### Abstract

While there is vast literature on principal-agent service contracts in which a principal pools the service capacities of multiple agents for economy of scale, here we focus on the case that exists in practice of an agent pooling multiple principals. Since it is reasonable to presume that an agent of good standing attracts multiple contract offers, his main strategic decision is to select his principals. It is generally known that a principal can extract all economic surplus from a risk-neutral agent while the agent breaks even. However, this is not the case for an agent contracting multiple principals while accounting for their interdependent failure characteristics. In this paper we describe a methodology that enables an agent to calculate the value of each potential principal and therefore to contract a Pareto optimal subset of principals in a market where neither principals’ nor agents’ collusion is allowed. Unfortunately, computational intractability of first order analysis forces us to rely on a Monte Carlo simulation to understand the agent’s choice of the principals. The computation of each principal’s contribution to the agent’s welfare is enabled by a specific cooperative game of independent interest. We show that under certain conditions the agent can do better than break-even and can realize profits convexly increasing in the cardinality of the contracted principals. Our findings not only equip agents with a mathematical instrument for assessment of service contract’s financial viability but also offer agents a holistic perspective for screening principals before accepting contract offers.

Original language | English (US) |
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Pages (from-to) | 23-59 |

Number of pages | 37 |

Journal | Mathematical Methods of Operations Research |

Volume | 90 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2019 |

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### Keywords

- Monte-Carlo simulation
- Non-cooperative and cooperative games
- Principal-agent
- System dynamics

### ASJC Scopus subject areas

- Software
- Mathematics(all)
- Management Science and Operations Research