It is sometimes pointed out that cooperative games can in a...

It is sometimes pointed out that cooperative games can in a certain sense be 'reduced to', or 'derived from', non-cooperative games. What does this mean? That is, what is the relation between cooperative and non-cooperative games? (a) What is an iterated game? (b) What does it mean to play tit for tat in the iterated prisoner's dilemma? (a) What does the term 'evolutionary stable strategy' mean? (b) Is evolutionary game theory a descriptive theory, or a normative theory, or something else?

It is sometimes pointed out that cooperative games can in a certain sense be 'reduced to', or 'derived from', non-cooperative games. What does this mean? That is, what is the relation between cooperative and non-cooperative games?
(a) What is an iterated game?
(b) What does it mean to play tit for tat in the iterated prisoner's dilemma?
(a) What does the term 'evolutionary stable strategy' mean?
(b) Is evolutionary game theory a descriptive theory, or a normative theory, or something else?

Key Concepts

Evolutionarily Stable Strategy (ESS)

An evolutionarily stable strategy (ESS) is a strategy which, if adopted by a population, cannot be overtaken by any alternative strategy because it yields a higher fitness or payoff when played against itself than any mutant strategy does. It is a central concept in evolutionary game theory that explains how strategic behavior can persist over time in a population and be resistant to invasions by competing strategies.

Cooperative vs Non-Cooperative Games

This concept deals with the distinction and interplay between games where binding agreements and collective strategies are allowed (cooperative games) and those where each player makes individual choices without collaboration (non-cooperative games). The idea that cooperative games can be 'reduced to' non-cooperative games points to modeling cooperation through enforced or voluntary agreements implemented within non-cooperative frameworks, often revealing how strategic considerations can mimic cooperative outcomes under certain conditions.

Iterated Games

An iterated game is a repeated interaction of a base game, where players engage in the same strategic decision-making scenario multiple times. This repetition introduces the potential for strategy evolution, reputation effects, and the possibility for players to reward or punish past behaviors, thereby fostering cooperative behavior and the emergence of long-term dynamics not seen in a one-shot game.

Tit for Tat

Tit for tat is a strategy in iterated games, particularly in the prisoner's dilemma, where a player replicates the opponent's previous action—cooperating if the opponent cooperated in the last round and defecting if the opponent defected. This approach promotes mutual cooperation while discouraging unilateral defection, as it provides a clear and immediate response to an opponent's actions, balancing retaliation and forgiveness.

Evolutionary Game Theory

Evolutionary game theory extends classical game theory by focusing on the dynamics of strategy change in populations over time, often driven by natural selection or learning processes. Rather than prescribing how rational agents should behave (normative), it describes how strategies evolve and stabilize in real-world situations, making it primarily a descriptive and explanatory tool for understanding behavioral dynamics in competitive and cooperative contexts.

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