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Unformatted text preview: Lecture I-II: Motivation and Decision Theory Markus M. M¨obius February 4, 2003 1 Motivating Experiment: Guess the average Setup: Each of you (the students in this course) have to declare an integer between 0 and 100 to guess ”2/3 of the average of all the responses”. More precisely, each student who guesses the highest integer which is not higher than 2/3 of the average of all responses, will receive a prize of 10 Dollars. This game can be solved by iterated dominance. However, being smart is not enough. Those who bid typically lose badly. You have to guess how ’dumn’ all the other students in the class are. Even if everyone is supersmart, but has low confidence in the smartness of others, the winning value can be quite high. In our class we got a winning bid of 17 and 1 person walked away with 10 Dollars. 2 What is game theory? Definition 1 Game theory is a formal way to analyze interaction among a group of rational agents who behave strategically. This definition contains a number of important concepts which are dis- cussed in order: Group: In any game there is more than one decision maker who is referred to as player. If there is a single player the game becomes a decision problem. Interaction: What one individual player does directly affects at least one other player in the group. Otherwise the game is simple a series of independent decision problems. 1 Strategic: Individual players account for this interdependence. Rational: While accounting for this interdependence each player chooses her best action. This condition can be weakened and we can assume that agents are boundedly rational. Behavioral economics analyzes decision prob- lems in which agents behave boundedly rational. Evolutionary game theory is game theory with boundedly rational agents. Example 1 Assume that 10 people go into a restaurant. Every person pays for her own meal. This is a decision problem. Now assume that everyone agrees before the meal to split the bill evenly amongst all 10 participants. Now we have a game. Game theory has found numerous applications in all fields of economics: 1. Trade: Levels of imports, exports, prices depend not only on your own tariffs but also on tariffs of other countries. 2. Labor: Internal labor market promotions like tournaments: your chances depend not only on effort but also on efforts of others. 3. IO: Price depends not only on your output but also on the output of your competitor (market structure ...). 4. PF: My benefits from contributing to a public good depend on what everyone else contributes. 5. Political Economy: Who/what I vote for depends on what everyone else is voting for. 3 Decision Theory under Certainty It makes sense to start by discussing trivial games - those we play against ourselves, e.g. decision problems. Agents face situations in which they have to make a choice. The actions of other agents do not influence my preference ordering over those choices - therefore there is no strategic interaction going on. Proper games will be discussed in the next lectures.on....
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