Infinite Repeated Game and Relational Contract. With the refinement of perfect equilibrium, we are pretty sure that the efficiency can be improved when a game is played infinitely (although first-best efficiency might still not be achieved). The threat of falling back to the non-corporative static equilibrium gives incentive to every team member to maintain a corporative outcome for each period. This idea of implicit cooperation is introduced to con- tracting which is referred to relational contract ( ▇▇▇▇▇ [2003]). In a relational con- tract, terms can be enforced implicitly other than explicitly (i.e. through a court), providing more flexibility of contracting. The long-term benefit from keeping to a productive relation can prevent players pursuing short-term interests through deviating. A relational contract contains the following elements: 1. A court-enforceable sharing rule. If the production occurs at period t, a for- mal contract specifying how the output will be shared should be established. If the sharing rule is linear, it then contains a share variable αt and a fixed income/payment βt. 2. A discretionary payment p. Since the payment is discretionary, p may depend both hard and soft information. Still, the budget within the team must be balanced such that Σ pt = 0 for each t. 3. The effort level each team member should take. 4. An action dt for all the team members specifying whether or not to join the production at period t. 5. An action ϕt for all the team members specifying whether or not to make the discretionary payment at period t. 6. The behavior after any of the team members renege. If one of the players renege, it’s natural for his opponents minimax this member’s pay-off, that is the trade been terminated and everyone receives their outside option, even though this punishment is costly (all the other team members will only have their outside options themselves afterwards). Note that we are currently focusing on deterministic case where the actions each team member makes determine a value of joint output. For non-deterministic case, which will be discussed later, team members’ actions determine a distribution rather than a value of output. 1 1 1 Let Ht = {h1, h2, . . . , ht} denote the pubic history at beginning of period t, ht = {Y t−1, St−1, lt−1, . . . , lt−1, pt−1, . . . , pt−1, dt−1, . . . , dt−1, ϕt−1, . . . , ϕt−1} denote the public information from the end of period t − 1 to the beginning of period t, and define h1 = ∅. We say a relational contract is self-enforcing if for any public history, they are willing to execute the discretionary payment pt, that is 1 t = · · · = ϕt = 1 Thus, a self-enforcing relational contract must satisfy the following constraints: 1. All team members must gain at least much as their outside options, that is for all i, πi ≥ π¯i (3.3) 2. The target effort level is implementable, that is IC constraints must hold. For all i and t, at ∈ arg max E[St(yt) + pt(Ht, lt, yt) − c(atj) + δ π (Ht, lt, yt)|Ht, atj, at ] 1 − δ i −i (3.4) 3. All team members are willing to implement the discretionary payment pt in all period t: pt(Ht, lt, yt) + δ π (Ht, lt, yt) ≥ δ π¯
Appears in 1 contract
Sources: PHD Thesis
Infinite Repeated Game and Relational Contract. With the refinement of perfect equilibrium, we are pretty sure that the efficiency can be improved when a game is played infinitely (although first-best efficiency might still not be achieved). The threat of falling back to the non-corporative static equilibrium gives incentive to every team member to maintain a corporative outcome for each period. This idea of implicit cooperation is introduced to con- tracting which is referred to relational contract ( ▇▇▇▇▇ [2003]). In a relational con- tract, terms can be enforced implicitly other than explicitly (i.e. through a court), providing more flexibility of contracting. The long-term benefit from keeping to a productive relation can prevent players pursuing short-term interests through deviating. A relational contract contains the following elements:
1. A court-enforceable sharing rule. If the production occurs at period t, a for- mal contract specifying how the output will be shared should be established. If the sharing rule is linear, it then contains a share variable αt and a fixed income/payment βt.
2. A discretionary payment p. Since the payment is discretionary, p may depend both hard and soft information. Still, the budget within the team must be balanced such that Σ pt = 0 for each t.
3. The effort level each team member should take.
4. An action dt for all the team members specifying whether or not to join the production at period t.
5. An action ϕt for all the team members specifying whether or not to make the discretionary payment at period t.
6. The behavior after any of the team members renege. If one of the players renege, it’s natural for his opponents minimax this member’s pay-off, that is the trade been terminated and everyone receives their outside option, even though this punishment is costly (all the other team members will only have their outside options themselves afterwards). Note that we are currently focusing on deterministic case where the actions each team member makes determine a value of joint output. For non-deterministic case, which will be discussed later, team members’ actions determine a distribution rather than a value of output. 1 1 1 Let Ht = {h1, h2, . . . , ht} denote the pubic history at beginning of period t, ht = {Y t−1, St−1, lt−1, . . . , lt−1, pt−1, . . . , pt−1, dt−1, . . . , dt−1, ϕt−1, . . . , ϕt−1} denote the public information from the end of period t − 1 to the beginning of period t, and define h1 = ∅. We say a relational contract is self-enforcing if for any public history, they are willing to execute the discretionary payment pt, that is 1 t = · · · = ϕt = 1 Thus, a self-enforcing relational contract must satisfy the following constraints:
1. All team members must gain at least much as their outside options, that is for all i, πi ≥ π¯i (3.3)
2. The target effort level is implementable, that is IC constraints must hold. For all i and t, at ∈ arg max E[St(yt) + pt(Ht, lt, yt) − c(atjc(atr) + δ π (Ht, lt, yt)|Ht, atjatr, at ] 1 − δ δ
i −i i (3.4)
3. All team members are willing to implement the discretionary payment pt in all period t: pt(Ht, lt, yt) + δ π (Ht, lt, yt) ≥ δ π¯
Appears in 1 contract
Sources: PHD Thesis