119Game Theory

Game theory is a theory dealing with the construction of rigorous models capable to describe situations of conflict and cooperation between rational decision makers. Traditionally, it serves as a foundation for decision-making in various disciplines, including economics, political campaigning, jury voting, auctions, procurement, negotiations. It points to actions that maximize some sort of payoff, subject to some constraints to be taken into account.

Theoretical minimum (in a nutshell)

To start reading this part, you should be already acquainted with the following areas of mathematics:

• Sums, and their manipulation methods,
• Basic probability theory,
• Trees, which we will be using to model the outcomes of many games,
• Basic notions of combinatorics,
• Basic notions of real analysis, in particular, derivatives of functions.

Concepts you will learn in this part of BookofProofs

• What are the basic ideas of the rational choice paradigm?
• Types of games and their characteristics, including static and dynamic games of complete and incomplete information.
• Notions of dominated and dominant strategies and the Nash equilibrium to tackle with static games of complete and incomplete information
• How to tackle games that unfold over time (dynamic games), in the case you have complete or incomplete information, including bargaining games and extended Bayesian games.

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