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.

 

[anathema]

I can provide some insights on this question. The formation of cooperative equilibrium in prisoner's dilemma-type games is influenced by various factors, including the number of players and the number of rounds. Let's break down the options provided and see how these factors might affect the outcome.

A. No communication and single round
In this scenario, there is no opportunity for players to communicate or strategize with each other. As such, the players are more likely to focus on their individual gain rather than working together. This makes it less likely for a cooperative equilibrium to form.

B. Single round and a large number of players
In a single round with a large number of players, there is a higher chance for factions to form. As you mentioned, you have noticed that larger groups tend to want to backstab the other team more. This is because there is less trust and cooperation among a larger group of players. As a result, it is less likely for a cooperative equilibrium to form.

C. Repeated rounds and a small number of players
In this scenario, there is an opportunity for players to communicate and strategize with each other, leading to a higher chance of cooperation. Additionally, with a smaller number of players, it is easier to build trust and maintain a cooperative equilibrium over multiple rounds.

D. Repeated rounds and a large number of players
Similar to option B, a larger number of players in repeated rounds can lead to the formation of factions and a decrease in trust and cooperation. However, the repeated rounds can also provide opportunities for players to learn from their previous choices and develop strategies for cooperation. This could potentially lead to a cooperative equilibrium forming, but it may be more challenging to maintain with a larger group of players.

In conclusion, the number of players and rounds can both have an impact on the formation of cooperative equilibrium in prisoner's dilemma-type games. However, it is not a straightforward relationship and can depend on various other factors such as communication and trust among players. I would recommend exploring further research on this topic to gain a better understanding of the dynamics at play in these games.

 

[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.