<p>For most purposes, there is no difference between (two-player) zero-sum and constant-sum games. One usually assumes in game theory that players <a href="https://en.wikipedia.org/wiki/Expected_utility_hypothesis" rel="nofollow noreferrer">maximize expected utility</a>. Payoff functions are von Neumann-Morgenstern utility functions. One does not change the preferences induced by such a payoff function if one adds or subtracts a constant. One can, therefore, transform every constant-sum game into a zero-sum game without changing preferences and behavior.</p>

CC BY-SA 4.0
2020-06-24T11:24:02.400Z
There are underlying assumptions here which raise issues in reality.  The first is that the game is zero-sum or constant-sum in utility terms rather than some other measure.  But there is experimental evidence that individuals show different behaviour when faced with large changes in total utility: if the possible outcomes are $+10$ or $-10$ people often try hard to reduce the risk of a $-10$ outcome, and make different decisions when faced with possible outcomes of say $+560$ or $+540$
Henry
CC BY-SA 4.0
2020-06-24T11:27:40.023Z
You are confusing money and utility.
Michael Greinecker
CC BY-SA 4.0
2020-06-23T19:50:52.503Z
2020-06-23T19:50:52.503Z
Michael Greinecker
<p>The title essentially says it all. I am asking since I came across the following statement: “Zero-sum games are also known as games of pure conflict”. This seemed to imply that zero-sum and pure conflict are synonyms, which confuses me since I figured that all constant-sum games should be games of pure conflict, by definition.
So, are all constant-sum games games of pure conflict or are there some constant sum games that do not follow this rule?</p>

<game-theory>
Are all constant-sum games games of pure conflict, or only zero-sum games?
Andre
# Are all constant-sum games games of pure conflict, or only zero-sum games?

(Asked by: username_0 on 2020-06-23)

The title essentially says it all. I am asking since I came across the following statement: “Zero-sum games are also known as games of pure conflict”. This seemed to imply that zero-sum and pure conflict are synonyms, which confuses me since I figured that all constant-sum games should be games of pure conflict, by definition.
So, are all constant-sum games games of pure conflict or are there some constant sum games that do not follow this rule?

**Tags:** game-theory


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## 1 answers

### Answer by username_1 on 2020-06-23. Score: 3 | Accepted answer

For most purposes, there is no difference between (two-player) zero-sum and constant-sum games. One usually assumes in game theory that players [maximize expected utility](https://en.wikipedia.org/wiki/Expected_utility_hypothesis). Payoff functions are von Neumann-Morgenstern utility functions. One does not change the preferences induced by such a payoff function if one adds or subtracts a constant. One can, therefore, transform every constant-sum game into a zero-sum game without changing preferences and behavior.

> **Comments:**
> **username_2**: There are underlying assumptions here which raise issues in reality.  The first is that the game is zero-sum or constant-sum in utility terms rather than some other measure.  But there is experimental evidence that individuals show different behaviour when faced with large changes in total utility: if the possible outcomes are $+10$ or $-10$ people often try hard to reduce the risk of a $-10$ outcome, and make different decisions when faced with possible outcomes of say $+560$ or $+540$  
> **username_1**: You are confusing money and utility.  

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