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# Rounding up Game Theory

In this step we will organize these concepts and point you to some other applications of game theory in social sciences.

In the previous steps we used many concepts from game theory to analyse the kitchen problem. In this step we will organize these concepts and point you to some other applications of game theory in social sciences.

Game theory is a study of situations of cooperation and conflict. It is concerned with all interactions in which various parties are involved and the final result depends on their decisions. To talk about a game we need the following elements:

1. There are at least two players. The players may be people, companies, species, countries, political parties etc.
2. The players choose between various strategies. The strategies describe what each player can do in a given interaction. Different players can have different strategies available. The strategies are called pure if they do not require randomizing choice. When a player decides randomly we talk about mixed strategies.
3. The choices of the players determine the outcome of a game. The outcome is simply what happens when every player makes their choice.
4. Each outcome gives a certain payoff to each player. The payoffs (sometimes referred to as utilities) describe preferences of each player regarding the outcomes. In the most basic case we talk about ordinal payoffs/utilities that determine only the order of preference for the possible outcomes. However, many studies in game theory assume cardinal payoffs/utilities that are built around the concept of risk.

Games can be presented in different forms. In the previous steps we used payoff matrices and put each player, their strategies, all possible outcomes and payoffs related to these outcomes in a simple table. In game theory this form is called a normal form game. Another common form for representing games are decision trees that are called the extensive form games.

Game theory tries to find solutions to games. The first question it asks is: “what will happen?”. Two basic concepts help to answer this question:

1. Best response of a given player to the strategies chosen by the other players is the strategy that ensures the highest possible payoff to this player in the given situation. Best response is always conditional. For each possible set of choices of the other players there might be a different best response.
2. Equilibrium is an outcome that is stable in the sense that no player has an incentive to unequivocally change their strategy hoping to switch to a different outcome. For this to be true the strategy of each player has to be the best response to the strategies of the other players. This most basic concept of equilibrium in game theory is called Nash equilibrium after the famous Nobel laureate mathematician John Nash.

From the perspective of game theory virtually anything can be a game. Political science uses game theory to analyse international conflicts and decisions of political parties. Economists use it to analyse the behaviour of consumers and producers or different auction formats. Psychologists use games to uncover motivations driving people’s choices in social situations. Sociologists try to understand how to solve various social dilemmas etc.

There are many external resources on game theory. If you want simple mathematics and many interesting examples from various disciplines the book Game Theory and Strategy by Philip D. Straffin is a good place to start.