Contract theory is effective in designing incentive compatible mechanisms in a monopoly market under incomplete information, where the employer needs to sign a contract with employees before fully knowing their private information. The key idea is to offer the right contract items so that all agents have the incentive to truthfully reveal their private information. In our problem, we can imagine the network as a labor market. The PU is the employer and offers a contract to the SUs. The contact consists of a set of contract items, which are combinations of spectrum access time (i.e., reward) and relay power (i.e., contribution). The SUs are employees, and each SU selects the best contract item according to its type. We want to design an optimal contract that maximizes the PU’s utility (average data rate) under the incomplete information of SUs’ types. We first consider the complete information scenario as a benchmark. Then we consider the optimal contract design in two incomplete information scenarios (where the PU does not know the precise type of every SU): weakly incomplete information, where the PU knows the percentage of every type, and strongly incomplete information, where the PU knows only the probability distribution of every type. Under incomplete information, a contract is feasible if and only if it is incentive compatible (IC ) and individually rational (IR) for each SU. We characterize the necessary and sufficient conditions for a contract to be IC and IR systematically. Under weakly incomplete information, we derive the optimal contract, which achieves the same maximum PU utility as in the complete information benchmark. Under strongly incomplete information, we propose a decompose-and-compare (DC) algorithm that achieves a close-to-optimal contract. Under strongly incomplete information, the PU’s utility loss is caused by two factors: the suboptimal contract and the incomplete information. We quantify the PU’s average utility loss due to the suboptimal algorithm (by comparing it with exhaustive searching) and incomplete information (by comparing it with complete information) through numerical examples.
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