Questions tagged [game-theory]
Puzzles that involve strategic decision making, usually involving either competitive or cooperative choices between a number of participants.
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Revealing the least helpful of three numbers
(This is a follow-up to Guessing whether the revealed number is higher.)
They're at it again. This time Andrew is secretly shown three real numbers, all independently, randomly, uniformly chosen from ...
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Guessing whether the revealed number is higher
Consider the following game:
Two real numbers are independently, randomly, uniformly chosen from the interval [0, 1].
Andrew is secretly shown the two numbers. He must choose one of the numbers and ...
- 1,704
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How fast can you win this (very stupid) game?
You and I get together to play the following (dumb) game:
Two positive integers N and K are fixed from the outset.
We both start the game with N coins and proceed to play some number of rounds like ...
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The Ultimate Battle of two players
The Ultimate Battle is a turn-based two-player game.
Player $i$ (1 or 2) has three stats: initial hit point $P_i$, attack $A_i$, and heal $H_i$. The values can differ between players. All values are ...
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Pirate's Game with a twist!
I recently encountered the Pirate's Game and I found the solution for the malevolent pirates where the strict majority is needed for the highest ranking pirate's survival. Rules:
We have $P$ pirates ...
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How long will it take for the horse to be captured?
Source: https://open.kattis.com/problems/ambush
Problem: When Farmer Oskar doesn’t watch his cows closely enough, they tend to wander off into the forest to hunt for horse spies. To catch an enemy ...
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Another Another 6 tries to guess a number between 1-100 [closed]
Inspired by Another 6 tries to guess a number between 1-100, what is the most efficient strategy of questions requiring yes/no answers to guess the number $k$, if $k$ is formed in the following way?
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Guarantee a win in choosing numbers from extremes of a row of numbers
2n random numbers are laid in a row. We take turns to take a number. Each time, one can choose from the number on the tail or the head of the sequence/row. The one with the bigger summation wins the ...
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Rock-Paper-Scissors but rock scores double
Suppose two perfect game theorists play rock paper scissors. Scoring is slightly different:
2 points when beating scissors with rock
1 point when beating rock with paper
1 point when beating paper ...
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Can you beat random?
It is known that one cannot beat a truly random player in Rock Paper Scissors.
Here you will play a variant of the game. In this variant you are not allowed to play the same shape twice in a row. So ...
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Which parent should you start playing against?
Let $k < n$, $k$ even, $n$ odd. Mary is to play $n$ chess games against her parents, alternating between her father and mother. To receive her allowance she must win $k$ games in a row. Given the ...
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Pursuit-evasion game [closed]
A criminal has been spotted along a straight single-filed road of length $L$ at position $P$, measured from the left endpoint of the road! Two police officers arrive to the road at positions $A$ and $...
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A question from Bob to Bob
Set-up:
John and Bob are playing a game that goes like this:
Bob is alone in a completely opaque, featureless room.
Bob chooses a question, though some types of questions are off-limits, which will ...
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Don't let 'em die!
There is an 8x8 array of sleeping humans with ten feet between adjacent humans, with sides in the four cardinal directions. A hero and a villain start ten feet west of the northwest human. The hero ...
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Game of the glasses on the windowsill
The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses ...
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