Abstracting and Verifying Strategy-Proofness for Auction Mechanisms

We are interested in finding algorithms which will allow an agent roaming between different electronic auction institutions to automatically verify the game-theoretic properties of a previously unseen auction protocol. A property may be that the protocol is robust to collusion or deception or that a given strategy is optimal. Model checking provides an automatic way of carrying out such proofs. However it may suffer from state space explosion for large models. To improve the performance of model checking, abstractions were used along with the Spin model checker. We considered two case studies: the Vickrey auction and a tractable combinatorial auction. Numerical results showed the limits of relying solely on Spin . To reduce the state space required by Spin , two property-preserving abstraction methods were applied: the first is the classical program slicing technique, which removes irrelevant variables with respect to the property; the second replaces large data, possibly infinite values of variables with smaller abstract values. This enabled us to model check the strategy-proofness property of the Vickrey auction for unbounded bid range and number of agents.