# Game Theory Homework

## Homework

### Homework 1

- Do some online research and reading about zero sum games. Write a report with at least 200 words and must include the following:
- What are zero sum games?
- Find two examples of zero sum games and EXPLAIN why they are zero sum games.

### Homework 2

- Game theory analyzes competitive situations to determine possible, probable, and optimal outcomes. One way to illustrate all possible outcomes for the prisoner's dilemma is the
`payoff bimattrix`

, as shown below:

Using the prisoner's dilemma as an example and at least 200 words to explain:

- what a
`dominant strategy`

is - what the
`Nash Equilibrium`

is

**Your explanation must be related to the example.**

### Homework 3

- Game theory is used in a variety of fields such as political science, sociology,and economics.
- Exam the following situation carefully:

Two pubs (aka the two players): Each one of two pubs charges its own price for a beer, either £2, £4, or £5. The cost of obtaining and serving the beer can be neglected. It is expected that 6000 beers per month are drunk in a bar by tourists, who choose one of the two pubs randomly, and 4000 beers per month are drunk by natives who go to the pub with the lowest price, and split evenly in case both pubs offer the same price. What prices would the bars select?

- To illustrate how to compute the payoffs for one of the possible situation, lets assume pub A charges £2 and pub B charges £4, then all natives will choose bar A.Therefore bar A will serve 4000 beers to the natives, and 3000 beers to tourists, serving 7000 beers in total, making 7000 x 2 =£14000. Pub B will only serve 3000 beers to tourists, making 3000 x 4 = £12000. The partially finished payoff bimatrix will look like this:

£2 | £4 | £5 | A | |

£2 | ||||

£4 | £14k, £12k | |||

£5 | ||||

B |

- Task 1: Copy and Paste the above table and finish the payoff bimatrix.
- Task 2: Identify the prices for both pubs that is Nash Equilibrium and explain why.