The Money Pot
Trust and Ultimatum Games
UGBA 143: Game Theory and Business Decisions
PAYDAY. NOW I HAVE TEN BUCKS.
I HAVE A MONEY POT. FOR EVERY DOLLAR THAT I LEAVE IN IT, THERE WILL BE THREE DOLLARS THE NEXT MORNING.
SO IT'S A DEAL?
1
2
The G

Overview
So far:
Mixed Strategies
UGBA 143: Game Theory and Business Decisions
Used Nash equilibrium to solve games Strategic outcome in which no player would unilaterally deviate to choose another strategy
Next:
What happens when we cannot find a

Three kingdoms
Ancient China, around 200AD
Three Kingdoms
UGBA 143: Game Theory and Business Decisions
Empire was divided into three parts Three kingdoms:
Wei (under House of Cao) Shu (under House of Liu) Wu (under House of Sun)
Main Question:

Overview
So far, we have looked at:
More Than Two Players
UGBA 143: Game Theory and Business Decisions
Normal form games Continuous games Typically, between two players Today: More complex strategic situations Many players
1 2
Cournot competit

Spring 2008, UGBA 143
Homework 6 Solution
Problem 1 (Price Competition)
Profit = Revenue - Cost Define A as profit for firm A, B as profit for firm B Total profit of A is: Profit/Unit * Total Quantity = (pA - 2) * QA Where QA 10 - pA a) Therefore,

Spring 2008, UGBA 143
Homework 1 Solution
1. (Pooled Testing)
General Set-up: Individual Testing: N tests (N = number of donors). Pooled Testing: at least 1 test, but possibly N more tests. p = probability of a given donor to be HIV-positive Note th

Spring 2008, UGBA 143
Homework 2 Solution
1. (Oil Drilling) a) We can first draw a simple probability tree as below:
i.)
We first want to find the probability of finding oil, given a favorable report. Recall Bayes rule, P(A|B) = P(A & B) / P(B). I

Spring 2008, UGBA 143
Homework 3 Solution
Problem 1 a) The decision tree for this problem is as follow:
Therefore, the best decision is to bid $1M dollars and the expected payoff for this decision is $69,000
b) In order to calculate the value of k

Spring 2008, UGBA 143
Homework 4 Solution
Problem 1
Here are the three game trees, with payoff in $1000s. The black dots represent the branches that will be chosen:
-5,-5 a Y -7,0 B Y -7,-7 N -7,0 Y 0,-7 2,2 c Y 2,2 B Y 2,2 N Y A N 0,2 B N -5,-5 A

Nash equilibrium
A set of strategies in which no player would
Nash Equilibrium
UGBA 143: Game Theory and Business Decisions
unilaterally switch to another alternative Previous examples:
Prisoners' Dilemma: both confess Location Game: both locate at

Overview
Last Lecture:
Best Response
UGBA 143: Game Theory and Business Decisions
Introduced notion of dominance Strategies that are uniformly good / bad to the decision maker, no matter what others do Today: Idea of "best response" Strategies that

Introduction to Uncertainty
UGBA 143: Game Theory and Business Decisions
One of the three boxes contains a prize; the other two are empty After choosing one of them (e.g. pink), one of the other boxes (e.g. red) is opened and revealed to be empty Wil

h is How muc se? in my ca
Expected Monetary Value
UGBA 143: Game Theory and Business Decisions
h will How muc ff? I knock o
1
2
Previous lecture
Probability models:
Summarize the set of all possible scenarios Estimate probabilities using data

Decision Making under Uncertainty
Decision Trees
UGBA 143 Game Theory and Business Decisions
So far: situations involving a single decision Practical business scenarios:
Multiple choices: Happen at different points in time Inter-related: Future pro

Overview
The Search Problem
UGBA 143: Game Theory and Business Decisions
Many practical scenarios involve a "search problem": to continue searching or to stop?
Drug development Product design Consumer shopping behavior Buying a house Marriage and h

Decision Trees - Overview
Displaying Alternatives
Value of Information
UGBA 143 Game Theory and Business Decisions
Adding Data Choosing Course of Action Using New Information
1
2
V-Haul Moving Company
Decision: dispatch small truck ($120) or lar

The Story
Pirates of the Caribbean
UGBA 143: Game Theory and Business Decisions
A group of five pirates has found a chest filled with 100 gold coins Need to decide how to split it They take turns to propose a motion, specifying how many coins each

Multi-Period Games
Game Trees
UGBA 143: Game Theory and Business Decisions
Can be represented using a "game tree" (also called extensive-form game) Each node represents a decision maker Each branch represents a possible alternative Each end of the

Two Smart Pigs
Dominant Strategies
UGBA 143: Game Theory and Business Decisions
Big Pig and Small Pig Food bin with dispenser at one end and lever at other end Pressing lever dispenses 600g of food and burns some calories (equivalent to 50g of food

Spring 2008, UGBA 143
Homework 5 Solution
Problem 1
a) The strategies below are truly final offers from labor union (L) and management (M), and the outcomes represent their losses (in cents, compared with their initial offers), based on the final wa