their option 2 if the first player chooses option 1, and their option 1 if the first player chooses option 1 (tat-for-tit) (Read, p. 466). The individual preferences are then analyzed to determine whether one player has a dominant strategy — that is, a strategy that is superior irrespective of the action taken by the other player (Read).

Although significant variations exist, a game model typically requires the following elements:

Players. These are assumed to be rational actors weighing costs and benefits as they pursue their own goals. There must be two or more players.

Rules of the game. These define the limits of action — what can and cannot be done in the game.

Strategies. These are the choices that the players can make within the rules of the game. A strategy is a complete set of choices from beginning to end of the game. For example, if a player can make three different decisions and each decision has two alternatives, the player has eight different strategies for the whole game.

Payoffs. These are the outcomes that accrue to players depending on the strategies they and their opponents choose. Payoffs may be either ordinal or cardinal.

Solutions. A solution is the set of payoffs arising from the strategies that rational players would choose under the rules of the game. In some cases there are multiple solutions and even multiple solution concepts — more than one line of reasoning that rational actors might employ (Flanagan, 1998).

According to Kreps (1990), game theory is divided into two branches: cooperative and non-cooperative game theory. In non-cooperative game theory, the unit of analysis is the individual participant, who is concerned with doing as well as possible for themselves subject to clearly defined rules and possibilities. If individuals undertake behavior that would be labeled "cooperation" in common parlance, it is because such cooperative behavior is in the best interest of each individual; each fears retaliation from others if cooperation breaks down. In cooperative game theory, the unit of analysis is most frequently the group or coalition; when a game is specified, part of the specification is what each coalition of players can achieve, without detailed reference to how the coalition would effect a particular outcome (Kreps, 1990).

There is also a relatively recent innovation known as evolutionary game theory (EGT), which is "a formal, mathematical approach within evolutionary economics, which thus far has been mainly applied to economics as a refinement of the Nash equilibrium concept" (Villena & Villena, 2004, p. 585).

Conclusion

In a two-person zero-sum game, each player formulates a strategy while ignoring the other player's — meaning that the rationality of both players, as an expression of their maximizing strategies, should not rely on knowledge of the other player's likewise rational strategy. Simultaneously, however, the game's solution is discernible to both players only if each has some level of information concerning the strategy the other player has selected, because that strategy is also the result of a rational choice (Schmidt, 2002). Consequently, the two-person zero-sum game of deception developed by Castanon, Pachter, and Chandler (2004) appears to represent a viable approach to identifying the best course of action in a battlefield situation involving persistent area denial and decoy tactics.

References

Blasch, E., Chen, G., & Pham, K. (2008, March). A Markov game model for space threat prediction. Proceedings of the SPIE, 6974.

Castanon, D., Pachter, A. M., & Chandler, P. R. (2004). A game of deception. 43rd IEEE Conference on Decision and Control, December 14–17, 2004, Atlantis, Paradise Island, Bahamas.

Cruz, Y. L., & Schumacher, C. J. (2007, April). Pop-up threat models for persistent area denial. Aerospace and Electronic Systems, 43(2), 509–521.

Edling, C. R. (2002). Mathematics in sociology. Annual Review of Sociology, 197.

Flanagan, T. (1998). Game theory and professional mixed-strategy models. Journal of Sport Behavior, 21(2), 121–122.

Fraenkel, J. R., & Wallen, N. E. (2001). Educational research: A guide to the process. Lawrence Erlbaum Associates.

Gratton, C., & Jones, I. (2003). Research methods for sport studies. Routledge.

Kelemen, M., & Kostera, M. (2002). Critical management research in Eastern Europe: Managing the transition. Palgrave.

Kelly, A. (2003). Decision making using game theory: An introduction for managers. Cambridge University Press.

Khan, A. (2000). Cost and optimization in government. Quorum Books.

Kreps, D. M. (1990). Game theory and economic modeling. Clarendon Press.

Read, D. (2004). Biblical games: Game theory and the Hebrew Bible. Journal of the Royal Anthropological Institute, 10(2), 466–467.

Shen, D., Chen, G., Cruz, J. B., Kwan, C., & Kruger, M. (2007). An adaptive Markov game model for threat intent inference. Aerospace Conference, 2007 IEEE, 1–13.

Schmidt, C. (2002). Game theory and economic analysis. Routledge.

Schofield, M. (1999, March–April). Exercises in diplomacy: Simulating future crises. The Futurist, 23(2), 8.

Villena, M. G., & Villena, M. J. (2004). Evolutionary game theory and Thorstein Veblen's evolutionary economics: Is EGT Veblenian? Journal of Economic Issues, 38(3), 585.

Weintraub, E. R. (1992). Toward a history of game theory. Duke University Press.