Applications of Communication Complexity for Game Theory

Imagine the following scenario. Two prisoners, prisoner A and prisoner B, who are in the prison for the same crime, are being interrogated simultaneously in separate rooms. They are each given 2 options: (a) Either cooperate with the other prisoner by staying silent or (b) Betray the other prisoner by snitching him out. They are each given deals (reduced prison sentences) for betraying the other prisoner. However, if it turns out that both of them had betrayed each other, then they will both serve longer sentences than if they had both stayed silent. So, there are four possible scenarios: (a) Both stay silent (b) Both betray each other (c) Prisoner A remains silent and prisoner B betrays and (d) Prisoner B remains silent and prisoner A betrays. Below is a matrix representing the “payoffs” for each prisoner for the four different scenarios (By “payoffs”, we mean the quantification of preferences for different scenarios, depending on the prison sentences they each get for each scenario).