# 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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### The opposite of a Tit-for-Tat strategy

The tit-for-tat strategy is a well-known strategy that can be applied, for example, in the Iterated Prisoner's Dilemma (IPD). Roughly, the idea is that you always repeat what the opponent did in the ...
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### Zero-Sum Games and Halting Problem

Wikipedia states on the page of the halting problem, "For any program f that might determine if programs halt, a "pathological" program g called with an input can pass its own source and its input to ...
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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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### Recover a matrix with minimum number of queries

Alice has a matrix $A \in \{0,1\}^{n \times m}$ such that the sum of each row is $1$. Bob tries to find the indices of the ones (he knows that the sum of each row is $1$). The type of questions Bob ...
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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. ...
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### Is this a valid heuristic for Dots and Boxes to reduce the branching factor of the search tree?

I am implementing an AI based on the MiniMax algorithm that plays the game Dots and Boxes. I would like to reduce the branching factor of the search tree, by introducing a heuristic rule that limits ...
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### Thirty-one game. Prediction of the winner

I have a problem with creating an algorithm to predict a winner of thirty-one game. Players from a deck of cards, take the Ace, 2, 3, 4, 5, and 6 of each suit. These 24 cards are laid out face up on ...
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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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### Is Dots and Boxes complementary to the game of Go?

I've read that La Pipopipette is known to be NP-hard. I have not yet found analysis specifying an exact complexity class for Dots and Boxes, or for some variations in the analysis of Go. Here's a ...
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### Winning strategy for a given game on graphs

The game goes as follows. Two players are playing a game, player 1 and player 2, in which the first player starts by naming a hero $h_1$, then player 2 responds with a villain $v_1$ who has played in ...
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### Least constraining value heuristic in Sudoku [closed]

I was trying to implement Least Constraining Value Heuristic in Sudoku but wasn't getting the idea on how to do it. Can someone share their idea for the same ?
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### What is the best solving algorithm for a game with stacks?

Game Explanation: Suppose there is a game with cards that have numbers from 1 to n. Each card has a different number so there are not two cards with the same number. The deck is scrambled. We chose ...
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### Why does Min-Max algorithm delays a good move indefinitely?

Consider a simple chess example: Q is white Queen. K, R is black King and black Rook respectively. A B 1 . Q 2 . . 3 K . 4 . . 5 . . 6 R . 7 . . 8 . R 1,2......
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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 ...
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### 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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### Marriage Problem: Is both sided stable matching strongly pareto optimal?

According to this problem: Unique Stable Solution in Stable Marriage Problem: Is it Pareto-efficient and a Nash Equilibrium? Is the both sided stable matching strongly pareto optimal for both sides? ...
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### Is there any algorithm so it can solve stable marriage problem with incomplete preference lists

I have a slightly different formulation of the stable marriage problem. Basically, I can match one man to one woman, but the preference list is incomplete, which means that a man has expressed ...
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### Two Minimax AIs playing against each other

I am trying to have my Minimax AI chess players play against each other. I was a bit confused about an implementation detail. Let's call black my first minimax AI ...
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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-...
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### Bertrand's ballot theorem

I want to understand the dynamic programming equation of https://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem theorem. it is this If i number of people voted for A and j number of people voted ...
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### Computing Nash equilibria in discrete auctions

I am trying to compute the (pure strategy) Nash equilibria of some discrete auctions. More precisely, let us define the strategy of each player as a function mapping from every valuation that they ...
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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 ...