# Game Theory ++

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## Objectives

### Developing the Information Technology and Algorithm learning strands, specifically:

• You will use software to create and edit presentations with images and text to show how The Pirate Game works.
• When researching a new game and it's theory you will evaluate and repurpose content for your own use.
• Using either a pay off matrix or tree you will show how a game works algorithmically.

## Introduction: Game Theory ++

### Document It: The Birthday Paradox

• In a group of 30 students what do you think the chances of two people sharing a birthday are?
• Open a text editor and write down your answer as a percentage.
• Watch the video…
• Were you correct?
• What was the correct answer?
• Can you explain it to the student next to you?

### Learn It: The Pirate Game

The scenario

• There are 5 rational pirates, A, B, C, D and E.
• They find 500 gold coins.
• They must decide how to distribute them.
• The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.
• The pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Each pirate would prefer to throw another overboard, if all other results would otherwise be equal. Each pirate is very greedy but values his life the most.
• What would be the strategy proposed by A?

Check out this video for the solution

### Badge It Silver

• Make a short (3-5 slide) PowerPoint presentation to show Pirate A what s/he should do.

### Revise It: Pay Off Matrix

• A good way to represent Game Theory examples is to use a pay off matrix.
• This is also called the normal form.
• Here is one we could use for the Prisoner's dilemma:
• The players and their possible actions are on the outside of the table. The outcomes are added in the inside of the table.

### Learn It: Trees

• Another good way to represent Game Theory examples is to use a tree.
• This is also called the extensive form.
• Here is one we could have used for the Prisoner's dilemma:
• Everytime there is a decision you make a new branch.

### Badge It: Gold / Platinum

• Here is a list of some 'games' we haven't covered yet:
• Stag Hunt
• Battle of the Sexes
• The Centipede Game
• The Beauty Contest
• Chicken
• Hawk/Dove game
• Diner's dilemma
• Dollar Auction
• Traveller's dilemma

You need to explain in a Word or Powerpoint file the game theory principles of one of the above games, such as:

• number of players
• payoffs
• actions / decisions that are available to the player
• strategy to 'win'
• You should show a graphical version of the outcomes as either a matrix or a tree.

The quality of your written answer will determine whether you are awarded Gold or Platinum.