Wenhan Huang

Hanyu Li, Wenhan Huang, Zhijian Duan et al.

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet economics and multi-agent learning. This paper reviews various algorithms computing the Nash equilibrium and its approximation solutions in finite normal-form games from both theoretical and empirical perspectives. For the theoretical part, we classify algorithms in the literature and present basic ideas on algorithm design and analysis. For the empirical part, we present a comprehensive comparison on the algorithms in the literature over different kinds of games. Based on these results, we provide practical suggestions on implementations and uses of these algorithms. Finally, we present a series of open problems from both theoretical and practical considerations.

Hongyin Chen, Zhaohua Chen, Yukun Cheng et al.

The design of permissioned blockchains places an access control requirement for members to read, access, and write information over the blockchains. In this paper, we study a hierarchical scenario to include three types of participants: providers, collectors, and governors. To be specific, providers forward transactions, collected from terminals, to collectors; collectors upload received transactions to governors after verifying and labeling them; and governors validate a part of received labeled transactions, pack valid ones into a block, and append a new block on the ledger. Collectors in the hierarchical model play a crucial role in the design: they have connections with both providers and governors, and are responsible for collecting, verifying, and uploading transactions. However, collectors are rational and some of them may behave maliciously (not necessarily for their own benefits). In this paper, we introduce a reputation protocol as a measure of the reliability of collectors in the permissioned blockchain environment. Its objective is to encourage collectors to behave truthfully and, in addition, to reduce the verification cost. The verification cost on provider $p$ is defined as the total number of invalid transactions provided by $p$ and checked by governors. Through theoretical analysis, our protocol with the reputation mechanism has a significant improvement in efficiency. Specifically, the verification loss that governors suffer is proved to be asymptotically $O(\sqrt{T_{total}})$ ($T_{total}$, representing the number of transactions verified by governors and provided by $p$), as long as there exists at least one collector who behaves well. At last, two typical cases where our model can be well applied are also demonstrated.