Payoff distribution

Definition

Payoff distribution refers to the allocation of the total gains or benefits resulting from a cooperative game among its players. In cooperative games, players can negotiate and form coalitions to achieve better outcomes collectively than they could individually. The way these payoffs are distributed among players can significantly influence their willingness to cooperate and the stability of the formed coalitions.

5 Must Know Facts For Your Next Test

1. Payoff distribution is central to understanding cooperation in games, as it directly impacts players' incentives to join and remain in coalitions.
2. Different methods of payoff distribution can lead to different outcomes in terms of stability and fairness within the coalition.
3. The Shapley value is one popular approach for determining a fair payoff distribution based on each player's contribution.
4. In some cases, the core may contain multiple distributions, leading to different stable arrangements for how payoffs can be shared among players.
5. Players often negotiate and strategize around payoff distributions, making it a crucial aspect of cooperative game theory.

Review Questions

• How does payoff distribution impact the stability of coalitions in cooperative games?
  • Payoff distribution directly influences coalition stability by affecting players' incentives. If the distribution is perceived as unfair or inequitable, players may have an incentive to leave the coalition and pursue alternative arrangements. A fair payoff distribution encourages cooperation and helps maintain stable coalitions, while an unfair one can lead to disbanding or conflict among members.
• What role does the Shapley value play in determining a fair payoff distribution among players in a cooperative game?
  • The Shapley value provides a systematic method for calculating a fair payoff distribution by considering each player's contribution to every possible coalition. It takes into account the marginal contributions of each player, ensuring that those who contribute more to achieving the overall gains receive a larger share of the payoffs. This method promotes fairness and can help prevent disputes over how payoffs are divided among coalition members.
• Evaluate the implications of using the core concept when discussing payoff distributions in cooperative games.
  • The core concept highlights the importance of stability in payoff distributions by ensuring that no subset of players would prefer to form their own coalition. If a payoff distribution falls within the core, it means that all players are receiving at least as much as they could achieve on their own. This evaluation is crucial because it helps identify viable solutions where all players are satisfied with their share, thus promoting long-term cooperation and preventing fragmentation of coalitions.

Related terms

coalition: A coalition is a group of players who agree to cooperate in order to achieve a common goal or increase their collective payoff in a cooperative game.

Shapley value: The Shapley value is a solution concept that provides a method for fairly distributing payoffs to players based on their marginal contributions to different coalitions.

core: The core is the set of payoff distributions in a cooperative game where no subset of players would prefer to break away from the grand coalition, as they cannot achieve a better outcome on their own.