The solution of the game can explain several important features of the
empirical relationships among votes, contributions and district service that
have been reported in the literature. To see how this is so, consider those
races in which the incumbent runs in the general election against an opponent.
Suppose that the population of such competitive campaigns is generated by
random sampling from the set of points where the flows of realizations of
system (1) that have (g, h) pairs near 
and initial values for (r,q,a,b) near 
can be at the end
of the time period of the second stage subgame. This would be a set of
campaigns generated by the players' actions being subject to small random
departures from equilibrium behavior. Such a population will be a random
sample of points from a convex region shaped roughly like the one shown in
Figure 2.
It is easy to see how a linear regression analysis would suggest that the challenger's financial resources are very strongly related to the election outcome, while the incumbent's resources are at best weakly related. Such is the finding repeatedly found by Jacobson (1980; 1985; 1990a; cf. Green and Krasno 1988; 1990; Thomas 1989; Levitt 1994). Simulating random data as indicated above and then in the simulated data regressing the probability that the incumbent wins on the contributions to the candidates reproduces the familiar regression results. A characteristic example, using ordinary least squares regression with 150 simulated observations, is
(standard errors in parentheses). As is usually observed in real data, the
linear effect of the challenger's campaign finances is statistically
significant and large, while the effect of the incumbent's campaign money is
statistically insignificant and tiny. Such a result is the correct outcome
for linear analysis of the data, but from the perspective of the current game
it is causally spurious.
Increases in
challenger finances do not cause the incumbent's vote share to fall. Rather
candidate finances, district service and votes are jointly determined by
strategic interactions among candidates, parties and financial contributors.
A linear analysis also produces spurious results for the effect district service from the incumbent has on the election outcome. Adding the incumbent's post-election service to the preceding regression gives
The estimate for the effect of the incumbent's campaign money is now statistically significant, but still tiny in comparison to the estimated effect of contributions to the challenger. The estimated effect of service is statistically significant, but with what some accounts (Cain, Ferejohn and Fiorina 1987; Fiorina 1989) would say is the wrong sign. Such an estimate echoes the difficulty Feldman and Jondrow (1984) and others (Stein and Bickers 1994) have encountered trying to find significant effects of local federal spending.