match two data.frames based on multiple columns

In case you would use match or %in% on multiple columns you could use interaction, paste or use a list to match on multiple columns.

df[match(interaction(mdf), interaction(df[c("car_1", "car_2")])),]

df[match(paste(mdf$car_1, mdf$car_2), paste(df$car_1, df$car_2),),]

df[match(asplit(mdf, 1), asplit(df[c("car_1", "car_2")], 1)),]

df[interaction(df[c("car_1", "car_2")]) %in% interaction(mdf),]

How about merge(df, mdf, all.x = FALSE, all.y = TRUE)?

Edit: If you have different column names you can specify which ones to merge on, e.g.:

names(mdf) <- c("car_3", "car_4")
merge(df, mdf, by.x = c("car_1", "car_2"), by.y = c("car_3", "car_4"), 
      all.x = FALSE, all.y = TRUE)

Another way would be:

library(dplyr)
inner_join(df, mdf)

#Joining by: c("car_1", "car_2")
#              car_1          car_2  mpg cyl disp
#1        Datsun 710 Ford Pantera L 22.8   4  108
#2    Hornet 4 Drive   Ferrari Dino 21.4   6  258
#3 Hornet Sportabout  Maserati Bora 18.7   8  360
#4           Valiant     Volvo 142E 18.1   6  225