<P>Recursive structure and equilibria in games
with private monitoring</P>
<P>
Massimiliano Amarante
Departments of Economics, Columbia University, New York, NY 10027, USA
(e-mail: <a href="mailtma734@columbia.edu" target="_blank" >ma734@columbia.edu</A>)
Received: February 11, 2002; revised version: July 22, 2002</P>
<P>
Summary. In each stage of a repeated game with private monitoring, the players
receive payoffs and privately observe signals which depend on the players’ actions
and the state ofworld. I showthat, contrary to a widely held belief, such games admit
a recursive structure. More precisely, I construct a representation of the original
sequential problem as a sequence of static games with incomplete information. This
establishes the ground for a characterization of strategies and, hence, of behavior
in interactive-decision settings where private information is present. Finally, the
representation is used to give a recursive characterization of the equilibrium payoff
set, by means of a multi-player generalization of dynamic programming.
Keywords and Phrases: Private monitoring, Incomplete information, Dynamic
programming.
JEL Classification Numbers: C73, D82.</P>
<P> </P>