Equivalence class verification of the contract net protocol-extension

Abstract

The contract net protocol is a task allocation protocol that facilitates negotiation between bidders and an auctioneer in a multi-agent system to form a contract. The contract net protocol-extension (CNP-ext) allows the bidders to interact with more than one auctioneer concurrently, and to update their bids until a bid is granted. This introduces flexibility and ensures better selection of a bid. In earlier work, we modelled the CNP-ext with coloured petri nets and showed that it terminates correctly. We also analysed the terminal states and proved that the agents have consistent beliefs at the end of negotiations. Lastly, we showed how the number of terminal states and channel bounds are related to the number of bidders. However, due to state space explosion, our results were restricted to five bidders. As all bidders are considered identical, symmetries exist in the state space. Hence, we decided to tackle this problem using equivalence classes. In this paper, after first presenting an introduction to the CNP-ext, we present a substantial revision to our CNP-ext model and an intentionally didactic description of its operation. Then, we use equivalence classes to analyse the protocol and, importantly, present a proof that our equivalence specification is consistent. Using this technique, we are able to extend the verification results to twenty-four bidders.