Bookcover of Supermodular Function
Booktitle:

# Supermodular Function

## Symmetric Game, Strategic Complements, General Equilibrium Theory, Coordination Game, Pseudo-Boolean Function

The (2013-01-10 )

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ISBN-13:

### 978-613-9-15751-8

ISBN-10:
613915751X
EAN:
9786139157518
Book language:
English
Blurb/Shorttext:
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The concept of supermodularity is used in the social sciences to analyze how one agent's decision affects the incentives of others. Consider a symmetric game with a smooth payoff function \,f\, defined over actions \,z_i\, of two or more players i \in {1,2,\dots,N}. Suppose the action space is continuous; for simplicity, suppose each action is chosen from an interval: z_i \in [a,b]. In this context, supermodularity of \,f\, implies that an increase in player \,i\,'s choice \,z_i\, increases the marginal payoff \frac{df}{dz_j} of action \,z_j\, for all other players \,j\,. That is, if any player \,i\, chooses a higher \,z_i\,, all other players \,j\, have an incentive to raise their choices \,z_j\, too. Following the terminology of Bulow, Geanakoplos, and Klemperer (1985), economists call this situation strategic complementarity, because players' strategies are complements to each other. This is the basic property underlying examples of multiple equilibria in coordination games.
Publishing house:
The
Website:
http://www.betascript-publishing.com
Edited by:
Indigo Theophanes Dax
Number of pages:
104
Published on:
2013-01-10
Stock:
Available
Category:
Mathematics
Price:
29.00 €
Keywords:
Strategic, coordination, equilibrium, theory, General, game, symmetric, Compléments