# Oligopoly games & strategies: Prisoners dilemma

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##### Intros

###### Lessons

**Oligopoly Games & Strategies: Prisoner's Dilemma**__Definition of a Game__- Rules
- Strategies
- Payoffs
- Outcome
- We will see these in Prisoner's Dilemma

__Rules of Prisoner's Dilemma, and Strategies__- Background of Prisoner's Dilemma
- Rules of each prisoner
- Strategies of each player
- Possible Outcomes

__The Payoff Matrix & Nash Equilibrium__- What each player gains/loss in each outcome
- Predicting the Outcome
- Nash equilibrium
- Best choice given the action of prisoner B
- Best choice given the action of prisoner A
- Equilibrium of the Game: Worst Outcome

__Prisoner's Dilemma in Duopoly__- Collusive Agreement (Comply or Cheat)
- Possible Outcomes for Complying or Cheating
- What happens to each firm in each outcome
- Payoff Matrix & Nash Equilibrium of Duopoly

##### Examples

###### Lessons

**Understanding Game Definitions**

Determine whether each action is allowed in a prisoner's dilemma.- Accuse each other
- Stay silent
- Communicate with each other
- Negotiate with the police
- Accuse first, then stay silent
- Stay silent first, and then accuse.

- Determine whether each statement is true or false in a prisoner's dilemma.
- There are always 4 outcomes
- Players can have more than two strategies
- The players cannot communicate with each other.
- Players always make choices base on their personal gain.

**Calculating the Payoff Matrix & Nash Equilibrium in Prisoner's Dilemma**

Suppose there is a two-player game in which they cannot communicate. Each player is asked a question and must answer honestly or lie. If both answer honestly, then each receives $100. If one answers honestly and one lies, then the liar receives $500 and the honest player gets nothing. If both lie, then each player receives $50.- Suppose there are two prisoners in which they cannot communicate. Each prisoner is interrogated by the police. If both prisoners stay silent, then both will be sentenced to jail for 2 years. If both accuse each other, then both will be sentenced to jail for 4 years. If one accuses and the other stays silent, then one of them will be sentenced to jail for 7 years, and the other prisoner will be free.
**Calculating the Payoff Matrix & Nash Equilibrium with Duopoly**

Firm A and firm B are both producers of soft drinks. Both firms are trying to figure out how much soft drinks is needed to be produced. They know the following:- If both limit productions to 10,000 gallons a week, they will make a maximum attainable profit of $100,000. So, each firm gains $50,000 a week.
- If one firm produces 10,000 gallons a week and the other firm produces 5,000 gallons a week, then the one who produces 10,000 gallons will gain an economic profit of $100,000, while the other will incur an economic loss of $25,000.
- If both increases their production 10,000 gallons a week, both firms will gain zero economic profit.

- Firm A and firm B are both producers of wallets. The firms decide to collude and form a cartel to share the market equally. If neither firm cheat on the agreement, then each makes $2 million profit. If one firm cheats, then the cheater make a profit of $3 million and the complier will lose $1 million. If both cheats, they will both break even. Assume that none of the firms can monitor the other actions.