##### Game Theory Chapter 1, 1/16/19

What is decision Theory

I am making the decisions opposite of someone else, but at least one of us doesn't really affect the other directly

What is market based economics

I am making decisions opposite of someone else, and I know my decisions impact them, and their decisions impact me

How is the market different from Blackjack?

In decision theory, we look for an optimal choice, or path

When examining markets, we look for an equilibrium, which means we need at least two sides making decisions at the same time

Moreover, there is something being traded and at least one side consists of "price-takers"

Major Types of Markets

Perfect competition

Monopoly

Oligopoly

Monopsony

Oligopsony

Types of Markets: Lots of buyers, lots of sellers

Perfect competition

Types of Markets: Lots of buyers, but one seller

Monopoly

Types of Markets: Lots of buyers and a few sellers

Oligopoly

Types of Markets: One buyer and lots of sellers

Monopsony

Types of Markets: A few buyers and lots of sellers

Oligopsony

What are the primary components of a game?

Agents, actions, and payoffs

What is a game

A situation of strategic interaction where players' actions are interdependent.

Strategic-meant to maximize utility

Interdependent-One players outcome depends on one players actions and an others actions

Awareness- Agents know how this works

Game theory vs casinos

Most casino games are exercises in chance, so your outcome doesn't strategically depend on another player.

Games such as poker however, do depend on other players.

What is game theory

A systematic study of strategic interaction among rational players

Because games are made up of agents, actions, and payoffs, what do we need to know? Agents

How many agents?

Do they have names? Do their names matter?

What are their preferences?

Because games are made up of agents, actions, and payoffs, what do we need to know? Actions

What kinds of actions can each player take? When?

Who can see who did which action?

What outcome results?

Because games are made up of agents, actions, and payoffs, what do we need to know? Payoffs

What are the values given to outcomes

What are the final payoffs given to each agent based on the actions they took

What do we assume about agents?

That they are rational and have common knowledge

**Agents:** Rationality assumption

Players have well-defined preferences over the set of all possible actions

Players choose actions to maximize these objectives given the actions of all the other players

**Agents: **Common Knowledge assumption

The game, it's rules, and rationality are all common knowledge.

For example, x=Midterm is march 6

X is common knowledge among all the students in this class:

Each student knows x

Each student knows that each student knows x

Goes on to infinity

If knowledge stops before infinity, it isn't common knowledge. Then, it is considered k-level knowledge, and k is where it has stopped.

What is the notation for when we know that our agents are rational and have common knowledge of the game and each other's rationality

Notation: I={1, 2, 3, ...., I} <-- Whenever we have this, we are talking about agents.

Example, I={Rob, Rick, Matt, Dealer}

Agents actions study

Agents must choose actions rationally

Doesn't matter if it is the full set or subset

What is the agent's **Actions** notation

Notation:

A=A_{1}, A_{2}, ..., A_{i}

Payoffs study

We can describe any manner of rational behavior that we want

We represent preferences with a payoff function, explained on the following card

What is the payoff function

A payoff function U_{i}, represents preferences for agent i
if, for any actions a in A_{i}, and b in A_{i}.

For example, U_{i}(a) > U_{i}(b) Only if the
agent prefers a to b.

Another example,

u(McMuffin)=2 utils

u(Cheeseburger)=1 util

u(Hamburger)= 0 utils

This means that preferences aren't ordinal(definition in following card)

What does it mean when preferences are ordinal?

This means that the order matters, not necessarily the value

What is the U_{i} notation

** {U _{i}}_{iεI}**