# Category Archives: Game Theory

Algorithms based on Game Theory

## Minimum Possible sum of digits in a positive multiple of N

Given a number N, find the minimum possible sum of digits that can be obtained from a positive Multiple of N. Constraints : 1<=N<=10^5. Examples:… Read More »

## Game Theory (Normal-form game) | Set 3 (Game with Mixed Strategy)

Consider the following payoff matrix with respect to player A and solve it optimally. Solution: If a game has no saddle point then the game… Read More »

## Game Theory (Normal – form game) | Set 1 (Introduction)

Game theory is a mathematical model used for decision making. It has applications in all fields of social science, as well as in logic and… Read More »

## Card Shuffle Problem | TCS Digital Advanced Coding Question

You have 100 cards, numbered 1 to 100. You distribute them into k piles and collect back the piles in order. For example, if you… Read More »

## Game Theory in Balanced Ternary Numeral System | (Moving 3k steps at a time)

Just like base 2 Binary numeral system having 0s and 1s as digits, Ternary(Trinary) Numeral System is a base 3 number system having 0s, 1s… Read More »

## Predict the winner in Coin Game

There are two players P1 and P2 and two piles of coins consisting of M and N coins respectively. At each turn, a player can… Read More »

## Predict the winner of the game on the basis of absolute difference of sum by selecting numbers

Given an array of N numbers. Two players X and Y play a game where at every step one player selects a number. One number… Read More »

## Find the number of players who roll the dice when the dice output sequence is given

Given a string S and a number X. There are M players who roll the dice. A player keeps on rolling the dice until he… Read More »

## Some Tricks to solve problems on Impartial games

How to solve problems that fall in the Finders keepers category in ‘Game Theory’? Note- Finders keepers game fall into the category of ‘Impartial Games’… Read More »

## Number of ways for playing first move optimally in a NIM game

Two players A and B are playing NIM Game with each other. Both are playing optimally. Player A starts the game. The task is to… Read More »

## Probability of A winning the match when individual probabilities of hitting the target given

Given four integers a, b, c and d. Player A & B try to score a penalty. Probability of A shooting the target is a… Read More »

## Chessboard Pawn-Pawn game

There is a 8*8 chessboard and two chess players having a single pawn each. A player has to move his pawn in each turn, either… Read More »

## Minimum number of integers required to fill the NxM grid

Given a grid of size (NxM) is to be filled with integers. Filling of cells in the grid should be done in the following manner:… Read More »

## A modified game of Nim

Given an array arr[] of integers, two players A and B are playing a game where A can remove any number of non-zero elements from… Read More »

## Find the winner by adding Pairwise difference of elements in the array until Possible

Given an array arr[] of positive distinct integers, two players A and B are playing a game. At each move, a player selects two numbers… Read More »