Bargaining (O 16, OR 7)
Reminder
We solved an extension of the ultimatum game to two periods and alternating offers:

A pie of size 1 is to be divided between two players.

Player 1 proposes a division x
The Ultimatum game
In the Ultimatum Game, Player 1 gets $100 and has to offer an allocation of the amount between
Player 2 and himself. That is, he chooses x[0,100] or an integer xcfw_0,1,2,.,100 and offers to give
Extensive
form games with perfect information
Formalities (O 5.1
5.2, OR 6.1)
Definition
An extensive game with perfect information = <N, H, P, (i)> consists of:
A set of players N.
A finit
Extensive Form Games with Perfect Information

Informal overview of the main ideas 
We would like to be able to analyze situations in which decisions are not made simultaneously.
For example, one firm decides
Maxminimization with mixed strategies
Consider a strategic game <N, (Ai), (ui)> and assume vNM preference.
A maxmin mixed strategy of player i is a mixed strategy that solves the problem:
max iAi min iAi Ui(i, i)
Evolutionary Stable Strategy (ESS)
The story

Members of a single population (people, animals) occasionally interact

Pairwise interaction

Actions taken: Inherited mode of behavior or mutation

The function
Mixed
Strategies: General notations for n
player games
Each player i can randomize among all her actions.
A mixed strategy of player i is given by i (Ai),
where
(Ai) is the set of all probability
distributions ove
Mixed strategies
Motivation
We saw that in the Odd/Even game (matching pennies), there is no pure strategy Nash equilibrium.
But if each player plays each action with probability 0.5, no one has incentive to deviate
Definitions from Class 1
Best response
For any list of strategies ai Ai
Bi(ai) = cfw_ai Ai : ui(ai, ai) ui(ai, ai), ai Ai
is the set of player is best actions given ai (the list of the other players a
The Colonel Blotto Game
o You are a commander of an army during wartime, which is about to do battle with the
enemys army
o Each commander decides how to allocate his 120 troops across 6 battlefields
o In a particular battlefield, the commander who assign