Zero-Sum Game Last Updated : 26 Feb, 2021 Summarize Comments Improve Suggest changes Share Like Article Like Report Zero-Sum Game:A zero-sum game is one in which no wealth is created or destroyed. So, in a two-player zero-sum game, whatever one player wins, the other loses. In this game, we can include at least two and a maximum to an infinite number of contestants. It assumes a version of perfect competition and perfect information. Let us consider a game in which n contestant takes part, and contestant i has Ni courses of action available to him. Then the number of outcomes to a play of the game will be N1, N2,..............., Nn. So, consider a possible outcome θ result in payment p(i, θ) to a contestant i. Then, the game is called a Zero-Sum Game, if every possible result θ, we have\sum_{i=1}^{n} p(i,θ) = 0 Lets us understand this by taking an example, three-man A, B, and C playing poker and put 100 bucks all, the winner takes all money. If A wins the game he gains 200 bucks but B and C lose 100 bucks each. So, the total payment to all contestants after the play is zero. Similarly, if B or C wins too. In financial markets, futures and options are considered non-zero games because contracts represent agreements between two parties and, if one investor loses, the asset is transferred to another investor. Poker, Gambling, Matching Pennies, Chess, Tennis are also some examples of Zero-Sum Game. Comment More infoAdvertise with us Next Article Game of Matchsticks A amartomar683 Follow Improve Article Tags : Mathematical Technical Scripter Game Theory DSA Practice Tags : Game TheoryMathematical Similar Reads Game Theory Game Theory is a topic in competitive programming that involves a certain type of problem, where there are some players who play a game based on given rules and the task is often to find the winner or the winning moves. Game Theory is often asked in short contests with a mixture of other topics like 15+ min read Variation in Nim Game Prerequisites: Sprague Grundy theorem Grundy NumbersNim is a famous game in which two players take turns removing items from distinct piles. During each turn, a player must remove one or more items from a single, non-empty pile. The winner of the game is whichever player removes the last item from t 8 min read Game of stones Given an integer N which is the number of stones in a pile and the game of stones is being played between you and your friend, the task is to find out whether you'll win or not. A player (on his/her turn) can remove 1 2 or 3 stones, the game continues in alternating turns. The one who is not able to 4 min read Game of Matchsticks Two friends, A and B, are playing the game of matchsticks. In this game, a group of N matchsticks is placed on the table. The players can pick any number of matchsticks from 1 to 4 (both inclusive) during their chance. The player who takes the last match stick wins the game. If A starts first, how m 6 min read Maximum games played by winner There are N players which are playing in a tournament. We need to find the maximum number of games the winner can play. In this tournament, two players are allowed to play against each other only if the difference between games played by them is not more than one. Examples: Input : N = 3 Output : 2 7 min read 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 the array that are multiples of 3. Similarly, B can remove multiples of 5. The player who can't remove any element loses the game. The task is to find the winner of the ga 7 min read Like