Game of Deception (Game Theory)

¶ … Game of Deception (Game Theory)

Developing a Game of Deception using Game Theory

Game theory is the theory of independent and interdependent decision making that 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 this author 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" (Kelly, 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. This author 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" (Edling, p. 197). Although game theory has been used for a wide range of industrial, sociological and environmental applications, historically, game theory has been used to model specific model military situations to identify superior alternatives (Schofield, 1999). Therefore, game theory 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, in the alternative, 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 were heard to lament 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. In this regard, 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 recent 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).

Of course, enemy ground vehicle operators will likely fail to cooperate with the interdiction team and will seek to avoid detection at all costs in order to fulfill their launch missions. In this regard, Castonon and his 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 combatant's strategic decisions concerning when to use a decoy vs. A missile vehicle, and when the aircraft should leave its patrol station and when to 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 Poison process and Brownian motion are variants (differential equations are used in constructing stochastic models as well as to model change in probability distributions)" (p. 197). The use of game theory for such military applications is certainly not new, but dates back to at least World War II and thereafter when concepts of zero-sum two-person games were used to evaluate weapons systems (Weintraub, 1992).

The approach advocated by Castonon et al. is also congruent with Shen and his colleagues (2007) who advise, "A Markov decision process (MDP) can effectively model the uncertainties in the noisy military environment" (p. 2). Likewise, a recent study by Blasch, Chen and Pham (2008) uses the Markov game theory to outline an approach that is capable of enhancing threat detection, validation, and mitigation for future situational awareness operations in outer space. The results of the study by Castonon and his associates 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 movements. These findings also represent the basis of the instant study, the purpose of which is described further below.

Purpose of Study

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

Methodology

To accomplish the above-stated research purpose, the proposed study will use a mixed methodology consisting of a review of the relevant peer-reviewed, scholarly and governmental literature concerning game theory in general and its application on the battlefield in particular together with a series of sample vignettes illustrating its application in real-world settings. This mixed approach is highly congruent with a number of social researchers who emphasize the need to review what is already published to determine what is known in the literature. For instance, 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). Likewise, Gratton and Jones (2003) emphasize that a review of the literature represents an essential starting point for almost all types of research projects today: "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" (Gratton & Jones, p. 51). A well conducted literature review will also succeed in identifying any existing gaps in the body of knowledge. In this regard, 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.

Importance of Study

The importance of maintaining an accurate assessment of a battlefield and its combatants cannot be overstated; however, modern technology represents a two-edged sword for the U.S. military. For instance, according to Cruz and Schumacher (2007), "Pop-up threats usually appear or disappear randomly in a battle field. If the next pop-up threat locations could be predicted it would assist a search or attack team, such as in a persistent area denial (PAD) mission, in getting a team of unmanned air vehicles (UAVs) to the threats sooner" (p. 509). Likewise, in a conventional military context, Davis and Shapiro describe anti-access and area denial as being "cost-imposing strategies," a description these authors suggest is particularly useful in the counterterrorism context. In addition, game theory can help avoid military confrontations altogether, thereby avoiding unnecessary friendly casualties. In this regard, Schofield (1999) emphasizes that, "The inevitability of armed conflict in the classical sense is not a foregone conclusion in a terrorist incident, but hinges on many variables" (p. 8). Finally, as Davis and Shapiro (2003) point out, "Projecting and sustaining power in distant antiaccess and area-denial environments is now one of the Department of Defense's key operational goals of the military transformation" (p. 42). In this environment, identifying more effective approaches to the management of these battlefield scenarios has assumed new relevance and importance.

Scope of Study

The scope of the proposed study will extend to an analysis of relevant resources published within the past 10 years (except for historical references) and in the English language.

Rationale of Study

Because resources are by definition scarce, it is vitally important for policymakers at all levels to make the most of the resources they possess and game theory appears to represent a valuable technique for maximizing the effectiveness of weapon systems today. According to Kreps (1990), "Game theory comprises formal mathematical models of 'games' that are examined deductively" (p. 7). Moreover, Read emphasizes that, "Game theory can be used to analyze the ordinary events of humans" (p. 466). Just as with more traditional economic theory, the advantages of using game theory include the following:

Game theory provides a clear and precise language for communicating insights and notions. In particular, it provides us with general categories of assumptions so that insights and intuitions can be transferred from one context to another and can be cross-checked between different contexts.

Game theory provides the ability to subject particular insights and intuitions to the test of logical consistency.

Game theory helps trace back from observations to underlying assumptions to determine what assumptions are really at the heart of particular conclusions (Kreps, 1990).

These advantages are particularly important in the context of waging war on non-state actors where the tactics involved may be focused on persistent area denial methods. As Davis and Shapiro (2003) emphasize, "When considering the future of rapid strike operations against the full range of terrorist targets, U.S. military planners must assume that adversary adaptations will include uniquely suited forms of antiaccess and area denial" (p. 43). Such uniquely suited forms of antiaccess and area denial tactics will require a more comprehensive approach than sheer firepower alone will provide. As Davis and Shapiro conclude, "These adaptations, together with the demand by senior policymakers to have viable military options against such targets, suggest that new combinations of combat power and high responsiveness may be necessary to deal with such contingencies" (p. 43).

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 by mathematicians seeking to solve the gambling problems associated with French nobility with too much time on their hands (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 yon 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. This demonstration occurs within the framework of a category of two-person zero-sum games in which chance (hazard) plays no part, at least no explicit part, and in which the 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 application of the fixed-point theorem, Von Neumann discovers the existence of a connection between the minimax problem in game theory and the saddle point problem as an equilibrium in economic theory.

1940: Von Neumann chooses the economist O. Morgenstern to assist him in the composition of what would become the first treatise of game theory. The title of their work is explicit: the theoretical understanding of games is presented as relevant to the analysis of economic behavior (Schmidt, p. 2).

Today, game theory is a popular analytical tool in economics and political science, and to a lesser degree, 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" (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 their decisions. In any event, the first player in a game has two strategies that can be used (i.e., option 1 or option 2); likewise, the opposing player has four strategies: (a) execute their option 1 regardless of what the first person does; (b) execute their option 2 regardless of what the first person does; - execute their option 1 if the first player chooses their option 1, and their option 2 if the first player chooses their option 2 (tit-for-tat); or (d) execute their option 2 if the first player chooses their option 1, and their option 1 if the first player chooses his or her option 1 (tat-for-tit) (Read, p. 466). The individual preferences are then analyzed to determine if one or the other player has a dominant strategy, in other words, a strategy that is superior for that player 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 for each decision there are two alternatives, he has eight different strategies for the whole game.

Payoffs. These are the outcomes that accrue to players depending on the choice of strategies they and their opponents make. 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. Indeed, sometimes there are multiple solution concepts, that is, more than one line of reasoning that rational actors might employ (Flanagan).

According to Kreps, game theory is divided into two branches: (a) cooperative and (b) non-cooperative game theory as follows:

In non-cooperative game theory the unit of analysis is the individual participant in the game who is concerned with doing as well for himself as possible subject to clearly defined rules and possibilities. If individuals happen to undertake behavior that in common parlance would be labeled 'co-operation,' then this is done because such co-operative behavior is in the best interests of each individual singly; each fears retaliation from others if co-operation breaks down.

In cooperative game theory, the unit of analysis is most frequently the group or, in the standard jargon, the coalition; when a game is specified, part of the specification is what each group or coalition of players can achieve, without too much reference to how the coalition would effect a particular outcome or result (Kreps).

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).

According to Kelly (2003), "A two-person zero-sum game is one in which the pay-offs add up to zero. They are strictly competitive in that what one player gains, the other loses. The game obeys a law of conservation of utility value, where utility value is never created or destroyed, only transferred from one player to another" (p. 77). The term "zero-sum game" is used to describe this because the gain achieved by one player is regarded as a loss to another; because the loss and gain cancel each other out, the net result is a sum of zero, therefore the name "zero-sum game"; in addition, this game is also known as a "constant sum game" since irrespective of the choices made or strategies used, the sum of the payoffs to both players will be a constant (Khan).

In a two-person, zero-sum game, then, the two players will always be completely competitive with opposing interests, with no possibility of, or potential benefit to be derived from, cooperation (Kelly). In this regard, Kelly adds that, "One player must win and at the expense of the other; a feature known as pareto-efficiency. More precisely, a pareto-efficiency is a situation in which the lot of one player cannot be improved without worsening the lot of at least one other player. Game theory is particularly well-suited to the analysis of zero-sum games and applications to everyday life (especially sporting contests) abound" (p. 77).

There are also two categories of zero-sum games: (a) finite and (b) infinite as follows:

Finite zero-sum games are those in which both players have a finite number of pure strategies.

Infinite zero-sum games are those in which at least one player has an infinite number of pure strategies from which to choose, but these types are relatively rare.