# Game Theory: How Cooperation and Competition Work

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Try Udemy for Business- By the end of this course you will be able to understand and use the formal models of game theory to interpret situations of both cooperation and competition

- This course is a gentle introduction to game theory, a limited background knowledge of economics is required, also some background in science and maths would be of an advantage but the course is designed to be accessible to a broad audience
- The course contains limited technical vocabulary but you will need to be familiar with basic scientific vocabulary

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.

2. 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.

3. 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.

4. 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.

- This course will be particularly relevant to those in the area of economics, business management and anyone with an interest in the social sciences

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 this video we look at some of the basic features to games, we talk about the two basic forms of representation, that of the normal-form in a matrix model and that of the extensive form as a tree graph that unfolds over time. We talk about the important role of information, where games may be defined as having imperfect or perfect information and how agents may use information to their advantage. We talked about symmetrical and asymmetrical payoffs in games. We briefly look at zero-sum games and non-zero sum games where the payoffs can get larger given cooperation. Finally we talk about the distinction between a cooperative and non-cooperative game and some of the factors that create these different types of games which we will be discussing further throughout the course.

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.

In game theory, a solution concept is a model or rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts.

Pareto optimality in game theory answers a very specific question of whether an outcome can be better than the other? Pareto optimality is a notion of efficiency or optimality for all the members involved. An outcome of a game is Pareto optimal if there is no other outcome that makes every player at least as well off and at least one player strictly better off. That is to say, a Pareto optimal outcome cannot be improved upon without hurting at least one player.

Cooperation is a process by which the components of a system work together to achieve the global properties. In other words, individual components that appear independent work together to create a complex whole, greater-than-the-sum-of-its-parts system. Virtually all of human civilization is a product of our capacity to work cooperatively. Indeed the complex systems that surround us, like our global economy and technologies like a jumbo jet are a testament to our extraordinary capacity for cooperation.

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.

The game theoretical version of the social dilemma is called the public goods game. Public goods games are usually employed to model the behavior of groups of individuals achieving a common goal. The public goods game has the same properties as the prisoner’s dilemma game, but describes a public good or a resource from which all may benefit regardless of whether or not they contributed to the good.

Cooperation is a massive resource for advancing individual and group capabilities, and over the course of thousands of years, we have evolved complex networks for collaboration and cooperation which we can call institutions of various form. These institutional structures help us to solve the many different forms of the tragedy of the commons that we encounter within large societies.

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.

The Evolutionarily Stable Strategy is very much similar to Nash Equilibrium in classical Game Theory, with a number of additions. Nash Equilibrium is a game equilibrium where it is not rational for any player to deviate from their present strategy. An evolutionarily stable strategy here is a state of game dynamics where, in a very large population of competitors, another mutant strategy cannot successfully enter the population to disturb the existing dynamic. Indeed, in the modern view, equilibrium should be thought of as the limiting outcome of an unspecified learning or evolutionary process that unfolds over time. In this view, equilibrium is the end of the story of how strategic thinking, competition, optimization, and learning work, not the beginning or middle of a one-shot game.

The replicator equation is the first and most important game dynamic studied in connection with evolutionary game theory. The replicator equation and other deterministic game dynamics have become essential tools over the past 40 years in applying evolutionary game theory to behavioral models in the biological and social sciences. These models show the growth rate of the proportion of organisms using a certain strategy. As we will illustrate, this growth rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole.

The emerging combination of network theory and game theory offers us an approach to looking at situations involving many interacting agents. The central idea is that there are different individuals making decisions and they are on a network and people care about the actions of their neighbors