SMU H3 Map
- Content map: SMU H3 Game Theory Map
What is Game Theory?
Definition
- Study of strategy and information, which influences decision-making
- Maximising utility given the information in a particular environment
- Takes into account the actions of other players
What Makes Up a Game?
Players
- Agents playing against each other in the game
Strategies
- The options that the players have
- The potential actions players can employ
Information Structure
- The sequence of moves
Payoffs
- Rewards or potential outcomes
- Shaped by the strategies of players
Types of Games
By Sequence
- Simultaneous: Players do not know what others choose
- Sequential: Players take turns and know the outcomes of the others’ choices
By Payoff
- Zero-Sum: Winner and loser
- Non-Zero-Sum: Players can jointly do better
By Information
- Complete Information: Players have information about all parts of the game
- Incomplete Information: Players do not have information about all parts of the game
Assumptions
Rationality of Players
- Maximise personal utility
- Capable of figuring out how
- Does not exclude altruistic behaviours
- Does not exclude different payoffs
- Ability to figure out the best plan of action works against experienced players
Common Knowledge
- Players are aware of how the game works
- Players know that other players are rational
Equilibrium
- Each player is doing their best given what the other is doing
- It is a stable situation or outcome
- No player has an incentive to switch to a different outcome
21 Flags Game
Details
- Sequentially make choices
- Perfect information
Rules
- There are 21 flags
- Each turn, a player can take 1, 2, or 3 flags
- The goal is to be the one to take the last flag
Strategy
- Use backward induction
- Set the game indicatour as the number of flags left
- Draw up a table:
| No. of Flags Left | Optimal Choice |
|---|---|
| 1, 2, 3 | (Win) Take all |
| 4 | (Lose) Any choice |
| 5 | Take 1 |
| 6 | Take 2 |
| 7 | Take 3 |
| 8 | (Lose) Any choice |
Beauty Contest Game
Details
- Simultaneous choices
- Perfect information
Rules
- Pick a random number
- All numbers are averaged
- The person with the number closest to half of the average wins
Strategy
- In the first round, the average of random numbers will likely be 50
- Half of the average is 25
- Iteratively, the game state evolves as:
- 25 → 12.5 → 6.25 → 3.125 → … → 0
- If everyone chooses 0, the outcome is also 0