Uncoupled Nash Equilibrium Procedures Reveal Exponential Communication Barriers to Reaching Equilibrium
The research explores how long it takes for players to reach equilibrium in certain game scenarios without direct connections. They look at situations where each player only knows their own potential winnings and investigate the communication needed to achieve a balanced outcome, called a Nash equilibrium. The results show that it takes a significant amount of communication, measured in bits, to reach these equilibriums. This communication requirement grows exponentially with the number of players when aiming for different types of equilibriums – pure, Bayesian, or mixed. Surprisingly, even simple methods result in this high communication complexity, showing the challenge of reaching balanced outcomes in uncoupled settings.