Economics Game Theory Questions Long
Evolutionary stable strategy (ESS) is a concept in game theory that refers to a strategy that, once adopted by a population of individuals, cannot be easily invaded by alternative strategies. In other words, an ESS is a strategy that, if prevalent in a population, will resist any invasion by other strategies, making it evolutionarily stable.
To understand the concept of ESS, it is important to first grasp the basic principles of game theory. Game theory is a mathematical framework used to analyze strategic interactions between rational decision-makers. In game theory, individuals are assumed to make decisions based on their own self-interest, aiming to maximize their own payoffs.
In the context of game theory, an evolutionary game is a model that simulates the evolution of strategies within a population over time. These games are often used to study the dynamics of biological and social systems, where individuals interact repeatedly and adapt their strategies based on the outcomes of their interactions.
In an evolutionary game, a strategy is considered evolutionarily stable if it is resistant to invasion by alternative strategies. This means that if a population is predominantly using a particular strategy, any individual adopting a different strategy should not be able to gain a higher payoff, thus preventing the alternative strategy from spreading and becoming prevalent.
To determine whether a strategy is an ESS, we need to consider the concept of fitness. Fitness refers to the reproductive success of individuals within a population. In game theory, fitness is often measured by the average payoff an individual receives when interacting with others.
An ESS is characterized by three conditions:
1. It must be an internally stable strategy: This means that individuals using the strategy should not have an incentive to deviate from it. If an individual using the strategy were to switch to an alternative strategy, their payoff should be lower.
2. It must be externally stable: This means that if a small group of individuals within the population adopts an alternative strategy, they should not be able to gain a higher payoff than those using the ESS. If the alternative strategy is not as successful, it will not spread and become prevalent.
3. It must be resistant to mutant strategies: This means that even if a rare mutant strategy emerges within the population, it should not be able to invade and replace the ESS. The ESS should have a higher payoff than the mutant strategy, preventing it from spreading.
Overall, an ESS represents a stable equilibrium in a population, where the prevalent strategy cannot be easily replaced by alternative strategies. It is a concept that helps us understand the dynamics of strategic interactions and the stability of strategies within evolving populations.