A Bargaining Model of Domestic Politics and the Cost of War
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sides in this case had ample access to information regarding p and c but used that information
to diﬀerent degrees of eﬀectiveness.
The standard sequential bargaining model provides a sharp prediction of a demand that
is accepted immediately, with no conﬂict. The stark predictions of this equilibrium model
can be enriched by injecting noise in decision making, while maintaining the equilibrium
requirement that distributions representing beliefs match the probability distributions of
decisions (a quantal response equilibrium). This equilibrium approach has been used with
successs in explaining behavior in long series of interactions in political participation games
(Goeree & Holt 2005). The equilibrium approach, however, may not be appropriate in games
played infrequently or only once, i.e. belief distributions may be too dispersed in the sense
that the noise parameter in beliefs is diﬀerent from the noise in actual decisions. Even worse,
there may be systematic biases caused by overconﬁdence or selective reliance on information
that is too favorable (e.g. Camerer 2002).
Here, we oﬀer a model that explicitly addresses players’ perceptions of the levels of
rationality of their opponents, and incorporates it in understanding how this perception
aﬀects demands and responses.
We adopt an approach where we calculate the quantal
response equilibrium for a common λ (expected rationality of one’s opponent) and look at the
predicted behavior for large values of λ, i.e. as behavior becomes fully rational in the limit.
This approach also permits us to derive numerical predictions about how the probability of
conﬂict varies with the balance of power, as measured by the proposer win probability, p.
Then we will discuss how to generalize this model to allow diﬀerent levels of rationality, i.e.
to allow players to attribute lower levels of rationality to the other player. This approach
is consistent with arguments on noisy introspection that incorporate players’ beliefs about
their opponents’ levels of rationality (e.g. Goeree & Holt 2000, Goeree & Holt 2004)
To incorporate noise into the model and produce predictions the deviate from the no-
conﬂict equilibrium, we present a QRE version of the model.
In the second stage, the
responder must evaluate expected payoﬀs from demanding x
. This expected payoﬀ is the