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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11
votes
4answers
690 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 ...
16
votes
2answers
606 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 ...
8
votes
2answers
471 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 ...
6
votes
2answers
347 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 ...
7
votes
3answers
341 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 ...
10
votes
3answers
258 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 ...
5
votes
3answers
359 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 (...
8
votes
2answers
203 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 ...
10
votes
3answers
696 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 ...
5
votes
2answers
207 views

Simple game of dice - what is the optimal strategy?

The game is pretty simple, whoever reaches 50 first wins, but there are a few important details: 2 players, one die. Players take turns. Rolled values are simply added up If you roll a 6, however, ...
27
votes
5answers
6k views

Shortest game of Monopoly

This video claims that the fastest game of monopoly involves 4 turns and 9 rolls of the dice. I am wondering if this is actually the shortest game or can we do better in theory? What is the ...
5
votes
2answers
244 views

Achieve the best outcome by a tactical statement

This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
7
votes
1answer
193 views

The sadistic chieftain and the lethal truel game

In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind. "I'll ...
10
votes
2answers
272 views

Add a divisor! A game

Let $k$ be a positive integer. Amy and Ben are playing a game, with the number $1$ written on the whiteboard initially. Amy and Ben do the following in order, starting with Amy: Suppose the number on ...
8
votes
4answers
441 views

Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
8
votes
3answers
346 views

Rock, Paper, Scissors, Anti-Rock

Alice and Bob are both well-known perfect logicians who have the ability to internally randomize and often pass their time by playing rock-paper-scissors. One day, tired of the usual RPS game, Alice ...
6
votes
1answer
491 views

Playing blindfolded 2048

Suppose you are playing many 2048 games, all blindfolded. As usual you can press left, right, down, or up to move the tiles. When there are no more moves the game terminates and you are told your ...
1
vote
3answers
138 views

playing “Coins on a table” against a distracted friend [duplicate]

This puzzle is a follow-up of Coins on a table (warning: the link contains the answer to the original question). You are playing a game against your friend Alice: first Alice places one coin on a ...
10
votes
1answer
399 views

Is Oh Tetris Oh! always a draw?

Alice and Bob were playing Oh-Tetris-Oh!, when they decided that every game must be a draw (played intelligently). Can you prove this? (Oh yes, the rules: A $10\times10$ grid, you can pick any ...
3
votes
2answers
128 views

How to effectively hide an earth rebooter thingy [The Good Place Season 4 spoilers]

This puzzle is unsolved. I don't know if there is a solution or how to solve it. I'm also not sure what type of puzzle this would be, so if anyone wants to correct the tags, feel free. Imagine you ...
6
votes
1answer
318 views

Russian Roulette (Redux!)

You are challenged to a game of Russian roulette with a six-chamber revolver, but you and your opponent are allowed to change the outcome of the game in different ways. Here's how the game will ...
8
votes
12answers
3k views

Time to call the bluff [closed]

You are located outside of two rooms which have a door between them. Each room has one or more computers whose total power is unknown, so they cannot be reliably used as proof-of-work to compare times,...
10
votes
1answer
323 views

Reverse dots and boxes – Guess the last move

Alice and Bob are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line of size 1 in one free spot on the grid (marked with light gray lines ...
12
votes
1answer
679 views

Reverse dots and… cubes? - Snowflake edition

A Reverse dots-and-boxes puzzle inspired by @jafe Albert and Robinson are playing a game of reverse dots and boxes. The players take turns adding one plane in one free spot on the grid (...
8
votes
2answers
751 views

Reverse dots and boxes, swastika edition

Alistair and Roberta are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light gray lines in ...
14
votes
2answers
738 views

Reverse dots and boxes

Alice and Bob are playing a game of reverse dots and boxes. The rules are simple: The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light ...
4
votes
1answer
256 views

Tactical Domino Placement Game

Alice and Bob take turns to place regular dominoes into a $7\times8$ board. The first player who cannot go loses. Is there a winning strategy for either player? Note that in this version the pips on ...
8
votes
1answer
312 views

No point shuffling, just pick your cards

Alice and Bob are playing a card game with the following rules: Alice selects two piles of 3 cards from a standard 52-card deck and places the piles in front of her, face up. Bob can see these ...
10
votes
1answer
324 views

Birthday girl's casino game

My daughter's birthday is coming up. Here's a fun party game we can play to celebrate. (Bring your wallet!) I have a pair of 6-sided dice, and a standard deck of 52 cards. You place your ...
5
votes
1answer
154 views

You versus Computer - Who will be the Winner?

You sit down to play a “new” game of chess. In this game only one Knight is on the regular 8x8 chessboard. Only regular legal moves of Knight are allowed. Game begins with computer going first to ...
11
votes
2answers
595 views

2019 gold coins to share

You and your friend has found in total 2019 gold coins in a treasure hunt. Since your friend found the place to dig up, he deserves a bit more gold than you so you offer a game to share the coins to ...
14
votes
4answers
584 views

Racetrack designers, assemble!

Note: Turns out the intended answer to this doesn't work after all (see comments to Sconibulus's answer). The rules have been changed slightly after the fact to ensure there can be valid answers (see ...
8
votes
3answers
385 views

Four-in-a-line Puzzle

Disclaimer: This is an open-problem, I don't have a complete solution for this puzzle yet. We are playing a $2$-player game: you as a challenger and me as a judge. Initially, there is an empty ...
5
votes
5answers
2k views

What is the optimal strategy for the Dictionary Game?

In the Dictionary Game, players take turns saying English words. The first player starts by choosing any word, which splits the dictionary in two parts. The next player chooses a part and picks a word ...
4
votes
2answers
319 views

100 prisoners' names in boxes, against smart warden

My question, which I do not know the answer to, concerns the classic 100 prisoners and 100 boxes puzzle, summarized below. The solution to this assumes the names are placed in boxes randomly, and gets ...
4
votes
1answer
395 views

Chess Massacre Variants-Play Find The Fastest Way?

I have thought up several variations of massacre chess. Massacre chess is a game where almost every single move is a capture. The idea here is that only the chosen type of piece can capture. It ...
5
votes
3answers
674 views

Should I kill all of my elves?

I've been playing a simplified variant of The Great Elf Game for a few days now and I'm struggling to identify an optimal strategy. Rules: You start with 12 elves. Each elf is sent to gather a tree ...
0
votes
1answer
99 views

A game of n players [duplicate]

There are n players. Each player has to choose an integer. The winner is the one with the lowest integer that has not already been chosen by another player. What is the optimal strategy? e.g....
9
votes
1answer
356 views

Paper, pencil and a bunch of bars

An entry for the Fortnightly Topic Challenge #40. Alice and Bob are two rational players who are playing a simple pencil-and-paper game. In the beginning, there are fifteen small vertical bars on ...
43
votes
4answers
5k views

Rock, Paper, Scissors and Trump

Alicia and Robert are two high-stakes gamblers who are playing a match of rock-paper-scissors. Each winning throw is worth 10 €, paid by the other player. These players have deep pockets, so matches ...
1
vote
2answers
686 views

Strategy in Coloring a 4x4 empty grid and the one who completes any 2x2 area of the grid is the loser

Alice and Bob are playing the following game: They have a 4x4 empty grid and take turns coloring one square each, starting with Alice. Assume that both players will colour the squares in with the same ...
7
votes
6answers
1k views

Single-pile Nim with Three Players

Three perfectly rational logicians (Alice, Bob and a Quetzalcoatlus) are playing a game. (Charlie couldn't make it, so he asked the Quetzalcoatlus to fill in for him.) The rules are very simple: ...
7
votes
1answer
269 views

Given an $8×8$ square and a set, which contains the pentominoes and four $1×1$ squares

I have a game. Given an $ 8 × 8 $ square and a set, which contains the pentominoes and four $ 1 × 1 $ squares. Players alternately pick one item from the set. Then players (starting with the player ...
1
vote
0answers
120 views

Solve american eagle statistics game [closed]

If you are one of 100 people playing American Eagle, a game where one person starts alone and has to tackle someone as people run past in order to "recruit" more tacklers for the next run across, and ...
7
votes
1answer
259 views

Domino Tiling Game

Two players are presented an $n\times n$ grid. They take turns placing a piece on the board until no more moves are possible. The last player able to make a move is the winner. The pieces are $2\times ...
6
votes
1answer
425 views

Games and Puzzles

Four teams take part in a week-long tournament in which every team plays every other team twice, and each team plays one game per day. The diagram below on the left shows the final scoreboard, part of ...
23
votes
3answers
2k views

Angels & Demons (Open question)

This puzzle was given to me by a friend of mine, who in turn heard it from someone else who neglected to provide the answer. The text of the puzzle as it was given to my friend is below: Angels ...
8
votes
5answers
578 views

Two person game, choosing an integer between 1 and 30?

Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
11
votes
3answers
395 views

Dollar Auction with Perfect Logicians

The dollar auction is a famous game that shows how seemingly logical choices can end up with very illogical results. Wikipedia says the best strategy is not to play, which is probably true in most ...
12
votes
2answers
1k views

Winning strategy in a calendar game

Consider a two-player game. The players move in turns to pick either a month or a day. The winner is the player who picks the date December 31 ($12/31$). The following rules apply: The game starts ...