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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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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 ...
itspaspas's user avatar
1 vote
1 answer
177 views

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 ...
user88178's user avatar
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-1 votes
3 answers
204 views

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? ...
A Math guy's user avatar
6 votes
1 answer
752 views

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 ...
quantrader23's user avatar
4 votes
6 answers
3k views

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 ...
mousetail's user avatar
  • 268
28 votes
4 answers
5k views

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 ...
Dmitry Kamenetsky's user avatar
20 votes
8 answers
3k views

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 ...
Simd's user avatar
  • 7,845
2 votes
1 answer
189 views

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 $...
Kevin's user avatar
  • 39
1 vote
5 answers
571 views

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 ...
user110391's user avatar
4 votes
1 answer
729 views

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 ...
mathlander's user avatar
  • 1,241
17 votes
1 answer
594 views

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 ...
Feryll's user avatar
  • 2,379
2 votes
0 answers
149 views

Trippples - optimisation [closed]

Trippples Introduction Tripples (BGG) is a board game from the 1970s. It is played on an 8x8 grid, and each tile on that grid (except the corner starting tiles, and four blank tiles) contain three ...
simonalexander2005's user avatar
7 votes
4 answers
398 views

How will the wolf catch the sheep in minimum time?

A wolf is trying to catch two sheep. At time $0$ the wolf's at $(0,0)$ and the sheep are at $(1,0)$. All animals move continuously in real time and react instantaneously according to each other's ...
Eric's user avatar
  • 6,536
9 votes
3 answers
1k views

Alternative solutions to a Michael Rabin puzzle

I first heard the puzzle below around 1990 while working at Carnegie Mellon University; the puzzle was attributed to Michael Rabin. After solving it, I realized that alternative solutions are ...
Timothy Chow's user avatar
9 votes
1 answer
673 views

Toroidal tic-tac-toe

Part of the Monthly Topic Challenge #10: Möbius Strips, Klein Bottles, and other unusual topological surfaces Warm-up for topological thinking. You are playing tic-tac-toe with the usual 3x3 grid,...
quarague's user avatar
  • 1,853
17 votes
6 answers
1k views

Can you stop copy Alice?

At time 0, Alice and you both move freely at speed 1 on the plane. As each hour passes, all copies of Alice will subdivide into 2, each moving at half the speed of the parent. So if left alone, at ...
Eric's user avatar
  • 6,536
8 votes
1 answer
445 views

Stickered Dice Game

You and your friend play a game. To begin with, each of you has an unlabelled die. On the table laid in front of you are 12 stickers labelled 1-12. The first player chooses one of the stickers and ...
mintmocha's user avatar
  • 175
0 votes
1 answer
285 views

I ask you to find a game, then a place in the game and finally make a screenshot

Clues to find the game: I drive a lot. Everything I eat tends to poison me. Passion neon. Do you like kombucha? Clue for location in the game: boys, boys, boys (I’m looking for a good time) Clue ...
Lali's user avatar
  • 27
9 votes
2 answers
480 views

Moving tokens game

I've been thinking about the following two player game played on a 3x3 grid: Red goes first and players alternate in taking turns. Red moves tokens horizontally right. Blue moves tokens vertically ...
Dmitry Kamenetsky's user avatar
3 votes
2 answers
253 views

Directed Graphs from numbers

Bob and Alice play a game. Bob sends a sequence of positive numbers to Alice and using that information she forms a directed graph. For each number in the sequence, she splits it into two non-empty ...
Manish Kundu's user avatar
  • 2,684
3 votes
1 answer
185 views

Trapping the Adventurer: the Value of a Gambling Game

An Adventurer is standing on the first of eight sequential platforms, ready to advance. But a Booby-trapper is positioning a trap to catch them in a game played over several rounds. Each round, the ...
taef's user avatar
  • 199
7 votes
3 answers
1k views

Beyond earth and countries fighting for land

Consider 2 countries, A,B that have discovered a new planet, the size of Earth. They have decided to split the planet into regions of minimum area $10^3 m^2$ and maximum area $10^5 m^2$, with borders ...
Cris's user avatar
  • 189
14 votes
2 answers
689 views

Who is most likely to win all the chips?

Alice, Bob and Charlie each have 5 chips. Starting from Alice, they take turns to act in the order of Alice, Bob and Charlie. The $n$-th person to act must take a total of $n$ chips from their ...
Eric's user avatar
  • 6,536
8 votes
2 answers
899 views

What number should the first person announce?

Five people each announce a number in turn. The number must be an integer in the range from $1$ to $100$, and different from the ones already announced by others. The winner (or winners) of the game ...
Eric's user avatar
  • 6,536
26 votes
9 answers
3k views

N prisoners locked in cells

N prisoners are locked in N separate cells, numbered 1 to N. The warden visits each cell in order with a bowl. Each prisoner can decide whether to put a single coin in the bowl, depending on its ...
Eric's user avatar
  • 6,536
2 votes
1 answer
173 views

Hitting twice with different choices

This game of two players has public parameters an integer $n\ge2$, and a probability $p$ with $1/n<p\le1$. E.g. $n=4$, $p=1/3$. In the first phase of a game, a player secretly decides $n$ ...
fgrieu's user avatar
  • 383
5 votes
2 answers
684 views

The Median Game - For Money

Inspired by this interesting puzzle which was quickly solved. Five friends play a simple game with the following rules: Players play consecutively one after the other. Each player must call out a ...
SQLnoob's user avatar
  • 8,570
11 votes
1 answer
649 views

The median game

Five friends play a simple game with the following rules: Players play consecutively one after the other. Each player must call out a whole number between 1 and 10 (inclusive), such that it hasn't ...
Dmitry Kamenetsky's user avatar
0 votes
5 answers
530 views

Two wrongs can make a right

Can you construct two single-player games A and B, such that: Every time you play game A you are guaranteed to lose. Every time you play game B you are guaranteed to lose. Every time you alternate ...
Dmitry Kamenetsky's user avatar
1 vote
2 answers
395 views

Pokemon battle puzzle: Chansey vs Wobbuffet

This is a 1v1 battle between two pokemons: Chansey vs Wobbuffet. Your task is to analyze the battle and predict its outcome. Information about the battle: The battle takes place in Generation III. ...
WhatsUp's user avatar
  • 7,397
3 votes
2 answers
500 views

Three-player Nim

Suppose I'm forced to enter the game of nim with two players who are perfectly logical people. The rules is simple: We play a set number of rounds. In every round, a random number of marbles (between ...
Fajar's user avatar
  • 31
4 votes
2 answers
533 views

Catch the angel in less than 7 units of time

The devil has trapped the angel in a regular hexagram of firewalls. The perimeter of the hexagram is 12. The devil starts at the apex of the hexagram. can move at speed $1$ to leave a trajectory of ...
Eric's user avatar
  • 6,536
19 votes
4 answers
1k views

How long can you survive at the devil's playground?

The devil has trapped you in his playground. The devil knows that you can't cross over the burning boundary of his circle, so he allows you to choose a position within the circle before he starts to ...
Eric's user avatar
  • 6,536
9 votes
0 answers
355 views

A Glutton and a Split Check

N, T, A, B are arbitrary constants in this problem. I have only definitively solved the N=1 subproblem, so, if the general problem cannot be solved, I will be satisfied to mark as accepted a solution ...
Feryll's user avatar
  • 2,379
-1 votes
1 answer
288 views

The Box of Tic-Tacs

You were kidnapped and had no way of escape. The kidnapper opens the lights, and in front of you is an opened box of Tic-Tacs. He claims that he ate from 0-5 Tic-Tacs, (with 60 from the newly-bought ...
tdserapio's user avatar
7 votes
2 answers
376 views

Can the fugitive escape?

A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively. In a fugitive move, the fugitive can travel no more than a ...
Eric's user avatar
  • 6,536
4 votes
1 answer
245 views

Winning strategy in game

Context: I played this game at one point (and lost) and now I'm wondering whether it was possible to win or not. We have a hexagonal board like this: I'm defining the following terms: Each hexagon ...
Righter's user avatar
  • 143
13 votes
3 answers
898 views

Outmaneuver your opponents in the duel

A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
Eric's user avatar
  • 6,536
1 vote
1 answer
254 views

Variation of 100 prisoners [duplicate]

There are 100 prisoners, each prisoner is given a number between 1 and 100 without knowing which number, the number can repeat and not all of the numbers must be given. Each prisoner in his turn can ...
asd's user avatar
  • 11
18 votes
1 answer
654 views

Lap Theory Optimal Betting Game

Three prisoners are seated at a table. Each of them has a mobile phone on their lap, and they are not allowed to look at anyone else’s phone (and obviously no other form of communication is allowed). ...
happystar's user avatar
  • 7,664
9 votes
2 answers
562 views

Three way duel, which guns to choose?

Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
Eric's user avatar
  • 6,536
12 votes
4 answers
792 views

A packing game!

Amy and Ben are playing a game which is suggested by a genie. Amy first chooses $a,b,c\in\mathbb{R}^+$. Then a empty cuboid box with internal measurements $a+b,b+c,c+a$, and infinite supply of cuboid ...
Culver Kwan's user avatar
  • 5,600
16 votes
2 answers
734 views

Topological Nim

You and your friend's new favorite game is "topological nim": You take your favorite compact metric space $X$ and a radius $r$. Each player removes an open disk of radius $r$ from the space ...
Feryll's user avatar
  • 2,379
10 votes
2 answers
669 views

Buzzword Bingo Boss Battle!

Two bosses of different companies take turns delivering long speeches. Every speech much “claim” at least one unused square by uttering the corresponding buzzword(s) in the table below. Victory is ...
happystar's user avatar
  • 7,664
10 votes
3 answers
675 views

A game of 101 stones—win at (not quite) all costs

In the land of Humilia, a tournament game is played between two players with 101 stones in a pot between them. On each turn, a player may take up to five stones from the pot (and must take at least ...
Feryll's user avatar
  • 2,379
8 votes
3 answers
1k views

The 15 Pebbles Game

This is a game for 2 players - Each player uses a different coloured marker or pencil, there are 15 pebbles in total. Players take turns to colour 1, 2 or 3 pebbles (player chooses how many). When all ...
MetaInformation's user avatar
10 votes
3 answers
432 views

Find a good strategy to survive the multiplayer duel

Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can ...
Eric's user avatar
  • 6,536
5 votes
3 answers
435 views

Playing the Square Chess

On an ordinary chess board (8x8) without any pieces on it as a starting position, two players will alternately place a pawn on any square (unoccupied) so that the first player that form a square (...
TSLF's user avatar
  • 6,656
9 votes
2 answers
325 views

A knight chased by four knights

This is a follow up to A knight chased by three knights Two players are playing a variant of chess on a 11x11 grid. The first player controls a white knight that starts in the centre square. The ...
Dmitry Kamenetsky's user avatar
12 votes
3 answers
862 views

A knight chased by three knights

Two players are playing a variant of chess on a 8x8 grid. The first player controls a white knight that starts in the top-left corner. The second player controls three black knights that start in the ...
Dmitry Kamenetsky's user avatar