equilibrium {nopp}

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, conf.level = 0.95)

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.

conf.level

significant level for empirical Monte Carlo or bootstrap confidence intervals.

Details

See vignette.

Value

an object of class nash.eq

Note

See the vignette for detailed explanations and other working examples.

Author(s)

Luigi Curini, Stefano M. Iacus

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

Curini, L., and Iacus, S.M. (2017) Nash Optimal Party Positions: The nopp R Package, Journal of Statistical Software, 81(11), 1–25

See Also

See Also as plot.nash.eq

Examples

## Not run: 
data(italy2006)

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

election <- set.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
set.seed(280715)
nash.eq <- equilibrium(model=m, data=election, boot=10)
nash.eq

# model 9: Monte Carlo simulation
set.seed(280715)
nash.eq <- equilibrium(model=m, data=election, MC=10)
nash.eq

## End(Not run)