Why Is Cooperative Equilibrium More Likely in Repeated Games with Fewer Players?

[vsage]

This isn't entirely related to one of the pure sciences and I don't need the math but anyway here's the question. "Cooperative equilibrium is most likely to form in prisoner's dilemma-type games of:

A. No communication and single round
B. Single round and a large number of players
C. Repeated rounds and a small number of players
D. Repeated rounds and a large number of players"

My economics book doesn't mention anything about whether a large of small amount of people affects whether a cooperative equilibrium is likely to arise. I thought it over for about an hour now and I can't seem to prove that more people = more cooperation or that factions would start to form and destroy the cooperative equilibrium. Having played this game before several times I've noticed that when I am in a larger group that the group tends to want to backstab the other team more.

 

[wais]

The correct answer is C. Repeated rounds and a small number of players.

In a prisoner's dilemma game, the optimal outcome for both players is to cooperate and receive a lower individual payoff than if they had both chosen to defect. However, in a one-time, no communication game, there is no incentive for either player to cooperate as they cannot communicate and trust each other's actions.

In a single round with a large number of players, there is a higher chance of defection as each player's individual impact on the outcome is smaller and they may not feel as much responsibility for the overall outcome.

On the other hand, in a repeated rounds game with a small number of players, there is a higher likelihood of developing trust and cooperation over time. Players have the opportunity to observe and learn from each other's actions, leading to the formation of a cooperative equilibrium. Additionally, in a small group, there is a stronger sense of responsibility and accountability for the overall outcome, making cooperation more beneficial for all players.

In summary, the combination of repeated rounds and a small number of players provides the necessary conditions for a cooperative equilibrium to form in a prisoner's dilemma game.