Game Theory Introduction
As we watch the news each day, many of us ask ourselves why people can’t cooperate, work together for economic prosperity and security for all, against war, why can’t we come together against the degradation of our environment? But in strong contrast to this, the central question in the study of human evolution is why humans are so extraordinary cooperative as compared with many other creatures. In most primate groups, competition is the norm, but humans form vast complex systems of cooperation. Humans live out their lives in societies and the outcomes to those social systems and our individual lives is largely a function of the nature of our interaction with others. A central question of interest across the social sciences, economics, and management is this question of how people interact with each other and the structures of cooperation and conflict that emerge out of these.
Of course, social interaction is a very complex phenomenon, we see people form friendships, trading partners, romantic partnerships, business compete in markets, countries go to war, the list of types of interaction between actors is almost endless. For thousands of years, we have searched for the answers to why humans cooperate or enter into conflict by looking at the nature of the individuals themselves. But there is another way of posing this question, where we look at the structure of the system wherein agents interact, and ask how does the innate structure of that system create the emergent outcomes.
The study of these systems is called game theory. Game theory is the formal study of situations of interdependence between adaptive agents and the dynamics of cooperation and competition that emerge out of this. These agents may be individual people, groups, social organizations, but they may also be biological creatures, they may be technologies. The concepts of game theory provide a language to formulate, structure, analyze, and understand strategic interactions between agents of all kind.
Since its advent during the mid 20th-century game theory has become a mainstream tool for researchers in many areas most notably, economics, management studies, psychology, political science, anthropology, computer science and biology. However, the limitations of classical game theory that developed during the mid 20th century are today well known. Thus, in this course, we will introduce you to the basics of classical game theory while making explicit the limitations of such models. We will build upon this basic understanding by then introducing you to new developments within the field such as evolutionary game theory and network game theory that try to expand this core framework.
In the first section, we will take an overview of game theory, we will introduce you to the models for representing games; the different elements involved in a game and the various factors that affect the nature and structure of a game being played. In the second section, we look at non-cooperative games. Here you will be introduced to the classical tools of game theory used for studying competitive strategic interaction based around the idea of Nash equilibrium. We will illustrate the dynamics of such interactions and various formal rules for solving non-cooperative games. In the third section, we turn our attention to the theme of cooperation. We start out with a general discourse on the nature of social cooperation before going on to explore these ideas within a number of popular models, such as the social dilemma, tragedy of the commons and public goods games; finally talking about ways for solving social dilemmas through enabling cooperative structures. The last section of the course deals with how games play out over time as we look at evolutionary game theory. Here we talk about how game theory has been generalized to whole populations of agents interacting over time through an evolutionary process, to create a constantly changing dynamic as structures of cooperation rise and fall. Finally, in this section we will talk about the new area of network game theory, that helps to model how games take place within some context that can be understood as a network of interdependencies.
This course is a gentle introduction to game theory and it should be accessible to all. Unlike a more traditional course in game theory, the aim of this course will not be on the formalities of classical game theory and solving for Nash equilibrium, but instead using this modeling framework as a tool for reasoning about the real world dynamics of cooperation and competition.
Game Theory Overview
This video gives an overview of game theory as part of our full course on the subject. In game theory, a game is any context within which adaptive agents interact and in so doing become interdependent. Interdependence means that the values associated with some property of one element become correlated with those of another. In this context, it means that the goal attainment of one agent becomes correlated with the others. The value or payoff to one agent in the interaction is associated with that of the others. This gives us a game, wherein agents have a value system, they can make choices and take actions that affect others and the outcome to those interactions will have a certain payoff for all the agents involved.
In game theory, a primary distinction is made between those game structures that are cooperative and those that are non-cooperative. As we will see the fundamental dynamics surrounding the whole game are altered as we go from games whose structure is innately competitive to those games where cooperation is the default position.
The social dilemma captures the core dynamic within groups requiring collective action, where there is a conflict between an individual’s immediate personal or selfish interests and the actions that maximize the interests of the group. At the heart of social dilemmas lies a disjunction between the costs to the individual and the cost to the whole, or benefits to the individual and benefits to the whole. We call this value that is not factored into the cost-benefit equation of the individual an externality, and it is externalities that create the disjunction between the parts and whole and result in the dilemma.
Evolutionary Game Theory
Classical game theory was developed during the mid 20th century primarily for application in economics and political science, but in the 1970s a number of biologists started to recognize how similar the games being studied were to the interaction between animals within ecosystems. Game theory then quickly became a hot topic in biology as they started to find it relevant to all sorts of animal and microbial interactions from the feeding of bats to the territorial defense of stickleback fish.