nopp (version 1.0.4)

equilibrium: Nash Optimal Party Positions

Description

Nash Optimal Party Positions

Usage

equilibrium(start, model, data, tolerance = 1e-05, max.iter = 100, 
coal = 0, alpha = 0, margin = NULL, fixed = NULL, gamma = 0, 
boot = 0, MC = 0, self.var = "self", prox.var="prox", 
position=NULL, votes=NULL, quadratic=TRUE)

Arguments

start

initial party positions. Numerical vector. Optional.

model

the mlogit model analysis

data

the data set

tolerance

tolerance in the convergence of Nash equilibrium. Default 1e-5

max.iter

max iteration to convergence in Nash equilibrium. Default 100

coal

a list specificing electoral coalitions. See Details.

alpha

the weight of coalition vote-share in party utility function. Default = 0. See Details.

margin

a list specifing the vote share margin to be maximized of a party/coalition against other party/coalition. See Details.

fixed

a list of fixed party positions. See Details.

gamma

the weight among nash and fixed arty position. Default=0. See Details.

boot

number of boostrap replications. See Details.

MC

number of Monte Carlo replications. See Details.

self.var

character: name of self-placement of respondent. See Details.

prox.var

character: name of party-placement variable. See Details.

position

a named list: of perceived position of parties. See Details.

votes

a named list: of actual vote share at election. See Details.

quadratic

a logical value: if FALSE the linear utility function is used to calculate the proximity. See Details.

Value

• an object of class nash.eq

Details

See vignette.

References

Adams, James F., Samuel Merrill III, and Bernard Grofman (2005). A Unified Theory of Party Competition. Cambridge: Cambridge University Press Merrill, Samuel III, and James Adams (2001), Computing Nash Equilibria in Probabilistic, Multiparty Spatial Models with Nonpolicy Components, Political Analysis, 9, 347--61

See Also

See Also as plot.nash.eq

Examples

data(italy2006)

str(italy2006)
italy2006[1:2,1:14]

election <- mlogit.data(italy2006 , shape="wide", choice="vote", 
varying=c(5:14), sep="_")
str(election)

m <- mlogit(vote~prox+partyID | gov_perf+sex+age+education, 
election, reflevel = "UL")
summary(m)

true.pos <- list(FI=7.59, UL=3.50, RC=1.95, AN=8.08, UDC=5.66)
true.votes <- list(FI=.24, UL=.40, RC=.10, AN=.18, UDC=.08)
# model 1: comparison against true votes and party positions
nash.eq <- equilibrium(model=m, data=election, pos=true.pos, 
 votes=true.votes)
nash.eq

par(mfrow=c(3,1))
plot(nash.eq)
par(mfrow=c(1,1))

# model 2: colation behaviours
coal1 <- list(FI=1, UL=2, RC=2, AN=1, UDC=1)
alpha1 <- list(FI=0.5, UL=0.5, RC=0.5, AN=0.5, UDC=0.5)
nash.eq <- equilibrium(model=m, data=election, coal=coal1, 
 alpha=alpha1)
nash.eq

# model 3: colation behaviours
coal1 <- list(FI=1, UL=2, RC=2, AN=1, UDC=1)
alpha1 <- list(FI=0.7, UL=0.8, RC=0.1, AN=0.5, UDC=0.9)
nash.eq <- equilibrium(model=m, data=election, coal=coal1, 
 alpha=alpha1)
nash.eq

# model 4: rivals tends to separate each other
nash.eq <- equilibrium(model=m, data=election, margin=list(FI="UL", UL="FI"))
nash.eq

# model 5: fixed position averaged with Nash equilibrium solution
nash.eq <- equilibrium(model=m, data=election, fixed=list(RC=1), gamma=0.2)
nash.eq

# model 6: rivals tends to separate each other with 
# fixed position averaged with Nash equilibrium solution
nash.eq <- equilibrium(model=m, data=election,  
margin=list(FI="UL", UL="FI"), fixed=list(RC=1), gamma=0.2)
nash.eq

# model 7: coalition and fixed position averaged with 
# Nash equilibrium solution
coal1 <- list(FI=1, UL=2, RC=2, AN=1, UDC=1)
alpha1 <- list(FI=0.7, UL=0.8, RC=0.5, AN=0.5, UDC=0.5)
nash.eq <- equilibrium(model=m, data=election,  coal=coal1, 
 alpha=alpha1, fixed=list(RC=1), gamma=0.2)
nash.eq

# model 8: Bootstrap analysis
nash.eq <- equilibrium(model=m, data=election, boot=10)
nash.eq

# model 9: Monte Carlo simulation
nash.eq <- equilibrium(model=m, data=election, MC=10)
nash.eq