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Zero-Sum Game

The term zero-sum game refers to the game and economic theory. It is a representation of a situation in which the advantage gained by one of the two parties is lost by the other. 

Zero-Sum Game explained

As stated above, in a situation of the zero-sum game a particular party wins, while the other one loses. It means that each outcome of this game is optimal, according to the Pareto theory.

The concept of zero-sum game was developed in game theory, and therefore zero-sum cases are often called so, but this does not mean that the game theory itself applies only to what usually counted as games.

The idea of optimal Pareto winnings in a zero-sum game generates an egoistic pattern when both parties constantly seek to minimize their opponent's winnings at any cost. The opponent's punishment standard can be met in both zero-sum and non-zero sum games. The player in the game has a fairly simple desire to maximize profits for himself, and the opponent wants to minimize them. 

Often a situation arises between two rivals in which they begin to understand, out of the habit of spite, that if one wins something, then the other suffers equally. That is, they begin to understand that their relationship is a zero-sum game. In zero-accumulation games, if one party can do any harm to the other, it must try to do so. But it also happens that in some situations the sequence of relationships is actually a non-zero accumulation game, in which some event may result in a gain for both or a loss for both. For example, there are often conflicts between countries over trade, but this is something that can benefit both sides.

In the same context, a game is considered a constant-sum game if the sum of the utilities received by all players is a constant. Since the characteristics of the game do not change when adding or subtracting a constant from all possible utilities, a constant-sum game can be reduced to a zero-sum game by subtracting that constant from each player's possible utilities.

In theory, trade is never a zero-sum game if the parties only enter into an exchange because they value what the other party gives more than what they give. The buyer of a loaf of bread only buys the bread if he is ready to pay the price asked for the bread. On the other hand, the seller would not sell the bread unless he made a profit. 

Non-Zero Sum Game

The non-zero game occurs when advantageous or losing decisions of one party do not necessarily lead to other party wins or losses. Thus, if a country with a surplus of oranges can export it to another country and import surplus watermelons from that other country in such a way that both countries profit from the trade, this is a non-zero sum case. Any other game that assumes the sum of all players' wins or losses to be different from where they started can be classified as the non-zero sum one.

Zero-Sum Game Example 

If you add up the total winnings of the participants and subtract the total losses, it will be equal to zero.

Examples of zero-sum games in everyday life include popular games such as poker or chess where one person wins and the other loses, resulting in zero net profit for each player. Contrary, as the non-zero sum game can be described a situation in which the combined gains and losses of the interacting parties may be less than or greater than null. The zero-sum game is also identified as a competitive one, while the non-zero sum games can be either rivaling or noncompetitive. The Prisoner's Dilemma is one of the traditional non-zero sum examples.

The simplest example of the zero-sum game is when the first player hides a coin with heads or tails up, and the second player tries to guess what side of the coin is on the top. If he fails to guess, he loses, if he guesses, he wins.

In this game, each participant has two strategies: the first one is to choose head and the second one is to choose tail. The set of situations in the game consists of four elements. The rows of the table contain strategies of the first player x, the columns contain strategies of the second player y. For each situation the winnings of the first and second players are given.

If the result is completely determined by the player who made the last move (if the move rules are identical for the players), the strategy can be found using the Grandi function.

Futures contracts and options are also classified along the zero-sum games. Nevertheless, a situation similar to the stock market, etc., is not a zero-sum game because investors can make a profit or a loss from the impact of stock prices on earnings forecasts or economic projections, rather than profit from the losses of other investors.

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