Game Theory

Types of games in economic theory:

1. Prisoner's Dilemma (non-cooperative game)

• Do I tell on my partner or not?

2. Coordination Games: exists with multiple strategies which can be illustrated through matrices:

• Pure Coordination: no conflict if interest or efficiency problem

• Battles of the Sexes: conflict of interest but not an efficiency problem

• Stag Hunt: an efficiency problem but no conflict of interest

3. Sequential Games: backward induction

Nash Equilibrium: set of strategies chosen by agents in a game such that no one agent would want to deviate given the strategies chosen by the others. The Nash equilibrium is defined by the strategy not the outcome.

Hotelling Problem

In the lecture example of the vendors on the beach, their options are between (0,1). So, their strategy is a unit between (0,1) as this is defined by their set. In the Hotelling example, the Nash equilibrium is 1/2

• NE: (1/2 , 1/2)

In our assessments in this module, there will always be a Nash Equilibrium, although non-existence is possible.

Coordination Game Example

• Two players

• 4 Outcomes

• Required to factor in the other players strategies

• No asymmetric Information

• Decision is to either go to boxing or theatre, given that Jack has gone to either the Boxing or Theatre, and now Jane must decide which strategy grants her the best outcome.

• The table above is considered a matrix in which the utility is displayed in each box. 

• The Nash Equilibrium is where the best strategy lies. 

• Therefore, NE(B,B), NE(T,T)

Sub-Game Perfect Nash Equilibrium in Sequential Game

Subgame perfect Nash equilibrium: 

• Incumbent firm holds a monopoly

• Entrant into market, waiting to decide so remains a 'potential entrant'

Use of tree diagrams, and a matrix to understand backward induction in the process of strategy creation.

Why OLS is BLUE

The Gauss-Markov theorem states that if your linear regression model satisfies the first 6 classical assumptions, then Ordinary Least Squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

In regression analysis, the coefficients in the equation are estimates of the actual population parameters:

• β (beta): represent the population parameter for each term in the model

• ℇ (epsilon): represent the random error that the model doesn't explain.

It is impossible to measure the entire population, so we obtain estimates denoted by:

• ^ over the betas: indicate that these are parameter estimates

• e: represents the residuals (estimates of the random error)