ECONOMY

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accepted, the game ends and all actors receive payoffs asspecifiedbytheaccepted
proposal. Otherwise, another proposer is selected, etc. 12 The process continues until
a proposal is accepted or the game ends.
Consider a simple version of the model where there are three political parties with
no party having a majority of the votes in the legislature. The BF model predicts that
the party with proposal power will propose a minimal winning coalition consisting
of him- or herself and one other member, leaving the third party with a zero payoff.
The proposing party will give a proposed coalition partner just the amount necessary
to secure an acceptance. This amount (or continuation value) equals the coalition
partner’s expected payoff if the proposal is rejected and the bargaining continues.
Proposals are thus always accepted in the first round. Note that the proposing party
maximizes its payoff by choosing as a coalition partner one of the parties with the
lowest continuation value. The division of spoils will in general be highly unequal,
especially if the parties are very impatient.
Consider a simple, two-period, example of the model where three parties divide $1.
If the money is not divided after two periods, each party receives nothing. Suppose
further that each party has an equal amount of seats and that in each period the
probability that any given party is chosen as the proposer is proportional to seat
share, i.e. each party is selected with probability 1/3. In the last period each recognized
proposer will propose to keep the entire $1 and allocate nothing to the other two
parties. This proposal will be accepted by the other parties. 13 Now consider each
party’s voting decision in period one. If the proposal is rejected, each party again
has a probability of 1/3 of being selected as proposer in the second period. But as we
just showed, in that case the proposer will get the entire $1. Therefore, the expected
payoff from rejecting a proposal is 1/3 for each party. This expected payoff is also called
the “continuation value.” Call it D i for each party I (here D i =1/3 for each i). Now
consider the incentives of a proposer in period one. By the same argument as above 14
each proposer will make a proposal that allocates $1 − D i (here $2/3) to himself, D i
to one other party (his “coalition partner”), and nothing to the remaining party. This
proposal will be accepted. 15
¹² A variant of this set-up allows (nested) amendments to a proposal before it is voted on. This is the
case of an open amendment rule (Baron and Ferejohn 1989).
¹³ Why would the non-proposing parties vote for a proposal where they receive nothing? The idea is
the following. Since the model assumes that all parties’ relevant motivations are fully captured by their
monetary rewards, parties would accept any ε-amount for sure. But then the proposer can make this ε as
small as he wishes. The technical reason is that a proposal that allocates everything to the proposer is the
only subgame perfect Nash equilibrium in the second period. From the proposer’s point of view offering
ε more than $0 cannot be optimal since he can always offer less than ε. From the other parties’ points of
view accepting $0 with probability one is optimal (they are indifferent), but voting to accept with any
probability less than one cannot be optimal, since in that case the proposer would be better off offering
some small ε which the parties would accept for sure.
¹⁴ See also the previous footnote.
¹⁵ In their general model, Baron and Ferejohn show that an analogous argument also holds if the
game is of potentially infinite duration. That is, parties are selected to propose until agreement is
reached. To ensure equilibrium existence future payoffs need to be discounted. The more they are
discounted, i.e. the more impatient the parties, the higher the payoff to the proposer. In subsequent years
Baron systematically applied the model to various aspects of government formation such as different