Repeated Games - Online Tutor, Practice Problems & Exam Prep

In repeated games, players make decisions multiple times, enhancing the potential for collusion. Strategies like tit for tat, where players mimic the previous actions of their opponent, and the trigger strategy, which punishes any cheating permanently, illustrate this dynamic. These strategies can lead to cooperative outcomes, maximizing profits, such as earning 1800 instead of 1600 when both players cheat. Understanding these concepts is crucial for analyzing market structures like oligopolies and the implications of game theory in economics.

Repeated Games

Alright, so now let's talk about a different kind of game, the repeated game. So, a repeated game is more realistic, right? When we were talking up to now, we were talking about one-time games, right, where you got to play one time and that was your best shot. You give it your best shot that one time and do what you can, right? But a repeated game, it's going to be a situation where we play the same game over and over again, right? This makes more sense in real life. Jack and Jill's output decisions, they're not just going to produce water one time for their town and that's it. They'll probably have to keep making these decisions week after week, month after month, right? They're going to have to keep making these decisions and this interdependence between them makes a bigger deal when we have to keep making these decisions over and over, right? So when we have to make this decision over and over, it's going to cause them to want to collude even more, right? So, what we're going to see is that this repeated game, right, it's that one-time game that we're playing over and over again. So, our strategies are going to be different because we're not just playing one time.

Okay, so we've got a couple strategies here. The first one is called tit for tat. Okay, a tit for tat strategy, I put it in kind of common terms here. That's the idea of I'm going to do whatever you did last time, okay? I cooperate this period, alright? So the first period, you're going to cooperate and then if you didn't cooperate, next period I'm going to cheat, right? So I'm always going to do what you did last period. If you cheated last period, this period I will cheat. If you cooperated last period, this period I will cooperate, right? So you're just retaliating based on what they did last period. The other strategy is the trigger strategy. So the trigger strategy is someone who's going to cooperate forever until you cheat once. If you cheat once, that's it, they're done with you, they're going to cheat forever going on, right? They're triggered and they're just going to keep cheating from that point on, alright? So you can imagine when we have our Jack and Jill decision, their decisions in the long run, right? When they're having to make this decision week after week, they're going to probably try and aim for a collaborative agreement, right? Somewhere where they can both be earning 1800 instead of the 1600 they would earn when they both cheat, right? So let's go ahead and try some practice problems with these new strategies that we learned.

Jack employs a tit-for-tat strategy. If Jill cooperates this period, how many gallons will Jack produce?

• A. 30 gallons
• B. 40 gallons
• C. 70 gallons
• D. Not enough information

Jack employs a tit-for-tat strategy. If Jill cheated last period, what will Jack's total profit equal this period?

• A. $1,500
• B. $1,600
• C. $1,800
• D. $2,000
• E. Not enough information

Here’s what students ask on this topic:

What is a repeated game in microeconomics?

A repeated game in microeconomics refers to a scenario where the same game is played multiple times by the same players. Unlike one-time games, repeated games allow players to adjust their strategies based on past interactions. This dynamic can lead to different outcomes, such as increased cooperation or collusion, as players may seek to maximize their long-term benefits. Strategies like tit for tat and trigger strategy are commonly used in repeated games to enforce cooperation or punish cheating. Understanding repeated games is crucial for analyzing behaviors in market structures like oligopolies.

How does the tit for tat strategy work in repeated games?

The tit for tat strategy in repeated games involves a player mimicking the previous action of their opponent. Initially, a player will cooperate. In subsequent rounds, the player will replicate whatever the opponent did in the previous round. If the opponent cooperated, the player will cooperate in the next round. If the opponent cheated, the player will cheat in the next round. This strategy promotes cooperation by rewarding cooperative behavior and punishing cheating, making it a powerful tool for sustaining long-term collaboration in repeated interactions.

What is the trigger strategy in repeated games?

The trigger strategy in repeated games is a strategy where a player cooperates until the opponent cheats. Once the opponent cheats, the player will cheat in all subsequent rounds. This strategy serves as a severe punishment for cheating, as it ensures that any deviation from cooperation results in a permanent loss of trust and ongoing retaliation. The trigger strategy can effectively deter cheating and promote sustained cooperation, as players understand the long-term consequences of their actions.

Why are repeated games important in understanding oligopolies?

Repeated games are important in understanding oligopolies because they illustrate how firms in an oligopoly can sustain cooperation and avoid price wars. In an oligopoly, firms interact repeatedly over time, making it possible for them to use strategies like tit for tat or trigger strategy to enforce collusion and maintain higher prices. By understanding repeated games, economists can better analyze how firms in an oligopoly might behave, predict market outcomes, and design policies to promote competition and prevent anti-competitive practices.

How do repeated games lead to cooperative outcomes?

Repeated games lead to cooperative outcomes by allowing players to build trust and enforce agreements over time. Strategies like tit for tat and trigger strategy encourage cooperation by rewarding collaborative behavior and punishing cheating. In a repeated game, players recognize that their actions in one round affect future interactions, making cooperation more attractive. By consistently cooperating, players can achieve higher long-term payoffs compared to the short-term gains from cheating. This dynamic fosters a stable environment where mutual cooperation becomes the rational choice.