An Agent Based Market Design Methodology for Combinatorial Auctions

Auction mechanisms have attracted a great deal of interest and have been used in diverse e-marketplaces. In particular, combinatorial auctions have the potential to play an important role in electronic transactions. Therefore, diverse combinatorial auction market types have been proposed to satisfy market needs. These combinatorial auction types have diverse market characteristics, which require an effective market design approach. This study proposes a comprehensive and systematic market design methodology for combinatorial auctions based on three phases: market architecture design, auction rule design, and winner determination design. A market architecture design is for designing market architecture types by Backward Chain Reasoning. Auction rules design is to design transaction rules for auctions. The specific auction process type is identified by the Backward Chain Reasoning process. Winner determination design is about determining the decision model for selecting optimal bids and auctioneers. Optimization models are identified by Forward Chain Reasoning. Also, we propose an agent based combinatorial auction market design system using Backward and Forward Chain Reasoning. Then we illustrate a design process for the general n-bilateral combinatorial auction market. This study serves as a guideline for practical implementation of combinatorial auction markets design.Combinatorial Auction, Market Design Methodology, Market Architecture Design, Auction Rule Design, Winner Determination Design, Agent-Based System

K-Implementation

This paper discusses an interested party who wishes to influence the behavior of agents in a game (multi-agent interaction), which is not under his control. The interested party cannot design a new game, cannot enforce agents' behavior, cannot enforce payments by the agents, and cannot prohibit strategies available to the agents. However, he can influence the outcome of the game by committing to non-negative monetary transfers for the different strategy profiles that may be selected by the agents. The interested party assumes that agents are rational in the commonly agreed sense that they do not use dominated strategies. Hence, a certain subset of outcomes is implemented in a given game if by adding non-negative payments, rational players will necessarily produce an outcome in this subset. Obviously, by making sufficiently big payments one can implement any desirable outcome. The question is what is the cost of implementation? In this paper we introduce the notion of k-implementation of a desired set of strategy profiles, where k stands for the amount of payment that need to be actually made in order to implement desirable outcomes. A major point in k-implementation is that monetary offers need not necessarily materialize when following desired behaviors. We define and study k-implementation in the contexts of games with complete and incomplete information. In the latter case we mainly focus on the VCG games. Our setting is later extended to deal with mixed strategies using correlation devices. Together, the paper introduces and studies the implementation of desirable outcomes by a reliable party who cannot modify game rules (i.e. provide protocols), complementing previous work in mechanism design, while making it more applicable to many realistic CS settings

Optimal advertising campaign generation for multiple brands using MOGA

The paper proposes a new modified multiobjective genetic algorithm (MOGA) for the problem of optimal television (TV) advertising campaign generation for multiple brands. This NP-hard combinatorial optimization problem with numerous constraints is one of the key issues for an advertising agency when producing the optimal TV mediaplan. The classical approach to the solution of this problem is the greedy heuristic, which relies on the strength of the preceding commercial breaks when selecting the next break to add to the campaign. While the greedy heuristic is capable of generating only a group of solutions that are closely related in the objective space, the proposed modified MOGA produces a Pareto-optimal set of chromosomes that: 1) outperform the greedy heuristic and 2) let the mediaplanner choose from a variety of uniformly distributed tradeoff solutions. To achieve these results, the special problem-specific solution encoding, genetic operators, and original local optimization routine were developed for the algorithm. These techniques allow the algorithm to manipulate with only feasible individuals, thus, significantly improving its performance that is complicated by the problem constraints. The efficiency of the developed optimization method is verified using the real data sets from the Canadian advertising industry

Network Inspection for Detecting Strategic Attacks

This article studies a problem of strategic network inspection, in which a defender (agency) is tasked with detecting the presence of multiple attacks in the network. An inspection strategy entails monitoring the network components, possibly in a randomized manner, using a given number of detectors. We formulate the network inspection problem $(\mathcal{P})$ as a large-scale bilevel optimization problem, in which the defender seeks to determine an inspection strategy with minimum number of detectors that ensures a target expected detection rate under worst-case attacks. We show that optimal solutions of $(\mathcal{P})$ can be obtained from the equilibria of a large-scale zero-sum game. Our equilibrium analysis involves both game-theoretic and combinatorial arguments, and leads to a computationally tractable approach to solve $(\mathcal{P})$. Firstly, we construct an approximate solution by utilizing solutions of minimum set cover (MSC) and maximum set packing (MSP) problems, and evaluate its detection performance. In fact, this construction generalizes some of the known results in network security games. Secondly, we leverage properties of the optimal detection rate to iteratively refine our MSC/MSP-based solution through a column generation procedure. Computational results on benchmark water networks demonstrate the scalability, performance, and operational feasibility of our approach. The results indicate that utilities can achieve a high level of protection in large-scale networks by strategically positioning a small number of detectors

Sparse Gr\"obner Bases: the Unmixed Case

Toric (or sparse) elimination theory is a framework developped during the last decades to exploit monomial structures in systems of Laurent polynomials. Roughly speaking, this amounts to computing in a \emph{semigroup algebra}, \emph{i.e.} an algebra generated by a subset of Laurent monomials. In order to solve symbolically sparse systems, we introduce \emph{sparse Gr\"obner bases}, an analog of classical Gr\"obner bases for semigroup algebras, and we propose sparse variants of the $F_5$ and FGLM algorithms to compute them. Our prototype "proof-of-concept" implementation shows large speed-ups (more than 100 for some examples) compared to optimized (classical) Gr\"obner bases software. Moreover, in the case where the generating subset of monomials corresponds to the points with integer coordinates in a normal lattice polytope $\mathcal P\subset\mathbb R^n$ and under regularity assumptions, we prove complexity bounds which depend on the combinatorial properties of $\mathcal P$. These bounds yield new estimates on the complexity of solving $0$-dim systems where all polynomials share the same Newton polytope (\emph{unmixed case}). For instance, we generalize the bound $\min(n_1,n_2)+1$ on the maximal degree in a Gr\"obner basis of a $0$-dim. bilinear system with blocks of variables of sizes $(n_1,n_2)$ to the multilinear case: $\sum n_i - \max(n_i)+1$. We also propose a variant of Fr\"oberg's conjecture which allows us to estimate the complexity of solving overdetermined sparse systems.Comment: 20 pages, Corollary 6.1 has been corrected, ISSAC 2014, Kobe : Japan (2014