Questions tagged [game-theory]
The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under [tag:combinatorial-game-theory], and algorithmic aspects (e.g. auctions) are under [tag:algorithmic-game-theory].
3,691 questions
Score of 7
3 answers
130 views
I roll a die repeatedly. Each roll I can choose to keep the die's value in \$ and stop rolling, or pay \$1 to roll again. What's the best strategy?
I roll a die repeatedly. Each roll I can choose to keep the die's value in \$ and stop rolling, or pay \$$1$ to roll again. What's the best strategy?
It seems obvious to me that at each stage, if ...
- reputation score 7139
Score of -6
0 answers
73 views
Kant's categorical imperative? Is this stag hunt instead of prisoner's dilemma? [closed]
2 years ago : https://gaming.stackexchange.com/questions/407658/as-to-why-we-dont-all-play-faceit-in-counterstrike-how-isnt-this-prisoners-d
Here's what I understand for competitive not casual mode in ...
- reputation score 14471
Score of 0
0 answers
81 views
An Angel Problem variant with Collatz-type dynamic step sizes: Does the Angel still have a winning strategy?
In John H. Conway's classic "Angel Problem," an angel with power $k$ moves on an infinite two-dimensional grid $\mathbb{Z}^2$, moving at most $k$ steps per turn (equivalent to the king's ...
user1771492
Score of 1
0 answers
69 views
Combinatorial Game in which draw is possible
In Erdos-Selfridge's paper "On a combinatorial Game", it is proved that there exists a family of $n$-sets of size $2^{n-1}$ such that if two players alternatively pick elements from the ...
- reputation score 205
Score of 6
1 answer
318 views
IMO 2026 Problem 3 (Liu Bang and Xiang Yu stick cutting game)
I am working on IMO 2026 Problem 3. I have work out the lower bound construction (Liu Bang's strategy), but I am seeking a better way for the bound.
Problem Statement
Let $n$ be a positive integer. ...
- reputation score 1969
Score of 4
1 answer
175 views
Finding a winning strategy for Alice in a Combinatorial Game
currently I've just come up with a combinatorial game like this:
Let $S = \{1, 2, \dots, 100\}$. Alice and Bob take turns choosing a number from set $S$ and removing it. The game ends when the sum of ...
- reputation score 41
Score of 3
1 answer
163 views
A graph-theory related game, Alice adds a vertex, Bob colors it
Alice and Bob are playing a graph theory related game, called Alpha-4.
The rules of Alpha-$4$ are:
Start from completely empty state: $4$ colors are given, for example $$\rm \{Red,Green,Blue,Yellow\} =...
- reputation score 563
Score of 0
0 answers
63 views
How does Nash Equilibrium Relate to Bellman Ford Dynamic Programming?
This is a question I have had for a long time.
I know that Nash equilibrium and Bellman Ford belong to different areas (Game Theory and Computer Science respectively), but they seem intimately linked, ...
- reputation score 75
Score of 1
1 answer
125 views
In TED-Ed's prisoner boxes riddle (or the 100 prisoners problem), how do the odds of success change if the musicians took their instrument when found?
Those familiar with TED-Ed's prisoner boxes riddle can skip below-->
10 members of a band wake up to find themselves tied up in a windowless, soundless practice room. Their manager explains:
"...
- reputation score 11
Score of 3
0 answers
83 views
Algorithms for extending the rules of the Sudoku game
I am studying the rules of Sudoku variants and became interested in the problem of partitioning the grid into arbitrary connected regions.
Rules
1) A standard $9 \times 9$ Sudoku grid is given.
2) The ...
- reputation score 31
Score of 4
0 answers
246 views
A two player abstract game called Cayley Connect from Cayley's group tables?
Lately I have been thinking about how to convert each finite group into a game (puzzle, piece of art or music). Here I present a two player game on a Cayley table:
Put your animals orthogonally (...
- reputation score 904
Score of 2
1 answer
134 views
A Territorial Expansion Game on an Odd $n \times n$ Board.
Two players, $A$ and $B$ play a game on an $n \times n$ board, where $n>1$ is an odd integer. Initially, one corner cell contains an $A$, and the opposite corner cell contains a $B$. The players ...
- reputation score 1573
Score of 0
0 answers
41 views
Disproving the existence of a Pure Bayes-Nash equilibrium for an all-pay auction
I'm having trouble showing whether a pure Bayes-Nash equilibrium exists in an all-pay auction.
In a two-player sealed-bid all-pay auction, both players submit an integer bid $a_i \in [0\dots100]$. ...
- reputation score 35
Score of 2
2 answers
83 views
Maximize number of distinct pairs after repeated random duplications
Start with 1 red ball and 1 black ball. Then repeat the following procedure: Duplicate a random ball, then you may remove any number of balls.
What is best strategy to maximize the number of red-black ...
- reputation score 1355
Score of 1
0 answers
65 views
Electrical circuit analysis for non-zero sum games
Question: is there a connection between electrical circuits and nonzero-sum games?
The reason I am asking is that I have very recently found out about such a connection for zero-sum games. It is ...
- reputation score 193
