Game Theory

Game Theory

Game theory is a branch of applied mathematics that is used to model multiactor interdependent decision making. Game theory is widely used in many social science disciplines, including political science, economics, sociology, and anthropology, where researchers are interested in outcomes when at least two actors interact with certain purposes.

Game theory is a method of modeling. A usual game theoretic model specifies some essential aspects of a situation of interest and tries to make logical inferences about ensuing outcomes given the initial setup. There can be a simple election model, for instance, where there are two candidates who want to win the election and n voters who want to elect the candidate who is going to make policies that are beneficial for the voters. Two candidates announce their respective policy platforms, and voters vote. Whoever gets the majority of votes wins and makes policies. Given the initial setting, the solution to the game provides logically deduced inferences about outcomes of interest, such as who can win under which conditions and which policies should follow.

In modeling a situation, a game theoretic model captures only essentials and inevitably leaves out unnecessary details. Thus, a game theoretic model does not and cannot perfectly reflect the reality. Thus, a game theoretic model may seem too abstract. Indeed, one of the common criticisms of game theory is that game theoretic models are too unrealistic. Yet abstraction is common for any kind of modeling. For instance, a model of an airplane or a model of an automobile usually does not feature every nut and bolt of an actual airplane or automobile. Instead, the models would probably have a cockpits and wings for airplanes and doors, tires, and wheels for cars, yet they would probably not have emergency oxygen masks, all cockpit buttons, and smoke detectors in the restrooms of airplane models and cup holders and detailed electrical lines connecting batteries to different parts of car models. Yet these models may still be useful for certain purposes. Similarly, a game theoretic model capturing the relationship between Congress and bureaucrats may feature only two actors even though Congress and bureaucrats are not unitary actors but rather composed of groups of individuals in reality. Congress and bureaucrats in the model would also be assumed to have a few primary goals, such as reelection and budget maximization even though there are many other potential motivations for each actor. Yet as is the case for the automobile and airplane models, the model can still be proven to be useful to study the relationship between Congress and bureaucrats.

There is no golden rule as to how abstract or realistic a model should be. In addition, there are a number of ways to model a situation by emphasizing certain aspects of the situation at the expense of other aspects being bracketed. Thus, it is hardly possible to tell if a model in itself is either right or wrong. Instead, a model can be judged by how useful and applicable it is to a modeled situation. Generally [Page 542]speaking, a researcher can make a model resemble the reality more faithfully with many details, but in doing so, the researcher has to face the usual trade-off between details and generalizability. That is, a detailed model may capture a particular situation more accurately but not be generalizable beyond the particular situation. A more abstract model, in contrast, may be more general and applicable to a broader set of situations but may seem too unrealistic to approximate a particular case. In addition, each addition of details would make the model more complicated and make the math difficult or even analytically intractable. Ultimately, the decision for the initial setup and how complicated a model should be depends on the researcher's purpose.

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