Bell-shaped game
From Encyclopedia of Mathematics
A game on the unit square whose pay-off function takes the form , where
is a positive analytic proper Pólya frequency function, i.e.:
1) is defined for all
;
2) for any and any sets
and
there is an inequality
;
3) for any set (correspondingly,
) there is a set
(correspondingly,
) such that
;
4) .
An example of a bell-shaped game is a game with pay-off function . The optimal strategies of players in a bell-shaped game are unique and are piecewise-constant distributions with a finite number of steps. The value of a game with pay-off function
, as
, moves towards zero, while the number of points in the supports of the optimal strategies grows unboundedly.
References
[1] | S. Karlin, "Mathematical methods and theory in games, programming and economics" , Addison-Wesley (1959) |
How to Cite This Entry:
Bell-shaped game. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bell-shaped_game&oldid=46004
Bell-shaped game. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bell-shaped_game&oldid=46004
This article was adapted from an original article by V.K. Domanskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article