for confused ideas.
— George Stigler
We would like to view social behavior as scientists and seek any "natural laws" that determine this behavior. Models of self interest offer one candidate for such laws. These models are relatively simple, powerful in their predictions, and might apply to all social behavior.
While we do examine both strengths and weaknesses of these models, we leave it to others to provide detailed empirical support or refutation of these models in these applications, but we do intend to demonstrate that these hypotheses should, at a minimum, be considered seriously because of their simplicity, their power, and their potentially wide scope.
As we contruct these models, we also illustrate the process of building models of social behavior. You will see how our predictions and our level of understanding change when we alter our assumptions, when we make seemingly innocuous changes to the feasible choices available, and when we focus on different characteristics that we expect to occur in equilibria. We hope that this experience improves your judgment when you create and modify models of social behavior or at least when you criticize (constructively, of course) models that others create.
The noblest pleasure is the joy of understanding.
— Leonardo DaVinci
We have 3 primary objectives:
- Develop skills in models of self interest: decision theory and game theory
- Learn through real applications throughout the social sciences
- Be accessible to undergraduates and general readers
Develop skills in models of self interest: decision theory and game theoryEdit
Our first objective for this course is to introduce you to models of self interest, that is, those based upon the mathematics of decision theory and game theory, and to allow you to develop skill with these models and their use for predicting and explaining social behavior. Social behavior, in general, involves actions taken by individuals that, at least when aggregated over a group, affect other individuals. We want to predict and explain this behavior. Viewing this as scientists, we would like to discover, in effect, any “natural laws” that determine this behavior, if not for all environments then for some. As with any scientific search for natural laws, science takes any candidates for such natural laws and their associated models of behavior, however obtained, determines consequences that must occur if they are to hold, and ultimately tests these predicted consequences against experience. This process is continually repeated with new candidates for natural laws, candidates that now come from incremental modifications of the best performing models and occassionally from models based upon a new approach. Over time, we find potential natural laws and models that predict and explain actual experience better than the alternatives. Thus, at least eventually, we find more accurate predictions and more powerful explanations, those which are simpler or applicable to a wider variety of environments. If almost all practitioners conclud that such a set of natural laws and their associated model is more successful than other candidates, and they adopt it as their best explanation for the phenomena under study, then this model would offer a paradigm for their field.
One candidate for such a law of social behavior, one that may offer the foundation for a paradigm for each of the social sciences, is that individuals behave to further their own self interest. Models of individuals furthering their own self interest are formalized with either decision theory or game theory. Decision theory is the mathematics of optimizing behavior, where choices are made that further self interest against an environment that does not change in response to these choices. In decision theory, each individual’s choices can be considered independently of choices that any other individual makes. It can be the foundation of either rational choice models or of evolutionary models. Game theory, building upon the foundation of decision theory, is the mathematics of strategic decisions, decisions where the value of the outcome to each individual depends upon the actions that other individuals take as well as actions that the decision maker takes herself. The rival’s choices may be influenced by the first individual’s choices. In game theory, an individual’s choices are interdependent with other individual’s choices. These "choices" might actually be rational choices that individuals make, or they may be the implicit "choices" that natural selection or cultural selection make, in that other alternatives become less frequent in later populations.
but they only take root in
minds well prepared to receive them.
— Joseph Henry
Our second objective for this course is to introduce you to these models of self-interested individuals through many of the actual applications that social scientists have actually wrestled with. We believe this is valuable for three reasons.
First, and most important, we conclude that a hypothesis that behavior is based upon self interest should be considered seriously throughout the social sciences. In the tradition of a good liberal arts education that highlights the interconnections between various fields, this course centers on the use of common models within these many, varied fields. We introduce you to models of individuals furthering their own self interest primarily through applications of these models over all areas of social behavior, whether the concern is competition versus cooperation; individuals acting alone or in alliances; or the use of money, sex, violence, or power. These models are applied to environments where individuals make rational choices, where natural selection favors the spread of the expression of some genes over others, or where cultural selection favors the spread of some ideas over others.
These applications come from the disciplines of economics, political science, psychology, biology, anthropology, and philosophy. Practioners in these disciplines have adopted these models to varying degrees. These models provide the foundation of the current paradigm for two of these disciplines, economics and biology, and for two fields within two more disciplines, positive political economy within political science and evolutionary psychology within psychology. These models and modifications of them are the leading contenders in cognitive science within psychology and within behavioral economics. In other fields, these models remain controversial.
We especially introduce these models outside of those disciplines where they are not yet a core of their paradigms, not only because these models show us interconnections between disciplines, but also because any success in these new environments shows these models to be stronger. Data consistent with predictions from any model seen to apply over more environments are less likely to be due to chance or artifacts of a specific environment. Further, for those social sciences that do not now have models of self interest as a core of their paradigms, great research opportunities exist transplanting well-known tools into new fields.
With each of these applications, we determine some of the predicted consequences from these models. We also describe briefly whether these consequences appear consistent or inconsistent with observations that others have made, but we largely leave the empirical testing to others with more expertise in these fields. We conclude that this hypothesis, that individuals further their own self interest, yields predictions that appear consistent with actual social behavior within many environments; it is relatively simple, though more subtle than it might appear at first. We believe these models, or modifications of them, could apply to a tremendously wide scope of environments where social behavior occurs in all of them.
The focus on these models of self interest that can provide a foundation for a paradigm that can be shared across all social behavior is a unique feature of this material over other courses or books on game theory or decision theory. Even though knowledge passes through disciplinary walls only with difficulty in almost all universities, especially through many of these disciplinary walls, we want the practioners and students in all of these disciplines to see beyond their own walls and see the greater power these models have because of their tremendous scope. No other course or book covers the wide scope of social behavior that this material does.
Second, we believe that constructing useful mathematics as we see the need for it in these applications better motivates why this mathematics has been developed and why various concepts are important, which in turn, better motivates most students to consider these concepts in greater depth. The usual approach of constructing the mathematics and then illustrate the math with simplified, idealized "stick figure" applications leaves some students cold, especially students that have not yet developed an appreciation for the beauty or even the usefulness of mathematics. The richer applications do require more words, but in this situation, we feel that these additional words ease understanding. Presenting decision theory and game theory in this manner, developing richer applications first and the math as necessary, makes this course unusual but we hope this approach is more effective for you.
Third, we believe that considering this wide range of social behavior and the incremental construction of more sophisticated models will help you develop better judgment when considering what elements of an environment should be included within a model that you will find useful for your purposes. We take care to consider the effect of various assumptions, when it's useful to incorporate more elements of the environment within the model, and when its more useful to make knowingly false assumptions. Making good choices of what to include within a model requires good judgment.
Be accessible to undergraduates and general readersEdit
Our third objective for this course is to make this material accessible to any undergraduate or general reader willing to examine social behavior through a mathematical prism, say at the level of a relatively mathematically adept sophomore. Our presentation primarily presumes some mathematical maturity, as we look at the world through these mathematical models, but not a great deal. As a test of this maturity and for some of the content, we presume the student has had a first calculus course; we do not presume any mathematical background beyond this one calculus course. To serve these students as well as the more advanced students, we intend to stress the intuition behind the questions, arguments, and conclusions, but without losing the rigor in any analysis considered for that application. In doing this, we do not present some questions, arguments, or conclusions in their most general form. We omit arguments or proofs that are not particularly insightful for the application. Some proofs we place in appendices. References should lead more advanced readers to any greater depth that they desire.
We introduce you to these models of self interest and their applications in four parts, roughly in order of their technical complexity. In each part, we apply the models developed across the social sciences, and depending upon the discipline these models may be applied to individuals making rational decisions, to natural selection favoring behavior that tends to follow with individuals having some particular DNA over other possibilities, to culture selection favoring behavior associated with some particular ideas over others, or to some combination of these mechanisms.
Decision theory provides the framework for many important models throughout the social sciences, but we are primarily interested in many of its concepts and tools that we need for both decision theory and game theory. Decision theory provides an infrastructure for us to develop models based upon furthering one's self interest. Preferences that are consistent or rational allow us to order feasible choices. We can express such choices as maximization problems: it's as if the individual makes a choice that maximizes the value of a "utility" function. We can even add uncertainty, further consistency requirements on our preferences, and describe that individual as maximizing his expected "utility."
The first part of our material introduces you to decision theory through applications in business, economics, political science, biology, and psychology. For some of these applications, we expect the individual to act as a rational decision maker, and we predict this outcome with our models. For others, we don't expect this exact mechanism to work, but we expect the individual to act as if he were a rational decision maker, while other elements of his environment, maybe the institutions in which he makes his choices or repeated experience, lead him to make these choices over time. We predict these outcomes with the same models. And for still other applications, a "dumb" evolutionary process is at work and over time an equilibrium is attained, and we can describe these outcomes too with these same models.
Game theory provides a taxonomy for interdependent interactions based on self interest. As with all good models, although such taxonomies may miss many crucial details in the particular application, they do capture basic strategic aspects of various situations, allowing us to better predict and explain outcomes for similar situations and to make linkages between applications. We intend to strengthen our common-sense intuition by starting with simple applications that we understand fairly well, and then in stages, consider slightly more compelx environments with the same tools where our existing intuitions are less reliable. Over time, as we see enough applications, we strengthen our intuitions and ultimately understand these interdependent environments more deeply.
The second part of our material introduces you to static games, games in which all players choose their own strategies simultaneously. These are the simplest games, so they are the best place to learn some of the most important game-theoretic concepts, and they also provide the framework for what have been the most important contributions of game theory so far in its application. We consider all that is feasible when we define the game's strategic form, and then we predict outcomes to occur in equilibrium for such situations by the characteristics that we expect of any equilibria. We will consider applications to market power in economics, strategic voting in political science, fight or flight responses in biology, strategic international trade policy, and sexual strategies in biology.
The third part of this material introduces you to dynamic games with complete information and their applications. The language of games in their extensive form, which we compare and contrast with their strategic form, permits us to ask questions about the dynamics of games that allow individuals to take actions that are contingent upon previous actions taken by others. These more sophisticated strategies may allow more cooperation and more efficient outcomes than are possible without them. We consider applications to the common resource problem in economics, bargaining, collusion in economics, reciprocity in animal behavior, the development of cultural norms in small towns versus large cities, the development of ethics, incentives for firms to merge, and the coordination of behavior with communication.
Incomplete Information GamesEdit
The fourth part of this material introduces you to dynamic games with incomplete information and their applications. With incomplete information, a player does not know with certainty what game he is playing, but some players may have some proprietary information, generally about their own payoffs. With these games, a player may learn about his environment or about the characteristics of other players from actions that others take. Such possibilities also allow for the opportunity for individuals to reveal or disguise the actual environment to other individuals. With these games, we see moral hazard, adverse selection, and signaling in the context of insurance, education, and used cars.
A recurring thread throughout this material is determining when individuals following their self interest is also in the interest of the group. In many situations, observers have seen what appear to be examples of altruism, the behavior of individuals that helps others but harms themselves. Are these examples of situations where models of self interest fail? In what situations can self-interested individuals cooperate with each other for the greatest benefit for the group?
In some of these situations, the simplest model leads directly to efficient behavior, so that following individual self interest is clearly mutually advantageous. In others, the simple model leads to inefficient behavior and enough cooperation for efficiency has not occurred. In these cases, we examine extensions of these models, usually creating a related dynamic game, and find six types of modifications that can lead to greater cooperation:
- kin selection — Individuals may sacrifice to help family members, but from the gene's point of view they are acting to promote this expression of the gene in later populations.
- Coasian bargaining — Individuals may choose to bargain and voluntarily accept income transfers that then modify their incentives enough to lead to an outcome that aids everyone.
- reciprocity — Individuals may choose to aid other individuals, even if it harms them in the short run, if they expect the recipients of this aid to reciprocate, and this swapping of favors may lead to an outcome that aids everyone.
- reputations — Individuals may be able to choose with whom they interact, and information is available that allows them to identify who has cooperated with others in the past, so that more individuals cooperate, yielding an outcome that aids everyone.
- relatively isolated sub-groups — In some situations, a general population splits into sub-groups and the success of these sub-groups depends upon this cooperation, so that when the general population re-forms more of the cooperators have survived.
- moral authority — Some individuals may promote the use of some behavioral rules that if followed would tend to lead to outcomes that aid everyone, offering their approval to individuals that follow them and their disapproval to those that don't, and the value of this approval or disapproval is enough for some individuals in some situations to follow these behavioral rules.
Ultimately, the behavior that we predict in these situations promotes the individual's self interest, even though the behavior may look altruistic to an outside observer. These extensions show how additional cooperation can occur so that the group's interests are pushed as far as possible, but they are not based upon altruistic behavior.
The biggest drawback resulting from trying to both examine applications throughout the social sciences and make the discussion accessible to undergraduates is the greater length of exposition required. Even so, the reading tends to be easier (less dense) than most alternative presentations of decision theory and game theory, and no student is expected to cover every application in detail. Whatever your background beyond a first calculus course, you may pick a path of interesting applications through this material while still understanding the major insights that these models of self interest provide. We mark particularly advanced sections with an asterisk. Once all of this material has been compiled, even after offering abriged versions of much of the best related literature for you, we find that covering all of the material here is not possible in a single undergraduate course. Nevertheless, this material offers several selective paths through it that remain coherent. If you are a social science student, one fruitful path is to focus on the basic tools plus applications in your discipline but only sample applications in the other disciplines. A non-social science student can fruitfully sample across the social sciences more evenly. To help you do choose applications more easily for the path that you choose, the following table indicates chapters or sections that deal with basic tools or applications in various disciplines.