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Register a new userOptimal Contract with Moral Hazard for Public Private Partnerships
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Public-Private Partnership (PPP) is a contract between a public entity and a consortium, in which the public outsources the construction and the maintenance of an equipment (hospital, university, prison...). One drawback of this contract is that the public may not be able to observe the effort of the consortium but only its impact on the social welfare of the project. We aim to characterize the optimal contract for a PPP in this setting of asymmetric information between the two parties. This leads to a stochastic control under partial information and it is also related to principal-agent problems with moral hazard. Considering a wider set of information for the public and using martingale arguments in the spirit of Sannikov, the optimization problem can be reduced to a standard stochastic control problem, that is solved numerically. We then prove that for the optimal contract, the effort of the consortium is explicitly characterized. In particular, it is shown that the optimal rent is not a linear function of the effort, contrary to some models of the economic literature on PPP contracts.
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This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, in continuous-time and with a continuous payment, with the possibility for the public to stop the contract. The public (she) pays a continuous rent to the consortium (he), while the latter gives a best response characterized by his effort. This effect impacts the drift of the social welfare, until a terminal date decided by the public when she stops the contract and gives compensation to the consortium. Usually, the public can not observe the effort done by the consortium, leading to a principal agents problem with moral hazard. We solve this optimal stochastic control with optimal stopping problem in this context of moral hazard. The public value function is characterized by the solution of an associated Hamilton Jacobi Bellman Variational Inequality. The public value function and the optimal effort and rent processes are computed numerically by using the Howard algorithm. In particular, the impact of the social welfares volatility on the optimal contract is studied.
This paper investigates Pareto optimal (PO, for short) insurance contracts in a behavioral finance framework, in which the insured evaluates contracts by the rank-dependent utility (RDU) theory and the insurer by the expected value premium principle. The incentive compatibility constraint is taken into account, so the contracts are free of moral hazard. The problem is initially formulated as a non-concave maximization problem involving Choquet expectation, then turned into a quantile optimization problem and tackled by calculus of variations method. The optimal contracts are expressed by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions. We provide a simple numerical scheme as well as a numerical example to calculate the optimal contracts. Let $theta$ and $m_0$ denote the relative safety loading and the mass of the potential loss at 0. We find that every moral-hazard-free contract is optimal for infinitely many RDU insureds if $0<theta<frac{m_0}{1-m_0}$; by contrast, some contracts such as the full coverage contract are never optimal for any RDU insured if $theta>frac{m_0}{1-m_0}$. We also derive all the PO contracts when either the compensations or the retentions loss monotonicity.
In cognitive radio networks (CRNs), spectrum trading is an efficient way for secondary users (SUs) to achieve dynamic spectrum access and to bring economic benefits for the primary users (PUs). Existing methods requires full payment from SU, which blocked many potential buyers, and thus limited the PUs expected income. To better improve PUs revenue from spectrum trading in a CRN, we introduce a financing contract, which is similar to a sealed non-cash auction that allows SU to do a financing. Unlike previous mechanism designs in CRN, the financing contract allows the SU to only pay part of the total amount when the contract is signed, known as the down payment. Then, after the spectrum is released and utilized, the SU pays the rest of payment, known as the installment payment, from the revenue generated by utilizing the spectrum. The way the financing contract carries out and the sealed non-cash auction works similarly. Thus, contract theory is employed here as the mathematical framework to solve the non-cash auction problem and form mutually beneficial relationships between PUs and SUs. As the PU may not have the full acknowledgement of the SUs financial status, nor the SUs capability in making revenue, the problems of adverse selection and moral hazard arise in the two scenarios, respectively. Therefore, a joint adverse selection and moral hazard model is considered here. In particular, we present three situations when either or both adverse selection and moral hazard are present during the trading. Furthermore, both discrete and continuous models are provided in this paper. Through extensive simulations, we show that the adverse selection and moral hazard cases serve as the upper and lower bounds of the general case where both problems are present.
Recently, the concept of fog computing which aims at providing time-sensitive data services has become popular. In this model, computation is performed at the edge of the network instead of sending vast amounts of data to the cloud. Thus, fog computing provides low latency, location awareness to end users, and improves quality-of-services (QoS). One key feature in this model is the designing of payment plan from network operator (NO) to fog nodes (FN) for the rental of their computing resources, such as computation capacity, spectrum, and transmission power. In this paper, we investigate the problem of how to design the efficient payment plan to maximize the NOs revenue while maintaining FNs incentive to cooperate through the moral hazard model in contract theory. We propose a multi-dimensional contract which considers the FNs characteristics such as location, computation capacity, storage, transmission bandwidth, and etc. First, a contract which pays the FNs by evaluating the resources they have provided from multiple aspects is proposed. Then, the utility maximization problem of the NO is formulated. Furthermore, we use the numerical results to analyze the optimal payment plan, and compare the NOs utility under different payment plans.
We consider the principal-agent problem with heterogeneous agents. Previous works assume that the principal signs independent incentive contracts with every agent to make them invest more efforts on the tasks. However, in many circumstances, these contracts need to be identical for the sake of fairness. We investigate the optimal common contract problem. To our knowledge, this is the first attempt to consider this natural and important generalization. We first show this problem is NP-complete. Then we provide a dynamic programming algorithm to compute the optimal contract in $O(n^2m)$ time, where $n,m$ are the number of agents and actions, under the assumption that the agents cost functions obey increasing difference property. At last, we generalize the setting such that each agent can choose to directly produce a reward in $[0,1]$. We provide an $O(log n)$-approximate algorithm for this generalization.
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