HyRiM (version 1.0.3)

disappointmentRate: computation of the disappointment rate

Description

For a minimizing player, the disappointment rate is the likelihood for the loss to exceed its expectation (thus disappoint the defender). For any random loss \(X\), it is given by \(Pr(X > E(X))\).

Usage

disappointmentRate(d)

Arguments

d

a lossDistribution object; typically the assurance from a previously computed equilibrium (see mgss)

Value

the likelihood to overshoot the expectation of the random loss \(X\) with distribution d, i.e., \(Pr(X > E(X))\).

Details

The disappointment rate can be taken as an auxiliary goal to optimize, though it is not supported for optimization in the current version of the package. Note that it does not make sense to consider this rate as an isolated (single) goal, since the optimal strategy would then be playing towards maximal losses (with explicit aid of the opponent) in order to minimize the mass to the left of the expected loss. However, it is a quantity of interest when the equilibrium has been computed, as it indicates how ``satisfying'' the equilibrium will be upon playing.

See the literature for further

References

see for example, F. Gul: "A Theory of Disappointment Aversion", Econometrica, vol. 59, no. 3, p. 667, 1991.

See Also

mgss

Examples

# NOT RUN {
library(compare)
library(orthopolynom)
## raw data (PURELY ARTIFICIAL, for demo purposes only)
# N=100 observations in each category
obs111<-c(rep(1,40),rep(3,20),rep(5,10),rep(7,20),rep(9,10)); 
obs112<-c(rep(1,50),rep(2,10),rep(4,10),rep(6,20),rep(8,10)); 
obs121<-c(rep(1,20),rep(4,30),rep(6,20),rep(8,10),rep(10,20));
obs122<-c(rep(1,40),rep(2.5,20),rep(5,20),rep(7.5,10),rep(9,10));
obs211<-c(rep(1,30),rep(2,30),rep(5,10),rep(8,10),rep(10,20));
obs212<-c(rep(1,10),rep(2,10),rep(4,20),rep(7,20),rep(10,40));
obs221<-c(rep(1,30),rep(3,30),rep(4,10),rep(7,20),rep(9,10));
obs222<-c(rep(1,10),rep(3,10),rep(5,50),rep(8,20),rep(10,10));
obs311<-c(rep(1,40),rep(2,30),rep(4,10),rep(7,10),rep(9,10));
obs312<-c(rep(1,20),rep(3,20),rep(4,20),rep(7,20),rep(10,20));
obs321<-c(rep(1,10),rep(3,40),rep(4,30),rep(7,10),rep(9,10));
obs322<-c(rep(1,10),rep(4,30),rep(5,30),rep(7,10),rep(10,20));

## compute payoff densities
f111<-lossDistribution(obs111)
f112<-lossDistribution(obs112)
f121<-lossDistribution(obs121)
f122<-lossDistribution(obs122)
f211<-lossDistribution(obs211)
f212<-lossDistribution(obs212)
f221<-lossDistribution(obs221)
f222<-lossDistribution(obs222)
f311<-lossDistribution(obs311)
f312<-lossDistribution(obs312)
f321<-lossDistribution(obs321)
f322<-lossDistribution(obs322)

payoffs<-list(f111,f112,f121, f122,f211,f212,f221,f222, f311,f312,f321,f322)
G <- mosg( n=2,
            m=2,
            payoffs,
            goals=3,
            goalDescriptions=c("g1", "g2", "g3"),
            defensesDescr = c("d1", "d2"),
            attacksDescr = c("a1", "a2"))
eq <- mgss(G,T=1000,weights=c(0.25,0.5,0.25))

# get the disappointment rate for the first security goal g1
disappointmentRate(eq$assurances$g1)
# }