Game theory in Joint Venture Marketing (R code)

by gatekeeper on 14.06.2020

Sometimes companies share common interest and goals. A good example would be a joint venture of digital agencies that are partially or fully owned by a large full-service agency. They would like to join forces and provide to new customers an optimal digital reach on sites where they previously lacked any visibility.

Let us assume, that three partner agencies are confident that they can gain from building and offering a common digital space. The more they are investing in this project, the more customers could be attracted and the more they will expect high potential return on their investment. Imagine this would be the potential return on investment.

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Suppose, agency 1 would like to invest $1.8 M, agency 2 — $0.9 M and agency 3 — $0.4 M. All companies would benefit but the big question is, how should the net amount earned on the total investment be split among the three agencies?

In order to give a proper solution the problem we can use the game theory to help determine the most likely outcomes. According the Wikipedia “Game theory is the study of mathematical models of strategic interaction among rational decision-makers”. In our case, we are referring to the cooperative game theory examining the behavior of colluding digital agencies.

Here is the R code I used to solve the problem:

install.packages("GameTheory")
library(GameTheory)


COALITIONS <- c(90000,36000,16000,135000,110000,65000,170500)
LEMAIRE<-DefineGame(3,COALITIONS)
summary(LEMAIRE)


NAMES <- c("Company 1","Company 2","Company 3")
LEMAIRESHAPLEY <- ShapleyValue(LEMAIRE,NAMES)
summary(LEMAIRESHAPLEY)

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The C‑vector should be calculated based on the possible sets of cooperation among the tree companies.

And here is the final answer, the solution concept of fairly distributed gains.

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