Common use of Linear Sharing Rule Clause in Contracts

Linear Sharing Rule. ‌ Here we would restrict our attention to a special kind of sharing rule which is most commonly seem in real life - linear sharing rule. 3.1. A sharing rule S : R → Rn, where n = 2, 3, . . . is said to be linear if: 1. For any Y ∈ R, the share to each team member i has the following struc- ture: si(Y ) = αiY + βi, where αi and βi are constants or functions that are independent of Y , where the share is non-negative: αi ≥ 0. 2. The budget is balanced such that Σ αi = 1 and Σ βi = 0. The definition says, a linear sharing rule contains two parts, for each team member i it specifies a portion αi of the output which must sum up to 1 and a constant income/payment βi which must sum up to 0. The simple structure of linear sharing rules makes them easily enforced by courts. Moreover, by using a linear sharing rule the team members are pretty sure that the shares they get si(Y ) is monotone increasing with the output Y , since Sir(Y ) = αi ≥ 0. However, the incentive provided by linear sharing rule is not strong enough to produce the first best outcome ( ▇▇▇▇▇▇▇▇▇ [1982]). This is due to the fact that any agent’s ▇▇▇▇▇ will save his/her effort cost fully while the negative impact on the output will be shared with others. If we stick to balancing the budget, the punishment from a linear sharing rule can never be strong enough to achieve an efficient outcome. In the static model in ▇▇▇▇▇▇▇▇▇ [1982], the action vector of the team aˆ constitutes a ▇▇▇▇ equilibrium if and only if for each i, aˆi solves ▇▇▇ ▇▇(f (ai, aˆ−i)) − ci(ai), subject to for each i, individual rationality is satisfied that is πi ≥ π¯i.

Linear Sharing Rule. ‌ Here we would restrict our attention to a special kind of sharing rule which is most commonly seem in real life - linear sharing rule. 3.1. A sharing rule S : R → Rn, where n = 2, 3, . . . is said to be linear if: 1. For any Y ∈ R, the share to each team member i has the following struc- ture: si(Y ) = αiY + βi, where αi and βi are constants or functions that are independent of Y , where the share is non-negative: αi ≥ 0. 2. The budget is balanced such that Σ αi = 1 and Σ βi = 0. The definition says, a linear sharing rule contains two parts, for each team member i it specifies a portion αi of the output which must sum up to 1 and a constant income/payment βi which must sum up to 0. The simple structure of linear sharing rules makes them easily enforced by courts. Moreover, by using a linear sharing rule the team members are pretty sure that the shares they get si(Y ) is monotone increasing with the output Y , since Sir(Y Sij(Y ) = αi ≥ 0. However, the incentive provided by linear sharing rule is not strong enough to produce the first best outcome ( ▇▇▇▇▇▇▇▇▇ [1982]). This is due to the fact that any agent’s ▇▇▇▇▇ will save his/her effort cost fully while the negative impact on the output will be shared with others. If we stick to balancing the budget, the punishment from a linear sharing rule can never be strong enough to achieve an efficient outcome. In the static model in ▇▇▇▇▇▇▇▇▇ [1982], the action vector of the team aˆ constitutes a ▇▇▇▇ equilibrium if and only if for each i, aˆi solves ▇▇▇ ▇▇(f (ai, aˆ−i)) − ci(ai), subject to for each i, individual rationality is satisfied that is πi ≥ π¯i.