Summindemandi

Summindemandi, also known as "sum of the minimum demands," is a concept in economics and game theory that refers to the total amount of resources that players in a game or market are willing to accept as a minimum. This concept is particularly relevant in cooperative game theory, where players can form coalitions to achieve better outcomes.

In a cooperative game, each player has a minimum demand, which is the least amount of payoff they require to participate in a coalition. The sum of these minimum demands across all players is the summindemandi. This value provides insights into the feasibility of forming coalitions and the stability of the resulting agreements.

The summindemandi is a crucial factor in determining the core of a cooperative game. The core is the set of payoff distributions that are stable, meaning no coalition of players can improve their payoffs by leaving the grand coalition. For a payoff distribution to be in the core, the sum of the payoffs to the players in any coalition must be at least as large as the sum of the minimum demands of those players.

In practical terms, the summindemandi helps in assessing whether a proposed payoff distribution is fair and stable. If the sum of the payoffs to a coalition is less than the sum of the minimum demands of its members, the coalition is likely to dissolve, leading to instability. Conversely, if the sum of the payoffs is at least as large as the sum of the minimum demands, the coalition is more likely to be stable.

The concept of summindemandi is fundamental in understanding the dynamics of cooperation and the distribution of resources in various economic and social contexts. It provides a quantitative measure of the minimum requirements for cooperation and helps in designing mechanisms to ensure stable and fair outcomes.