Game Theory

Non-Strategic Situations

• Perfect competition – firms are price-takers, and they do not have to worry about the prices of their competitors

• Monopoly – no competitors to worry about

Strategic Situations

Everything in between a Monopoly and Perfect Competition

Game Theory

• Mathematical models to study strategic interactions

• An interaction can be ‘cooperative’ such as when business partners successfully collaborate on a project

• An interaction can be ‘competitive’ (or conflicting) like two or more firms fighting for market share, rival politicians in an election, etc

• Game theory is a tool-kit to study conflict and cooperation between intelligent and rational decision makers

Two Basic Models of Games

1. Simultaneously played games (Normal form/Strategic form) 

2. Sequentially played games (Extensive form) 

Simultaneously Played Games (Normal form/Strategic form)

• Simultaneously played games are the games where the players have to choose their decisions or actions simultaneously

• Simultaneous does not quite literally mean choosing at the same time; but means that the players choose a decision without knowing what others are doing

Sequentially Played Games (Extensive form)

• Moves are made sequentially, one after the other

• Players can see clearly what move have been taken so far before they make their own choice

Normal Form Game

Three elements:  

1. Players  

2. Strategies  

3. Payoffs/Utilities

   

How to Solve a Game

• There are many ways to solve a game, and different economists have many slightly different ways of reaching the same result

• However, a solution to a game must have the following qualities: 

  • The outcome is stable: This means nobody has an incentive to move from an outcome

  • The outcome is reached by rational thinking: This means players are assumed to think in a logical way to maximise their expected payoff

• One of the main methods used to then solve such a game is finding best responses and using this to identify a Nash equilibrium

Iterated Dominance

games where actions can be ‘sequentially deleted’ because they are illogical to play if our agent is rational

Repeated Games

The normal form games we have explored above are one shot games

• One Shot Games: The interaction happens just once

In reality, many games are likely to be repeated games

• Repeated Games: The interaction happens many times or periodically

There are two types of repeated games:  

1. Finitely repeated games  

2. Infinitely repeated games

Infinitely Repeated Games

Two strategies:

• Grim trigger: I will first cooperate. But as soon as you defect, I will defect for the remainder of the iterated game

• Tit for tat: I will first cooperate, then I will subsequently replicate your previous action. If you previously were cooperative, I am cooperative. If not, I am not

Tit-for-tat has been very successfully used as a strategy for the repeated prisoner's dilemma

Entry Deterrence

• Two firms: Potential entrant (player 1) and Incumbent (player 2) 

• The entrant has two choices: Enter or Stay out (of the industry) 

• If entrant stays out, incumbent gets a large profit and entrant gets zero

• If the entrant decides to enter, then incumbent must choose whether to accommodate the entrant or enter into a price war

• If incumbent starts a price war, then both firms suffer

• If incumbent accommodates the entrant, then they both obtain modest profits

Behavioural Games

People are not always self-interested. For example, sometimes they may make decisions based on their social preferences

• Inequality aversion 

• Kindness reciprocity 

• Guilt aversion

• …

People may not always best respond to each other. They may use other reasonings