Game Strategy (pick the lowest unrepeated number)

  • Context: High School 
  • Thread starter Thread starter kaleidoscope
  • Start date Start date
  • Tags Tags
    Game Strategy
Click For Summary
SUMMARY

The game discussed involves N players selecting a number between 0 and 100, with the objective of choosing the lowest unrepeated number. A common strategy is to select 0, based on the assumption that others will avoid it due to the belief that multiple players will choose the same number. However, a more strategic choice could be an extremely small number, such as 0.0000000000000000000000000000000000000000000001, to avoid duplication. The game lacks a pure Nash equilibrium, with a mixed strategy emerging when players randomly select from the available numbers using a uniform distribution.

PREREQUISITES
  • Understanding of game theory concepts, particularly Nash equilibrium
  • Familiarity with non-cooperative game scenarios
  • Knowledge of probability distributions and their applications
  • Basic mathematical reasoning for strategic decision-making
NEXT STEPS
  • Research "Nash equilibrium in non-cooperative games"
  • Explore "mixed strategy equilibria" and their implications
  • Study "probability distributions in game theory"
  • Examine "strategic decision-making in competitive environments"
USEFUL FOR

This discussion is beneficial for game theorists, competitive strategists, psychologists studying decision-making, and anyone interested in understanding strategic interactions in games.

kaleidoscope
Messages
66
Reaction score
0
This is a game with N players where each player secretly picks a number from 0 to 100. The winner is the player who picks the lowest unrepeated number. Which number would you pick? What would be your strategy?
 
Mathematics news on Phys.org
It's probably not the smartest number to choose, but I'd choose 0. Only because if I assume that every other player has the mentality that at least two people will choose 0, nobody would choose 0. However, if someone else thinks the same way I do, then I'll probably lose.
 
I'm thinking that more than one will have the strategy of post #2. So I'd choose 0.0000000000000000000000000000000000000000000001
 
In the non-cooperative scenario, this game has no pure Nash equilibrium. The mixed one is attained when all players pick one of the N numbers randomly, using a uniform distribution.
 
the guy who answers this1 needs to be a psychologist not a mathwiz
 

Similar threads

High School "Land capture" graph paper game
  • · Replies 13 ·
Replies
13
Views
2K
Graduate A game of seemingly mutually independent events
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Help finding winning strategies in the following tile game?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Creating a fair playing field for an odd number of players
  • · Replies 6 ·
Replies
6
Views
2K
High School Geometry Puzzle with 20 points in a cross pattern
  • · Replies 31 ·
2
Replies
31
Views
3K
High School Validating Darts Tournament Skill Levels: A Non-Intrusive Approach
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Game theory, quantum physics and the Bell inequality (paper)
  • · Replies 2 ·
Replies
2
Views
3K
Comp Sci Designing HTML+CSS for 23 toothpicks game
  • · Replies 4 ·
Replies
4
Views
2K
Game theory: competitive auction for the money in a chest
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Puzzles where both players play optimally
  • · Replies 1 ·
Replies
1
Views
8K