Topic 5: Game Theory

Question 1

Coordination Game

Answer 1

Players benefit from making the same, or compatible decisions
- Strategies focus on mutual benefit
- Challenge of communication and aligning choices

Question 2

Balanced Coordination Game

Answer 2

Players have the same preferences for each outcome

Question 3

Unbalanced Coordination Game

Answer 3

Players have different preferences for the outcomes but they would still benefit from coordinating, even if the outcome is not their most preferred

Question 4

Focal Point

Answer 4

When there are multiple Nash equilibria, a focal point can identify which is more likely.

A focal point is an outcome of a coordination game that is more likely to be chosen without prior communication as it stands out as natural or prominent in some way.

Question 5

Battle of the Sexes

Answer 5

Demonstrates focal points.

What movie to watch? Romcom(R), or Action(A)
Both (R,R) and (A,A) are Nash equilibria but there may be a focal point on one, making it more likely. E.g. the RomCom could be more culturally relevant, so is more likely to be picked

Question 6

Stag Hunt

Answer 6

Demonstrates challenge of predicting an outcome due to tension between cooperation and self-interest

Both players benefit from hunting the stag (S) but the risk of mistrust may cause a player to hunt the hare (H)

Question 7

Matching Pennies

Answer 7

Has no Nash Equilibria in pure strategies

Question 8

Pareto optimal

Answer 8

An outcome is one where neither player can improve their outcome without reducing the other player’s outcome

Question 9

Pareto front

Answer 9

The set of optimal trade-offs between conflicting objectives i.e. no objective can be improved without worsening the other

Question 10

Social Optimality

Answer 10

Socially optimal outcomes maximises the sum of all player’s pay-offs

Question 11

Ultimatum Game

Answer 11

Demonstrates how the behaviour of a human in real-life is different to that of a completely rational agent

• A proposer is given a sum of money and must decide how to split it with the responder
• The responder can accept the offer, receiving the proposed split, or reject the offer, with both players receiving nothing

Assuming rational agents, the proposer should offer the smallest possible amount and the responder should accept as getting something is better than nothing

• However, in real life, humans often reject low offers due to perceived unfairness

Question 12

How to Predict Behaviour in Game Theory

Answer 12

1. Eliminate any strictly dominated strategies
2. Identify any Nash equilibria
3. Use focal points to identify more likely Nash equilibria
4. Identify mixed strategies Nash equilibria
5. Identify Pareto-optimal outcomes
6. Identify socially-optimal outcomes