SFB 303 Discussion Paper No. B - 125
Author: Moldovanu, Benny
Title: Bargained Equilibria For Assignment Games Without Side Payments
Abstract: The intersection of the core and the kernel of games with side payments
has a very interesting property: A payoff vector is in this intersection if
and only if each pair obtains the standard solution in its reduced game,
where the standard solution is the only efficient, symmetric and covariant
solution to a two-person bargaining problem with side payments.
A set with similar properties for general games without side payments is
shown not to exist. The equations leading to such a solution may be
We show the existence of a set of equilibria for assignment games without
side payments, which naturally generalize the intersection of the core and
the kernel of similar games with side payments. All the main properties of
the old solution are preserved.
In the model, bargaining between members of a matched pair is modelled using
the paradigms of axiomatic bargaining theory. The disagreement point is
endogenuously determined, taking in account outside options which are based
on the current payoff of other players. An allocation is in equilibrium if
and only if each pair is in equilibrium (obtains a "standard" solution to
its reduced game).
Existence of equilibria is established via a bargaining process which
converge to the set of equilibria. We generalize also the results and
approach pionereed by Rochford(1984) for the side-payments case.
Our main tools are reduced games and consistency properties: The main idea
is one of stability of solutions under partial implementation by subgroups
of players which form expectations about outside options. This relates the
results to other recent works (Peleg(1985,1986), Hart, Mas-Collel(1989),
Creation-Date: October 1989
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