# Category Archives: Game Theory

Algorithms based on Game Theory

## Check if the game is valid or not

Three players P1, P2 and P3 are playing a game. But at a time only two players can play the game, so they decided, at… Read More »

## Variation in Nim Game

Prerequisites: Sprague Gruncy theorem Grundy Numbers Nim is a famous game in which two players take turns removing items from distinct piles. During each turn,… Read More »

## Game of replacing array elements

There are two players A and B who are interested in playing a game of numbers. In each move a player pick two distinct number,… Read More »

## Game of N stones where each player can remove 1, 3 or 4

Two players are playing a game with n stones where player 1 always plays first. The two players move in alternating turns and plays optimally.… Read More »

## The prisoner’s dilemma in Game theory

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The… Read More »

## Choice of Area

Consider a game, in which you have two types of powers, A and B and there are 3 types of Areas X, Y and Z.… Read More »

## Minimax Algorithm in Game Theory | Set 5 (Zobrist Hashing)

Previous posts on this topic : Minimax Algorithm in Game Theory, Evaluation Function in Game Theory, Tic-Tac-Toe AI – Finding optimal move, Alpha-Beta Pruning. Zobrist… Read More »

## Minimax Algorithm in Game Theory | Set 4 (Alpha-Beta Pruning)

Prerequisites: Minimax Algorithm in Game Theory, Evaluation Function in Game Theory Alpha-Beta pruning is not actually a new algorithm, rather an optimization technique for minimax… Read More »

## Implementation of Tic-Tac-Toe game

Rules of the Game The game is to be played between two people (in this program between HUMAN and COMPUTER). One of the player chooses… Read More »

## Minimax Algorithm in Game Theory | Set 3 (Tic-Tac-Toe AI – Finding optimal move)

Prerequisites: Minimax Algorithm in Game Theory, Evaluation Function in Game Theory Let us combine what we have learnt so far about minimax and evaluation function… Read More »

## Minimax Algorithm in Game Theory | Set 2 (Introduction to Evaluation Function)

Prerequisite : Minimax Algorithm in Game Theory As seen in the above article, each leaf node had a value associated with it. We had stored… Read More »

## Minimax Algorithm in Game Theory | Set 1 (Introduction)

Minimax is a kind of backtracking algorithm that is used in decision making and game theory to find the optimal move for a player, assuming… Read More »

## Combinatorial Game Theory | Set 4 (Sprague – Grundy Theorem)

Prerequisites : Grundy Numbers/Nimbers and Mex We have already seen in Set 2 (http://www.geeksforgeeks.org/combinatorial-game-theory-set-2-game-nim/), that we can find who wins in a game of Nim… Read More »

## Combinatorial Game Theory | Set 3 (Grundy Numbers/Nimbers and Mex)

We have introduced Combinatorial Game Theory in Set 1 and discussed Game of Nim in Set 2. Grundy Number is a number that defines a… Read More »

## Combinatorial Game Theory | Set 2 (Game of Nim)

We strongly recommend to refer below article as a prerequisite of this. Combinatorial Game Theory | Set 1 (Introduction) In this post, Game of Nim… Read More »