correlated with the Trustee's perception of what he or she thought the Investor epected to be repaid. These models hinge on delicate details of iterated beliefs (.s belief about B's belief about .s fairness), so they are more technically complicated but can also eplain a wider range of results (see Benabou and Tirole, 2006; Dillenberger and Sadowski, 2006). Models of this sort are also better equipped to explain deliberate avoidance of information. For example, in dictator games where the dictator can either keep nine dollars or can play a ten-dollar dictator game (knowing the Recipient ill not know which path was chosen), players oten choose the easy nine dolar payment (Dana, Cain and Dawes, 2006). Since they could just play the ten-dolar game and keep all ten dollars, the ten-dollars sacriice is presumably the price paid to avoid knowing that another person knows you have been selish (see also Dana, Weber and Kuang, 2007).
1. Course Description
This is an introductory course in game theory, which will provide you with mathematical tools for analyzing strategic situations ‐ your optimal decision depends on what other people will do. In particular, we will study central solution concepts in game theory such as Nash equilibrium, subgame perfect equilibrium, and Bayesian equilibrium. Game theory has been widely recognized as an important analytical tool in such fields as economics, management, political science, phycology and biology. To illustrate its analytical value, we will cover a variety of applications that include international relations, development, business competition, auctions, marriage market, and so forth. There is no prerequisite for this course, although some background on microeconomics and familiarity of probabilistic thinking would be helpful.
Strategy and Outcome
Strategy in dynamic game = Complete plan of actions What each player will do in every possible chance of move.
Even if some actions will not be taken in the actual play, players specify all contingent action plan.
You and your n − 1 roommates (n ≧ 2) each have five hours of free time that could be used to clean your apartment. You all dislike cleaning, but you all like having a clean apartment: each person i’s payoff is the total hours spent (by everyone) cleaning, minus a number c (> 0) times the hours spent individually cleaning. That is,
Players can reach Nash equilibrium only by rational reasoning in some games, e.g., Prisoners’ dilemma.
However, rationality alone is often insufficient to lead to NE. (see Battle of the sexes, Chicken game, etc.) A correct belief about players’ future strategies
5. Bayesian Nash Equilibrium (12 points)
There are three different bills, $5, $10, and $20. Two individuals randomly receive one bill each. The (ex ante) probability of an individual receiving each bill is therefore 1/3. Each individual knows only her own bill, and is simultaneously given the option of exchanging her bill for the other individual’s bill. The bills will be exchanged if and only if both individuals wish to do so; otherwise no exchange occurs. That is, each individuals can choose either exchange (E) or not (N), and exchange occurs only when both choose E. We assume that individuals’ objective is to maximize their expected monetary payoff ($).
e z . The prices of the three goods are given by (p, q, 1) and the consumer’s wealth is given by ω.
(a) Formulate the utility maximization problem of this consumer.
(b) Note that this consumer’s preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).