# Questions tagged [game-theory]

Theory of dynamic processes with several competing actors that try to achieve some goal in a strategic way.

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### Parity games and acceptance conditions of automata on infinite words

I would like to understand the ideas behind parity games and their winning conditions. Where do they come from?
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### Voronoi game in discrete space

Here i want to discuss about Linear Voronoi game. The game consists of two players, and a finite set of users placed along a line. Each player has 2m facilities, where m>0 is a fixed integer. The ...
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### Why is Game Theory used to explain implementations of 3GPP D2D communication?

My question is about D2D as it relates to 3GPP (release 13+, I believe). All I have read on the subject uses Game Theory as a mechanism to explain usage. Why would authors use Game Theory for ...
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### Stable matching of producers, consumers and objects

Has the following version of the stable matching problem been studied? There are $k$ types of objects. There are $n$ producers, each of whom can produce a single object of any type, and has a ...
490 views

### Modification of Nim Game Winning Strategy

Here is the variation: We have some P piles of numbers,each having some pi numbers , and in each turn a player may choose a pile, and then a number from the chosen pile. All the numbers greater than ...
360 views

### Utilization of static evaluation functions in chess

Disclaimer: I'm very new to computer science & game programming I'm having trouble with understanding how to implement a static evaluation function in chess. The logic seems simple like just ...
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### Game of Nim (Find winning states in large range)

If I want to solve a game of nim with 3 piles containing (x, 2x, 3x) respectively I know that the solution of (winning) iff x^2x^3x != 0 but if x can be in the range from 1 to 2^61 so How many ...
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### The probability that a person succeeds to pick the longest stick from a randomly ordered n sticks of distinct lengths following the optimal strategy?

To begin with, consider two persons(Px and Py) are playing a game. Px is the organiser of the game who has n sticks of distinct lengths and displaying them one by one to Py in a random order, with ...
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### Expected number of coins

Alice and bob play a game. Bob has a well-shuffled deck of $M=4999$ white cards and $N=4999$ green cards. Each permutation of cards in the deck is equally likely. Alice has set some rules for Bob. ...
93 views

### Assuming an infinite amount of computing resources, would the minmax algorithm always win in chess?

The minmax algorithm is a popular strategy used to design chess engines. Usually, since the state-space of chess is huge, we choose a fixed depth and evaluate the game tree down to that level, and ...
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### Is there any model of Game of Life compatible with hypercomputation?

I found a question in Mathematics Stack Exchange which asks a very similar question (https://math.stackexchange.com/questions/1023812/hypercomputation-higher-dimensional-variants-of-conways-game-of-...
423 views

### A nim game variant with pass move

This variant is almost similar to the normal nim game which states - Two players take turns to remove one or more items from a single, non-empty pile. The player who removes the last item from the ...
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### Optimal Word Guessing Algorithm in $O(n \log n)$

Say that your friend picks a word $(w_1, w_2,\dots,w_n)$ according to a known probability distribution $(p_1,p_2,\dots,p_n)$. You ask yes or no questions until you are certain which word has been ...
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### Game Theory Schulz Method

Hey I was wondering I did all the 3 neccessary things so Head to Head comparision, Diagraph and the Head to Head Strength Comparision with the help of the Diagraph. In first method there is no ...
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### Finding an Algorithm for the HAPPY-CAT problem

I'm trying to develop an the algorithm for the problem: The cat-and-mouse game is played by two players, “Cat” and “Mouse,” on an arbitrary undirected graph. At a given point, each player occupies a ...
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### Trust in online platforms dealing with virtual goods

I am implementing an online platform, where third-parties sell virtual goods to clients on a subscription basis. Let's take for example ebooks as a virtual good in this case. How can the third-parties ...
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### How do evaluation functions influence the optimal sequence of moves?

Assume you have a game tree and the features $(f_1, f_2, f_3,\ldots,f_n )$ that describe the state of the game at any node. Also assume that you are using depth-limited minimax and always expand up to ...
280 views

### What is the best heuristic function for evaluating the state in game of sprouts?

We are developing game of sprouts bot using min-max algorithm. We need a good heuristic function for evaluating the state of the game/player. Can someone please suggest?
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### Board Game algorithms

I have to find an evaluation function in which we evaluate the state of the game in each round. The game is like " roborally " , it is 2 player-Game in which there are a board and cards ...
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### Simultaneously optimal strategies for both players in zero-sum games

Given a matrix $A \in \mathbb{R}^{m \times n}$ that describes a zero-sum game. What are necessary and sufficient conditions for cases in which the k-th pure strategy of the row-player and the l-th ...
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### Degrees of Separation Minimization & Pathfinding Elimination Strategy for Large Networks

Assume you have a graph/network N; Boundary Conditions: each vertex/node $n \in N$ can support a maximum number of $e_{max}$ connections Nodes can join and leave the graph. Each node $n$ has an ...
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### Algorithm to find the optimal strategy to feed your cousin (Long question)

I have a programming problem, instead of describing the whole domain it's easier for me to create an analogy. The numbers I use in this example are completely arbitrary. Your cousin is coming over ...
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### Computing losing positions in modified Wythoff's game efficiently

Wythoff's game is as follows: there are two players $A$ and $B$ ( $A$ being the first player ) and there are $2$ piles of stones. When his turn a player can remove one or more stones from anyone pile ...
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### A 9 token game of Nim tree construction

Trying to construct the full tree for a 9 game token of Nim and am slightly confused. I don't understand how two players, min and max, will make their pick. For example, max picks first and can only ...
86 views

### Is $AM = AM[2]$?

Any $k$ round AM can be reduced just two rounds whereby Arthus just does the $k$ coin tosses and passes on the information to Merlin. Merlin sees all the coin toss results and computes everything ...
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### Nash Equilibrium in Tree of Bounded Degree

I have an exercise which I can't solve. Exercise. Consider a game where the players have $2$ pure strategies each and assume that the graph $G$ is a tree with maximum degree $3$. Give a polynomial ...
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### A single heap nim game

Consider a game where two players remove sticks from a heap. The players move alternately, and the player who removes the last stick wins the game. A set P = {p1,p2,…,pk} determines the allowed moves....
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### Where is the recursion, in the minimax-decision algorithm?

The below is from an article titled: Minimax: Recursive Implementation To be a recursive function, you need to call yourself. What part of this pseudo code is calling itself? How does depth-...