# Oligopoly games & strategies: Prisoners dilemma

##### Intros
###### Lessons
1. Oligopoly Games & Strategies: Prisoner's Dilemma
2. Definition of a Game
• Rules
• Strategies
• Payoffs
• Outcome
• We will see these in Prisoner's Dilemma
3. Rules of Prisoner's Dilemma, and Strategies
• Background of Prisoner's Dilemma
• Rules of each prisoner
• Strategies of each player
• Possible Outcomes
4. 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
5. 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
1. Understanding Game Definitions
Determine whether each action is allowed in a prisoner's dilemma.
1. Accuse each other
2. Stay silent
3. Communicate with each other
4. Negotiate with the police
5. Accuse first, then stay silent
6. Stay silent first, and then accuse.
2. Determine whether each statement is true or false in a prisoner's dilemma.
1. There are always 4 outcomes
2. Players can have more than two strategies
3. The players cannot communicate with each other.
4. Players always make choices base on their personal gain.
3. 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. 1. Describe the strategies and outcomes 2. Make the payoff matrix. 3. What is the Nash equilibrium? 4. 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. 1. Describe the strategies and outcomes. 2. Make the payoff matrix. 3. What is the Nash equilibrium? 5. 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: 1. 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. 2. 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. 3. If both increases their production 10,000 gallons a week, both firms will gain zero economic profit. 1. Construct a payoff matrix. 2. Find the Nash equilibrium. 6. 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.
1. What are the strategies of the game?
2. Construct the payoff matrix.
3. What is the Nash equilibrium?