Zero sum game
In game theory , zero-sum games describe situations, i.e. games in the generalized sense, in which the sum of the wins and losses of all players is equal to zero.
In game theory, zero-sum games are equivalent to games with constant sum ( constant-sum games ). In these games, the common payout amount is not zero, but rather a constant, but if the payout is considered to have been distributed to the players in advance, they are playing for a redistribution with a total of zero. Examples of zero-sum games are all games and sports , in which played against each other for the win, for example, poker or chess . It should be noted that the observed gains and losses are understood outside of the game - in a game of chess, both players usually lose game material compared to the start of the game, but it is only about the payment of the game "to the outside", here for example as "a point in a tournament".
A zero-sum game in the economic sense is a competitive situation in which the economic success or profit of one participant contrasts with the failure or loss of another in the same amount.
The general case of the non- zero-sum game is often referred to as coopetition . You can still distinguish whether the sum is zero at any point in time or whether there are certain times during the moves in which it is not equal to zero or indefinite. A special case of the non-zero-sum game is the so-called win-win game, in which all participants can win at the same time, but this game outcome cannot be achieved automatically.
Examples
- All strategy games for two players, in which the result is only about win, draw and loss, can be viewed as zero-sum games if you rate a win with +1 point, a draw with 0 points and a loss with −1 point. At the end of such a game the total is always zero (A wins and B loses: +1 + −1; or a tie: 0 + 0; or A loses and B wins: −1 + +1).
- Individual sports competitions, such as a soccer game, are generally not constant sum games depending on the rating (the soccer rating, for example, allows 1 or 3 points to be paid out), the entire competition (e.g. a soccer league, but also the 100 m sprint competition at a sports festival ) can mostly be understood as a constant sum game (and thus mathematically zero-sum game), since the places are played out among all participants and the associated prices (material type as well as qualifications, etc.) remain constant, regardless of who specifically gets them.
- In Doppelkopf , every single game is a zero-sum game, as the game value is credited to two players and subtracted from two players in a normal game. In a solo, the declarer gets three times the number of points and the other three players get the single number of points. The property of the zero-sum game is used when writing down the results, because the sum of the points of all players must be 0 in each line.
Game theory
In game theory , zero-sum games with complete information and two opponents are the easiest to grasp. For these games there is always a calculable winning strategy with a randomness , although it is sometimes so complex that it has not yet been found, as in chess or go .
First the situation of the zero-sum game in game theory was considered and later applied to analogous examples.
No zero-sum games
No zero-sum games are games in which the sum of wins and the sum of losses are different, such as minus-sum games or plus-sum games, or where there is no win or loss. Points, money or other metrics count as profit or loss.
These include:
- Roulette if you don't see the bank as a player
- Lottery , if you only look at the people who buy tickets - only part of the income is distributed as profit
- Games in which everyone wins through cooperation, for example , such as the Prisoner's Dilemma
- Games in which everyone loses due to certain forms of competition, see also Rational Trap , Braess Paradox , Competitive Paradox , Race to the bottom .
The German Bundesliga was previously played as a game with a constant sum: there were 2 plus points for a win, 1 plus and 1 minus point for a draw and 2 minus points for a defeat. The total of points for both teams was always 2 plus points and 2 minus points after the game, i.e. a total of 0. Since the 1995/96 season, a win has been rewarded with 3 instead of 2 points, so that the total of points is either 3 (in the event of victory or defeat) or 2 (in the event of a tie) is. It is no longer a zero-sum game. If one were not looking at the points but only the goal difference (goals scored are positive, goals received are negative), football would be a zero-sum game, because the goal difference N of the winning team is offset by the goal difference of −N of the losers. An entire football season can also be understood as a constant sum game, since in the end the different places with their respective “payouts” (promotion, relegation, bonuses, entitlement to participate in other competitions) are always awarded.
Conflict theory
In conflict theory , one speaks of a zero-sum game when the conflicting parties are so entangled with one another that if one wins, the other automatically loses accordingly. Or if one party (or all) believe that as soon as one would win, the other would have to lose accordingly. It is irrelevant whether the parties to the conflict are a single person, groups, organizations, states or entire cultures or religions. Common strategies are struggle , where there are winners and losers, and compromise , where everyone wins a little and loses a little.
Conflict resolution usually presupposes that those involved " get out of the zero-sum game ", that is, adopt the idea that there can be solutions in which all those involved have a profit (also called win-win ). A permanent solution should be found together that is supported and accepted by all parties involved. This requires mutual respect and a serious interest in the needs, fears and motivations of each other.
Figurative meaning
Colloquially - for example in politics - the “zero-sum game” is often understood to mean that “nobody wins and nobody loses anything”. But that does not correspond to the actual game theory meaning of the word.
Individual evidence
- ↑ Manfred J. Holler , Gerhard Illing : Introduction to game theory. 7th edition. Springer, Berlin et al. 2009, ISBN 978-3-540-69372-7 , p. 55.
