Game theory – the basics

I will try to summarize what I am learning this year in a sociology lecture on game theory. What is it all about? Obviously there is an inclusion of strategies, rules and all that used in computer games within the scoop of what game theory is analyzing. Everyone who wants to get into this topic has to think about some prerequisites first: what is the deal of game theory and what is it not. Games of Strategy, a textbook from Avinash Dixit and Susan Skeath is the basis for my learning and hence the article’s citations and links are related to this book in particular. I don’t know yet wether I will start summarizing this semestre’s German lectures on game theory as well but it could be possible that whenever I think there is some useful information I will publish it here, merely in German tongue then.

What it is (not) all about

We have to think in certain dichotomies to get closer to the point of game theory. At least game theory analyzes interactive decision making. In other words we could have written that it is the science of rational behavior (cf. p. 5). There is a difference between decisions and games; latter are in the one and only focus of interest of game theory. Decisions are just actions to be made without concerns about any responses or reactions. Inspite games are actions made with mutual awareness of the game’s participants. They have to look for what the other players decided.

Apart from that game theory does not look on any game that is just played and could be won by chance or with the usage of personal skills. It’s not meant to be that any skills are necessary in the games of game theory. There are a lot of strategies and moves that could be thought of as skills. At least every game that is influenced by private information and/or commitment is undoubtedly put in the focus of game theory analysis. Examples stumble one upon the other – you might want to think of sports (chess, tennis, football, and so forth) but dating, politics, economics and much more are scoops of the territory that game theory feels responsible for.

The same procedure…
or items of strategic games classification

Think of Kant who wrote that “thoughts without content are empty and notions without terms are blind”. The latter part of the sentence might stand as a reason for our further investigating in classificational items for strategic games. By doing classification we get a more subtle notion of what game theory is all about.

Strategic games maybe classified according wether they are constituted by sequential or simultaneous moves/actions. In another respect strategic games tend to be placed somewhere between the poles of (total) conflict and (some) commonality. Participants that stand in total conflict try to get the best out of every action they make. There is no chance that both will get the same gains. For that reason games played under circumstances of total conflict are called zero-sum games. They’re called like that just because of their outcome. There might be a use of participating commonly in a game, for example to make use of synergy effects when fusioning (economy). Further on one can classify strategic games wether they are played once or repeatedly and in both cases it can be subdifferentiated between games with the same or changing players. The quality of information or the amount of information a player has might classify a strategic game. Players that have full information mostly are in the position to use signals as devices. Don’t worry, in later articles every single case will be provided with an example. On the other hand a player who has less information as another one uses the device of screening. It’s just like you say something and want to hear a specific reply. Wether or not the counterpart in the game does it the way you thought of, you can collect some more facts.

Are the rules fixed or can they be manipulated? Do or even can participants cooperate or need they not. All those classifications should provide you with a small insight into what possible strategic games can be. There are a lot of everyday situations that are under a certain respect strategic games.

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