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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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8 votes
1 answer

Reverse Puzzling 3

This is a continuation of Reverse Puzzling 2 "Okay George, let's try this one. Pretty simple." I gave George the puzzle. He picked up his marker and quickly sketched out the following. &...
AZGreenTea's user avatar
  • 1,916
32 votes
6 answers

Will a greedy algorithm solve Tatham's Flood?

I was just investigating some of the puzzles on Simon Tatham's website, and came across Flood, in which we start with an $n\times n$ grid of cells each of which is filled with one of $k$ predetermined ...
Rand al'Thor's user avatar
19 votes
4 answers

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
13 votes
3 answers

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
12 votes
3 answers

Tic-tac-toe 1000 in a row

Consider a variant of Tic-Tac-Toe and Gomoku on a board that's infinite in every direction. X wins by getting a line of 1000 X's ...
xnor's user avatar
  • 27.4k
12 votes
4 answers

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
  • 6,169
12 votes
3 answers

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
11 votes
1 answer

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
8 votes
6 answers

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: ...
Bass's user avatar
  • 77.7k
7 votes
2 answers

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
6 votes
2 answers

The Fanatic Fever(twist on the 5 pirates puzzle)

While raiding a tropical island, 6 pirates have an incredibly unlucky day. While they scoured the island in search of treasure, one of them was infected with the Fanatic Fever, a disease which hits ...
Ethan Fine's user avatar
5 votes
1 answer

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 ...
Rewan Demontay's user avatar
5 votes
2 answers

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 ...
Eric's user avatar
  • 6,536
3 votes
2 answers

How to generalise Partition of the pie for N envy people?

There is well known task: How to divide a pie between two people, so each will think that he got equal or more that the other one? It has the following solution: I know that it is possible to ...
klm123's user avatar
  • 16.3k
2 votes
3 answers

This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
matousc's user avatar
  • 307
1 vote
1 answer

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