Introduction to Game Theory

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What is a game?
The word game may make you think of things like poker, chess or backgammon, within the context of this course its meaning is far broader. A game is basically a decision problem in which several parties are involved. Generally these parties have different and conflicting interests, and often there is no solution to the decision problem that will make all parties happy. The parties in the conflict are normally called players (or agents), but one should keep in mind that these may just as well be firms competing for their market shares, animals fighting over a territory, children trying to get the biggest piece of cake, or politicians fighting over the distribution of budgets. We encounter very fundamental issues like rationality, expectations, fairness, power, cooperation, threats, manipulations, risk, stability. In some games everything depends on strategic possibilities of the players. In such games we also encounter information structures; what does each player know about the other player’s possibilities and goals. Does A know that B knows that A knows that B knows etc? Game Theory: Game Theory analyzes different types of games and their solution concepts. Analyzing, or solving, a game boils down to answering a mathematical question and then interpreting the result. In the games that we discuss in the Game Theory course the solution depends on strategic possibilities of the players. We will discuss the games in order of increasing strategic possibilities, which means that as the course progresses, the games become more complex. Many examples shall be discussed to clarify the issues and many exercises will be provided to learn how to compute solutions.