In skranz/StratTourn: Tournament of game theoretic strategies

library(StratTourn)
library(shiny)
setwd("D:/libraries/StratTourn")




tourn = load.tournament("Tourn_Noisy_PD_20140910_143903_2.tou")
# Data for each match
md = tourn$dt
md = add.other.var(md,c("strat","u"))
md$delta.u = md$u - md$other.u
# Names of all strategies
strats = unique(md$strat)

# Data for each round
file = tourn$rs.file
rd = fread(file)
rd = as.tbl(as.data.frame(rd))
rd = add.other.var(rd,c("strat","u"))

# Names of all strategies
strats = unique(rd$strat)

# Perhaps select a subset of strategies
used.strats = strats
ard = rd

if (!identical(used.strats,strats)) {
  rows = rd$strat %in% used.strats & rd$other.strat %in% used.strats
  rd = ard[rows,]
}

Reciprocity and niceness indicators

rd = ard
ds = summarise(group_by(rd, match.id, i, strat, other.strat),
  T = length(t),
  u.mean = mean(u),
  other.u.mean = mean(other.u),              
  u.first = u[1],
  other.u.first = other.u[1],
  u.without.last = mean(u[-length(u)]),
  other.u.without.first = mean(other.u[-1])
)


reg = function(formula,dat) {
  if (length(dat)==0)
    return(NULL)
  res = lm(formula,data=dat, weights=u.weight)
  vec = round(coef(res),4)
  as.data.frame(t(vec))
}

ds = as.data.frame(ds)
ds$u.weight = ds$T-1
if (length(ds)==0)
  return(NULL)
df = do(group_by(ds,strat), reg(other.u.without.first~u.without.last,dat=.))
colnames(df) = c("strat","beta0","reciprocity")
#df1 = do(group_by(d,strat), reg(other.u.mean~u.mean,dat=.))

rdf = as.data.frame(strat.rank.from.matches(dt = md,tourn = tourn))
ndf = as.data.frame(mean.over.matches(dt = md,var="other.u",tourn = tourn))
fdf = as.data.frame(summarise(group_by(ds, strat), other.first=round(mean(other.u.first),4)))


d = merge(select(rdf,strat,rank,mean),select(df,strat,reciprocity), by="strat")
d = merge(d, ndf[c("strat","other.u")])
d = merge(d, fdf, by="strat")
colnames(d)[c(3,5)]=c("payoff","other.payoff")
d[,3:5] = round(d[,3:5],4)
d = arrange(d, rank)
d$`other-own` = d$other.payoff-d$payoff
view(d)

Computation of reciprocity

Reciprocity is the general concept to respond to positive actions with positive actions and to respond to negative actions with negative actions. We basically run the following regressions for each strategy using average payoffs of all matches:

u.other = beta0 + beta1*u + epsilon

(we call beta1 = reciprocity)

The interpretation of beta1=reciprocity, is that if player i has one unit higher average payoff then the other player j has on average beta1 units higher payoff.

Actually, our regression is slightly adapted. The variable u.other is the mean payoff of the other strategy not including period t=1. The variable u is the mean payoff including the first period, but not the last period. This shifting corrects for the fact that reciprocity is a reaction to observed behavior of the other player. This correction becomes in particular relevant for low discount factors in which we observe many short games of length T=1 or T=2.

Large, positive values of beta1 are one indicator that the strategy behaves reciprocal. However, the estimates of beta1 depend strongly on the other strategies. A low or negative value of beta1 does not neccessarily mean that the strategy is not reciprocal.

skranz/StratTourn documentation built on May 30, 2019, 2:02 a.m.