coalitions, when relevant, between parties 1 and 2, or between parties 3 and 4. We
thus rule out minority governments, as well as surplus coalitions, by assumption.
Finally, we assume that a government is always formed and that each party is
included in government with a probability equal to its seat share in the legislature,
given the restrictions on feasible coalitions.7
At the end of the government formation stage, each party P can thus be in
one of three states, indexed by G: outside of government (G = O); in a coalition
government (G = C); or in a single-party government (G = S). Given the rules
of the game and the restrictions on feasible coalitions, the three indexes (P, N, G)
summarize all the relevant political outcomes up to this stage.
2.2.3. Policy formation and payoffs
Once a government has formed, the parties in government set economic policy.
We start by describing their payoffs.
Parties are opportunistic: they care only about political rents in the current
period and seats in the next legislature. Specifically, consider party P, with gov-
ernment status G in a system with N parties, and let N WGP denote its expected
payoff at the start of the policy formation stage. This continuation payoff is linked
to that of the party formation stage by: NWP = E(N WGP), where the expectations
operator E refers to the uncertainty in government formation. We assume:
NWGP = rGP + E(NsPG)RP , (2.4)
where rGP denotes the rents captured by party P in the current legislature and
RP denotes the expected value of seats in the next legislature, NsPG denotes the
seat share of party P in the next legislature, conditional on current government
status G, and the expectations operator E(∙) refers to the electoral uncertainty
remaining at the policy formation stage. Note that current (r) and future (R)
rents do not depend on the number of parties in the legislature, N. This is a
feature of the equilibrium, that will be derived in the next section. But the
expected seat share, E(NsPG), is indexed by N, because its equilibrium value does
7 Taking minority governments seriously would require specifying a richer model of policy
formation than the one coinsidered below. In particular, we would have to take into account
the strategic interactions in the legislature, given the specific rules for government breakup and
formation. Laver and Shepsle (1996) and Diermeier, Eraslan and Merlo (2003) provide detailed
game-theoretic analyses of government formation, but neglect most of the remaining political
interactions (party formation, policy formation, and elections).