Realising Common Knowledge Assumptions in Agent Auctions

Game theory is popular in agent systems for designing auctions with desirable properties. However, many of these properties will only hold if the game and its properties are common knowledge among the agents. For example, in an auction where truthful bidding is an equilibrium strategy, unless this is common knowledge, it may not be rational for an agent to bid truthfully. It is currently not clear how this state of common knowledge can be achieved, especially in open agent societies where agents may encounter previously unseen auction specifications. We need a method for communicating the rules of the game to the agents, and the agents need to be able to determine its properties. We present a machine-readable language in which the rules of the game can be written. We show that it is not feasible for an agent to determine the properties of any arbitrary specification, unless information about the properties is communicated and/or certain restrictions are placed on the specification. We look at two special cases where common knowledge is achievable: auctions with identical players where the two highest bidders determine the price, and Groves mechanisms with a restriction on the pricing rule.