Just a recap today…
A game is composed of players or the interacting parties, rules or “who can do what”, and results or outcomes. Game theory is build atop of other theories, with each representing the three components of a game:
– decision theory
– representation theory
– solution theory
Decision Theory – is an extension of the von Neumann-Morgenstern decision theory that relate to making a decision under uncertainty. Decision theory relates to game theory in that it provides a way to represent preferences. Games are all about preferences and as such utility of the chosen preference.
Representation Theory – allows a formal way of representing rules of a give game. Two representation theories pertain to our discussion: normal form and extensive form.
Normal form: complete plan that considers all contingencies are presented at the start of the game. It has a static view of the game in how it is played.
Extensive form: it is like a decision tree or a flow chart in that each level of the tree is build only when the node has been reached. Players have choices and those choices are made in real-time
Solution Theory – it deals with how to assign solutions to games. It works based on the premise that each player is looking out for itself. One of the main solution concepts that we will talk about is Nash’s Equilibrium which basically states that no one player can change its strategy and improve its utility.
Game theory puts these three theories together to try and explain a social interaction. A solution prescribes how rational players should behave and not how they would actually behave in the real-world.