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Questions tagged [game-theory]

Game theory is the study of mathematical models of strategic interaction between rational decision-makers.

Game theory formalizes the familiar notion of "games," usually meaning artificial situations

Classical problems of game theory are "can the first player to move force a win in the game of Chess/Checkers/Go?" - "How can cooperation between inherently egoistic agents arise?"

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Is there a perfect algorithm for chess?

I was recently in a discussion with a non-coder person on the possibilities of chess computers. I'm not well versed in theory, but think I know enough. I argued that there could not exist a deterministic Turing machine that always won or stalemated…
Overflown
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How to create a good evaluation function for a game?

I write programs to play board game variants sometimes. The basic strategy is standard alpha-beta pruning or similar searches, sometimes augmented by the usual approaches to endgames or openings. I've mostly played around with chess variants, so…
A. Rex
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Optimal Algorithm for Winning Hangman

In the game Hangman, is it the case that a greedy letter-frequency algorithm is equivalent to a best-chance-of-winning algorithm? Is there ever a case where it's worth sacrificing preservation of your remaining lives, for the sake of a better chance…
Ronald
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In the game 2048, what is the biggest theoretical tile?

In the game 2048 what is the biggest tile that can be achieved, assuming a player playing optimally and tile spawning at the most optimal place? Naively I would say that the biggest achievable tile is 65536 * 2 = 131072 because it seems that the…
foo
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Has Anyone Tried to Implement or Participated in a "Productivity Game" at Work?

In The Practical Guide to Defect Prevention, the authors mention that one creative way to boost productivity in software development is to implement "productivity games" where employees compete against each other in a way similar to gaining…
Jeff Moser
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C# Algorithmic Game Theory API

I recently came accross Gambit - http://www.gambit-project.org/doc/index.html - a C++ algorithmic game theory API. Is anyone aware of a .NET Game Theory Library?
Josh Reuben
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Problem with memory allocation in Julia code

I used a function in Python/Numpy to solve a problem in combinatorial game theory. import numpy as np from time import time def problem(c): start = time() N = np.array([0, 0]) U = np.arange(c) for _ in U: bits =…
Steven Newton
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Solving a graph game

I've struggled some time with a problem from a programming contest (Andrew Stankevich Contest 21) about a game that goes like follows: Nick and Peter like to play the following game [...]. They draw an undirected bipartite graph G on a sheet of…
Niklas B.
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Have you applied Game Theory on a project?

I haven't studied game theory, but it fascinates me. My intuition is that it isn't used by most "enterprise app" developers. However, it is clearly relevant to the large online sites (e.g. recommendation systems), and a huge influence on SO. Have…
Michael Easter
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Game on the tree, cutting branch

We have a forest of rooted trees. Two players makes alternating moves according to the following rule: one move is to cut vertex and all its children. Player which makes last move (no vertices remain) wins. How can we compute Grundy function for the…
Anton Postnikov
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Please tell me the efficient algorithm of Range Mex Query

I have a question about this problem. Question You are given a sequence a[0], a 1],..., a[N-1], and set of range (l[i], r[i]) (0 <= i <= Q - 1). Calculate mex(a[l[i]], a[l[i] + 1],..., a[r[i] - 1]) for all (l[i], r[i]). The function mex is minimum…
square1001
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Strategies for for games with incomplete information

Are there general strategies for games with incomplete information, especially trick-taking games like Bridge and Doppelkopf? I am interested in ways to implement AI strategies for such games. The bounty is for the answer with the best description…
fuz
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How to work out the complexity of the game 2048?

Edit: This question is not a duplicate of What is the optimal algorithm for the game 2048? That question asks 'what is the best way to win the game?' This question asks 'how can we work out the complexity of the game?' They are completely…
finoutlook
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Tower Breakers - nim game variation with divisors

I have encountered a game called Tower Breakers, which seems a variation of the nim game. There are two players, player 1 and player 2. Initially there are n towers, where each tower is of height m, both n and m positive integers. Player 1 begins,…
Oriol
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Algorithm to calculate the odds of a team winning a sports match given full history

Assumptions: The teams never change The teams don't improve in skill The entire history of each team's performance against some subset of other teams is known The number of games played between teams is large, but potentially sparse (each team…
John Shedletsky
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