Feasible Payoff Set

Definition

The feasible payoff set refers to the collection of all possible outcomes or payoffs that players in a game can achieve while adhering to the constraints imposed by the game's rules and strategies. This set is crucial in understanding how players can reach equilibrium payoffs, as it helps identify which outcomes are attainable based on the strategies they choose. The concept also plays a vital role in folk theorems, which assert that any payoff within this set can potentially be sustained as an equilibrium under certain conditions.

5 Must Know Facts For Your Next Test

1. The feasible payoff set is defined by the available strategies and preferences of players involved in a game.
2. Folk theorems highlight that as long as players are able to communicate and enforce agreements, any payoff within the feasible payoff set can be sustained as an equilibrium.
3. The shape of the feasible payoff set can vary significantly depending on the number of players and their strategies, leading to different possible outcomes.
4. Understanding the feasible payoff set allows economists to predict how players will behave in different strategic environments, influencing real-world decision-making.
5. In non-cooperative games, the feasible payoff set is often smaller than in cooperative games because players cannot form binding agreements.

Review Questions

• How does the feasible payoff set relate to achieving Nash Equilibrium in a game?
  • The feasible payoff set is integral to understanding Nash Equilibrium because it defines the outcomes that players can achieve given their strategies. A Nash Equilibrium occurs when players settle on a strategy profile where no one has an incentive to deviate, meaning the chosen payoffs must lie within the feasible payoff set. If an equilibrium point is outside this set, it cannot be realized as it violates the constraints of available strategies.
• Discuss how folk theorems utilize the concept of the feasible payoff set to explain cooperation in repeated games.
  • Folk theorems leverage the feasible payoff set by asserting that, in repeated games, players can achieve a wide range of outcomes beyond those predicted by one-shot games. By allowing for communication and repeated interactions, any payoff within this set can become stable as long as players are able to enforce cooperative behavior. This shifts focus from immediate payoffs to long-term strategies, showing how cooperation can emerge even among self-interested agents.
• Evaluate how understanding the feasible payoff set influences strategic decision-making in competitive markets.
  • Understanding the feasible payoff set significantly influences strategic decision-making because it helps identify potential outcomes that firms can realistically achieve based on their choices and competitive environment. Firms analyze their strategies relative to others, focusing on points within this set to optimize their payoffs. This evaluation guides them in making informed decisions about pricing, production levels, and market entry, ultimately shaping competitive dynamics and market efficiency.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit by unilaterally changing their strategy, given that other players' strategies remain unchanged.

Pareto Efficiency: A state where no player's situation can be improved without worsening another player's situation, indicating an optimal allocation of resources.

Cooperative Game Theory: A branch of game theory that studies how groups of players can form coalitions and how they can distribute payoffs among themselves.