<p>There is a recent paper which may help you:
<a href="http://link.springer.com/article/10.1007/s00199-015-0864-0" rel="nofollow">Games with strategic complements and substitutes</a> (Monaco and Sabarwal (2015))</p>

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2015-03-30T13:51:13.507Z
2015-03-30T14:56:19.033Z
2015-03-30T14:56:19.033Z
guest12345
<p>Nice properties of the set of Nash equilibria can be shown for supermodular games(see <a href="http://cowles.econ.yale.edu/P/cp/p08b/p0875.pdf" rel="nofollow">here</a>). But for a two-player game in which </p>

<ol>
<li>Strategy spaces for two player, $S_1$ and $S_2$ are finite, and both of them are subsets of $\mathbb R$.</li>
<li>$u_1$ exhibits <a href="http://web.stanford.edu/~jdlevin/Econ%20286/Supermodular%20Games.pdf" rel="nofollow">increasing differences</a> while $u_2$ exhibits decreasing differences.</li>
</ol>

<p>What can we say about it?</p>

<mathematical-economics><game-theory><reference-request><academic-graduate>
Are there some nice properties for a finite two-player game having an increasing differences utility and a decreasing differences utility?
Epicurus
# Are there some nice properties for a finite two-player game having an increasing differences utility and a decreasing differences utility?

(Asked by: username_0 on 2015-03-26)

Nice properties of the set of Nash equilibria can be shown for supermodular games(see [here](http://cowles.econ.yale.edu/P/cp/p08b/p0875.pdf)). But for a two-player game in which

1. Strategy spaces for two player, $S\_1$ and $S\_2$ are finite, and both of them are subsets of $\mathbb R$.
2. $u\_1$ exhibits [increasing differences](http://web.stanford.edu/~jdlevin/Econ%20286/Supermodular%20Games.pdf) while $u\_2$ exhibits decreasing differences.

What can we say about it?

**Tags:** mathematical-economics, game-theory, reference-request, academic-graduate

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## 1 answers

### Answer by username_1 on 2015-03-30. Score: 4 | Accepted answer

There is a recent paper which may help you:
[Games with strategic complements and substitutes](http://link.springer.com/article/10.1007/s00199-015-0864-0) (Monaco and Sabarwal (2015))


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