Interdependence, preferences, and beliefs
In this post, we introduce the building blocks of game theory: strategic interdependence, preferences and beliefs. This will allow us to discuss the game structure, rationality, and common knowledge in later posts.
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Strategic interdependence
What complicates and fascinates the study of social interaction is the idea of strategic interdependence. Whether you’re cooperating or competing with somebody else, your best course of action often depends on what the other person is doing.
Infinite regress
Strategic interdependence sometimes invokes the problem of infinite regress. This is where Person A’s decision depends on Person B, and Person B’s decision depends on Person A, which depends on Person B, and so on. One goal of game theory is to solve situations with strategic interdependence without succumbing to infinite regress.
“Game theory focuses directly on the most pressing issue of all: finding the right strategies and making the right decisions. … [It] is particularly effective when there are many interdependent factors, and no decision can be made in isolation from a host of other decisions.”
Adam Brandenburger, & Barry Nalebuff. (1996). Co-opetition.
Strategic situations
A strategic situation describes the environment, the people (or players), their choices (or actions) and the consequences of said choices. To specify and analyse a strategic situation in game theory, we need to know two things about the players: (1) their preferences and (2) their beliefs.
Preferences
Preferences describe someone’s inclination or predisposition towards alternatives, choices, or outcomes. To describe preferences in game theory, economists tend to make two simplifying assumptions: completeness and transitivity.
Completeness
The first assumption is complete preferences. That is, people must know what they like and dislike. If given a choice between two products, they can tell you which they prefer more (or if they prefer them equally).
Transitivity
The second assumption is transitive preferences. That is, if you prefer apples to bananas, and bananas to oranges, then you also prefer apples to oranges. Transitivity is a form of consistency.
Utility
If preferences are complete and transitive, economists can describe preferences with numbers. They call this utility. If you prefer apples to oranges, then the utility you attach to apples is higher than that of oranges. Utility allows us to rank and compare preferences using numbers. In this way, we are also assuming that people with complete and transitive preferences take actions to maximize their utility.
Beliefs
To belabor the point, your utility depends not only on your actions, but on the actions of others as well. It follows that to make decisions (and maximize utility), you need to form beliefs about what others might do. People form beliefs in many ways. Some develop beliefs through experiential learning and repeated interactions. Others develop beliefs through simulated introspection and reasoning.
Self-awareness, empathy and theory-of-mind
Beliefs and preferences are the building blocks of decision-making. They are implicit in almost every choice that people, businesses, and nations make. Of course, many factors determine a person’s beliefs and preferences. This includes culture, genetics, history, and so on. So it’s important to recognize that payoffs are subjective; and that people make decisions based on how they perceive things to be.
It follows that to analyze situations well, we have to understand how people perceive. Great decision-makers exhibit higher self-awareness, empathy, and theory-of-mind. These attributes help them to understand the beliefs and preferences that underpin their reasoning and the reasoning of others. Bad decision-makers, by contrast, tend to impose their own values in their judgement of others. They wrongly assume that everybody will think and act in the same way they do.
Further reading
- Strategic interdependence, preferences, and beliefs — The building blocks of game theory
- Extensive and normal form games — The structure of strategic situations
- Common knowledge, rationality, and reasonableness in introductory game theory
- Dominant strategies, dominated strategies and iterative deletion — Simplifying the game
- Nash equilibrium — A fundamental solution concept, and the hallmark of game theory
- Sequential games and subgame perfect Nash equilibrium