An All-Pay Auction Approach to Reallocation

The auction has been advocated as a valuable metaphor in the design of decentralized mechanisms for various problems. The walrasian auction was proposed as a suitable mechanism for resource reallocation in distributed planning. Economic theory ooers ample opportunities to develop distributed walrasian mechanisms for reallocation in \mar-kets" with many agents and innnitely divisible resources. However , in cases where resources are essentially indivisible and markets relatively small, the perspective is considerably worse. In this paper, we address such reallocation problems. After pointing out the deeciencies of walrasian-like mechanisms in the chosen problem context, we propose an alternative mechanism based on the metaphor of an all-pay auction. The key feature of this Informed Gambling mechanism is that agents are required to commit themselves to exchange proposals in the face of uncertainty about the market situation. We present an example that illustrates how the mechanism renders acceptable reallocations where walrasian mechanisms fail. 1 TOOL REALLOCATION We investigate auction-based mechanisms for a class of problems that can be described as \tool reallocation problems". A tool is a resource that is essentially indivisible. Typical examples of indivisible resource types are computer workstationss5], oil tankers, and low-capacity communication channels. The essential characteristic here is that agents generally require only a small number of resources of the types they desire. Tool reallocation problems constitute a subclass of resource reallocation problems, for which mechanism design is particularly diicult, because the standard assumptions of economic equilibrium theory (viz., innnite resource divisibility and negligible innuence of individual agents) are violated. At the other hand, many real-world problems in the area of distributed planning are in this category. These problems therefore deserve to be attended to within DAI. In this paper, we do so by assessing the performance of our Informed Gambling (IG) mechanism in comparison with an established micro-economic equilibrium notion, the walrasian equilibrium. We measure global performance in a relative-utilitarian fashion 4], that is, community welfare is deened to be the mean of the agents' relative utilities. These relative utilities equal the fraction of the utility an agent would attain if it possessed all the tools in the community. 2 TOOL TYPES Reallocation problems where agents need multiple tools of different types to accomplish a given task are the primary target problem for our Informed Gambling (IG) mechanism. For an account on this general reallocation problem, we refer to 3]. In this paper, we focus on a simpliied …