Connectivity in the presence of an opponent

The paper introduces two player connectivity games played on finite bipartite graphs. Algorithms that solve these connectivity games can be used as subroutines for solving M\"uller games. M\"uller games constitute a well established class of games in model checking and verification. In connectivity games, the objective of one of the players is to visit every node of the game graph infinitely often. The first contribution of this paper is our proof that solving connectivity games can be reduced to the incremental strongly connected component maintenance (ISCCM) problem, an important problem in graph algorithms and data structures. The second contribution is that we non-trivially adapt two known algorithms for the ISCCM problem to provide two efficient algorithms that solve the connectivity games problem. Finally, based on the techniques developed, we recast Horn's polynomial time algorithm that solves explicitly given M\"uller games and provide an alternative proof of its correctness. Our algorithms are more efficient than that of Horn's algorithm. Our solution for connectivity games is used as a subroutine in the algorithm

Characterizations of Network Auctions and Generalizations of VCG

With the growth of networks, promoting products through social networks has become an important problem. For auctions in social networks, items are needed to be sold to agents in a network, where each agent can bid and also diffuse the sale information to her neighbors. Thus, the agents' social relations are intervened with their bids in the auctions. In network auctions, the classical VCG mechanism fails to retain key properties. In order to better understand network auctions, in this paper, we characterize network auctions for the single-unit setting with respect to weak budget balance, individual rationality, incentive compatibility, efficiency, and other properties. For example, we present sufficient conditions for mechanisms to be efficient and (weakly) incentive compatible. With the help of these properties and new concepts such as rewards, participation rewards, and so on, we show how to design efficient mechanisms to satisfy incentive compatibility as much as possible, and incentive compatibility mechanisms to maximize the revenue. Our results provide insights into understanding auctions in social networks.Comment: To appear in ECAI 202

Differentially Private Diffusion Auction: The Single-unit Case

Diffusion auction refers to an emerging paradigm of online marketplace where an auctioneer utilises a social network to attract potential buyers. Diffusion auction poses significant privacy risks. From the auction outcome, it is possible to infer hidden, and potentially sensitive, preferences of buyers. To mitigate such risks, we initiate the study of differential privacy (DP) in diffusion auction mechanisms. DP is a well-established notion of privacy that protects a system against inference attacks. Achieving DP in diffusion auctions is non-trivial as the well-designed auction rules are required to incentivise the buyers to truthfully report their neighbourhood. We study the single-unit case and design two differentially private diffusion mechanisms (DPDMs): recursive DPDM and layered DPDM. We prove that these mechanisms guarantee differential privacy, incentive compatibility and individual rationality for both valuations and neighbourhood. We then empirically compare their performance on real and synthetic datasets

Multi-unit Auction over a Social Network

Diffusion auction is an emerging business model where a seller aims to incentivise buyers in a social network to diffuse the auction information thereby attracting potential buyers. We focus on designing mechanisms for multi-unit diffusion auctions. Despite numerous attempts at this problem, existing mechanisms either fail to be incentive compatible (IC) or achieve only an unsatisfactory level of social welfare (SW). Here, we propose a novel graph exploration technique to realise multi-item diffusion auction. This technique ensures that potential competition among buyers stay ``localised'' so as to facilitate truthful bidding. Using this technique, we design multi-unit diffusion auction mechanisms MUDAN and MUDAN-$m$. Both mechanisms satisfy, among other properties, IC and $1/m$-weak efficiency. We also show that they achieve optimal social welfare for the class of rewardless diffusion auctions. While MUDAN addresses the bottleneck case when each buyer demands only a single item, MUDAN-$m$ handles the more general, multi-demand setting. We further demonstrate that these mechanisms achieve near-optimal social welfare through experiments

Learning Density-Based Correlated Equilibria for Markov Games

Correlated Equilibrium (CE) is a well-established solution concept that captures coordination among agents and enjoys good algorithmic properties. In real-world multi-agent systems, in addition to being in an equilibrium, agents' policies are often expected to meet requirements with respect to safety, and fairness. Such additional requirements can often be expressed in terms of the state density which measures the state-visitation frequencies during the course of a game. However, existing CE notions or CE-finding approaches cannot explicitly specify a CE with particular properties concerning state density; they do so implicitly by either modifying reward functions or using value functions as the selection criteria. The resulting CE may thus not fully fulfil the state-density requirements. In this paper, we propose Density-Based Correlated Equilibria (DBCE), a new notion of CE that explicitly takes state density as selection criterion. Concretely, we instantiate DBCE by specifying different state-density requirements motivated by real-world applications. To compute DBCE, we put forward the Density Based Correlated Policy Iteration algorithm for the underlying control problem. We perform experiments on various games where results demonstrate the advantage of our CE-finding approach over existing methods in scenarios with state-density concerns

Facility Location Games with Entrance Fees

The facility location game is an extensively studied problem in mechanism design. In the classical model, the cost of each agent is her distance to the nearest facility. In this paper, we consider a novel model where each facility charges an entrance fee, which is a function of the facility's location. Thus, in our model, the cost of each agent is the sum of the distance to the facility and the entrance fee of the facility. The generalized model captures more real-life scenarios. In our model, the entrance fee function can be an arbitrary function, and the corresponding preferences of agents may not be single-peaked anymore: this makes the problem complex and requires new techniques in the analysis. We systematically study the model and design strategyproof mechanisms with nice approximation ratios and also complement these with nearly-tight impossibility results. Specifically, for one-facility and two-facility games, we provide upper and lower bounds for the approximation ratios given by deterministic and randomized mechanisms, with respect to the utilitarian and egalitarian objectives. Most of our bounds are tight, and these bounds are independent of the entrance fee functions. Our results also match the results of the classical model

A Blockchain-Based Storage System with Financial Incentives for Load-balancing

Most storage systems adopt distributed architecture to reach high reliability. In these distributed systems, a well-balanced data distribution can improve storage reliability. However, existing schemes rely on dealers to distribute data, bring back the risk of single-point failure again. In this paper, we propose a blockchain-based storage system with financial incentives for load-balancing. Nodes in the system are rational and compete for data to earn a reward. The only source of storage rewards is from users' payment for leasing storage. To reach load-balancing, we design a new incentive scheme, which contains an income function to reward the nodes who own proper data and punish the nodes who own excessive data. In the system, each node continuously generates a proof of storage. We present a chain structure using the proofs to detect node failures and record data distribution. The state of distribution could be taken as input to the income function for reward allocation. We decouple the role of nodes from miners to reduce their workload, making the system more compatible. Our simulation experiments show efficient performance in the data distribution. The system can always recover to a balanced status as the blockchain grows up.This work was supported in part by the NSFC General Technology Basic Research Joint Fund under Grant U1836212, in part by the Graduate Technological Innovation Project of Beijing Institute of Technology under Grant 2019CX10014 in part by Anhui Provincial Natural Science Foundation under Grant 2008085MF196, and in part by the National Natural Science Foundation of China under Grant 62002094