The application of game theory involves analyzing situations wherein players respond differently according to the actions of other players in an effort to maximize their payouts. For instance, according to Wei, Vasilakos, Zheng and Xiong (2010), "Game theory studies the problems in which players maximize their returns which depend also on actions of other players" (p. 254). Because countless human experiences involve this type of analysis, it is not surprising that game theory has been applied to a wide range of scenarios that involve identifying optimal decision-making processes. In this regard, Wei et al. (2010) advise, "Numerous studies have proposed game-theoretic method to solve the optimization problem of resource allocation in network systems from the viewpoint of resource owners" (p. 254). One such study, "A Game-Theoretical Approach to the Benefits of Cloud Computing," Kunsemoller and Holger (2012) actually applies a game-theoretical model which closely mirrors the Monty Hall problem's (MHP) choice scenario (discussed further below). The interaction model developed by Kunsemoller and Holger (2012) "maps both contractors' courses of action using game theory" with the goal of estimating future pricing (p. 150). The interaction model provides for the first player, the client, to use the cloud or to build its own data center. The opposing player, the cloud provider, offers three different pricing regimens with corresponding payoffs (Kunsemoller & Holger, 2012). As with the MHP, the final round of the contest allows the first player a subsequent choice to accept or decline an offer: "An extensive form game is used, as the provider is making its offer and subsequently the client is free to accept it or not" (Kunsemoller & Holger, 2012, p. 150).
Define what it meant by an application of a theory to an actual problem or situation.
Applying a theory to a real-world problem or situation means that people besides the researchers are going to be involved, an eventuality that inevitably presents numerous confounding factors. In this case, applying game theory to a real-world problem or situation can help illuminate what really motivates people to behave the way they do in different settings with dynamic features. For example, according to Gill (2011), "Game theory gives a more suitable framework in which to represent our ignorance of the mechanics of the set-up (where the car is hidden) and of the mechanics of the host's choice, than subjectivist probability" (p. 59). In some cases, researchers apply game theory appropriately, while in others, the stretch the boundaries of the theory to include so many extraneous factors as to become non-game-theory-like in nature and these issues are discussed further below.
Critically evaluate the appropriateness of the uses to which the theory has been applied and consider the following and answer them:
Are the applications premised upon an accurate understanding of the theory and its scope?
In many cases, researchers present a comprehensive and thorough understanding of game theory and its scope. For instance, a study by Yolken and Bambos (2011) provides an interactive pricing and allocating model for utility computing resources that assumes that client tasks are represented as job flows in a controlled queuing system that draws on game theory. According to the Yolken and Bambos model, "These jobs arrive to the system through a fixed, random process, are stored in a buffer, and then are serviced by the resource in a first come, first served manner" (2011, p. 166). The model is interactive by allowing an ongoing evaluation of pricing schemes based on current aggregate bid patterns among system users. In this regard, Yolken and Bambos note that, "The service rate, however, is set through an auction-like, proportional share mechanism -- users submit bids to the system operator and then receive service which is a function of their bids and the bids of the other users. Clients, therefore, must balance the delay experienced by their jobs vs. The added cost of buying additional resource capacity." (2011, p. 166). Taken together, this application of game theory is premised upon an accurate understanding of the theory and its scope as reflected by the authors' note that, "Using ideas from game theory, we show that such a scheme has a unique Nash Equilibrium and moreover that this point can be reached in a distributed, asynchronous manner" (Yolken & Bambos, 2011, p. 166).
Do the applications "go beyond" what the theory claims? One study that exaggerated the ability of game theory to predict behavior in dynamic situation was Gill (2011). In reality, the number of contestants in the MHP scenario who actually won the car after switching their choice is likely very small, even over a long period of time, since conceptually each contestant has a 50-50 chance of winning based on their original selection and the percentage of contestants who win after switching compared to those who do not is likely very small. Nevertheless, Gill (2011) emphasizes that arcane statistics have demonstrated that contestants have a statistically better chance of winning the car if they switch, but the actual number of contestants that manage to win using this formula compared to those who do not will still be relatively small, even over the course of several years.
Therefore, it would be disingenuous to suggest that contestants in the MHP scenario could stand to benefit from studying several years of old shows on video and keeping track of who won the car each day after switching and who did not to determine the optimal approach, but this is precisely what Gill (2011) argues needs to be done. In this regard, Gill (2011) suggests that, "The usual rationale for human rational expectations in economics is that humans learn from mistakes. However, the same person did not get to play several times in the final round of the Monty Hall show, and apparently no-one kept a tally of what had happened to previous contestants, so learning simply did not take place. Nobody thought there would be a point in learning!" (p. 66).
Assuming that there are five syndicated televised episodes of Monty Hall's show each week, there would be a one-in-three chance of a contestant picking the car on the first round. Because there will be at least one door left that does not contain the car whether the contestant picked the correct door or not, Monty Hall will always be able to offer a switch, whether the contestant has picked the door with the car or not. Common sense argues that at this point, contestants have a 50-50 chance of being right and winning the car whether they switch doors or not. Alas, common sense has no place in this analysis and Gill (2011) emphasizes that it is to the contestants' advantage to switch, "but the literature offers many reasons why this is the correct answer" (p. 58).
Despite being the correct answer, common sense appears to hold sway over most people when confronted with the MHP. According to Gill (2011), when confronted with the choice to switch, "Players used their brains, came to the conclusion that there was no advantage in switching, and mostly stuck to their original choice" (p. 66). Indeed, it is reasonable to suggest that there was far more at work in this decision than simply brains, and anyone can readily testify to the power of a hunch, a "gut" feeling or intuition when confronted with the need to make the right choice, a tendency that may have some cultural overtones. For instance, in the West, contestants may feel compelled to remain steadfast in their decisions as a sign of fortitude and character. In this regard, Gill (2011) notes that common sense prevails at this point: "There would be a much larger emotional loss to their ego on switching and losing, than on staying and losing. Sticking to…