Computing Bayes-Nash Equilibria in Combinatorial Auctions with Continuous Value and Action Spaces

Combinatorial auctions (CAs) are widely used in practice, which is why understanding their incentive properties is an important problem. However, finding Bayes-Nash equilibria (BNEs) of CAs analytically is tedious, and prior algorithmic work has only considered limited solution concepts (e.g. restricted action spaces). In this paper, we present a fast, general algorithm for computing symmetric pure ε-BNEs in CAs with continuous values and actions. In contrast to prior work, we separate the search phase (for finding the BNE) from the verification step (for estimating the ε), and always consider the full (continuous) action space in the best response computation. We evaluate our method in the well-studied LLG domain, against a benchmark of 16 CAs for which analytical BNEs are known. In all cases, our algorithm converges quickly, matching the known results with high precision. Furthermore, for CAs with quasi-linear utility functions and independently distributed valuations, we derive a theoretical bound on ε. Finally, we introduce the new Multi-Minded LLLLGG domain with eight goods and six bidders, and apply our algorithm to finding an equilibrium in this domain. Our algorithm is the first to find an accurate BNE in a CA of this size.

On experimental investigation of the web-based stock-exchange model

In this paper, the updated model USEGM simulating the stock exchange is investigated. The updated model includes the transaction costs to reflect the reality better. To represent users that prefer linear utility functions, USEGM adds the new models which minimize absolute prediction errors to the traditional ones minimizing square deviations. However, the main objective of USEGM is not forecasting, but simulation of financial time series that are affected by predictions of the participants. The model has been compared with actual financial time series.

Agent negotiation on resources with nonlinear utility functions

To date, researches on agent multi-issue negotiation are mostly based on linear utility functions. However, the relationship between utilities and resources is usually saturated nonlinear. To this end, we expand linear utility functions to nonlinear cases according to the law of diminishing marginal utility. Furthermore, we propose a negotiation model on multiple divisible resources with two phases to realize Pareto optimal results. The computational complexity of the proposed algorithm is polynomial order. Experimental results show that the optimized efficiency of the proposed algorithm is distinctly higher than prior work.

Consumer Welfare and Market Structure in a Model of Competition between Open Source and Proprietary Software

I consider a Vickrey-Salop model of spatial product differentiation with quasi-linear utility functions and contrast two modes of production, the proprietary model where entrepreneurs sell software to the users, and the open source model where users participate in software development. I show that the OS model of production may be more efficient from the point of view of welfare than the proprietary model, but that an OS industry is vulnerable to entry by entrepreneurs while a proprietary industry can resist entry by OS projects. A mixed industry where OS and proprietary development methods coexist may exhibit large OS projects cohabiting with more specialized proprietary projects, and is more efficient than the proprietary model of production from the point of view of welfare.