where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

2005년 대한 생화학·분자생물학회 하계학술대회를 다녀와서

Journal of the ACM

Mathematical programming

Preface (R.J. Aumann, S. Hart). Strategic equilibrium (E. van Damme). Foundations of strategic equilibrium (J. Hillas, E. Kohlberg). Incomplete information (R.J. Aumann, A. Heifetz). Non-zero-sum two-person games (T.E.S. Raghavan). Computing equilibria for two-person games (B. von Stengel). Non-cooperative games with many players (M. Ali Khan, Y. Sun). Stochastic games (J-F. Mertens). Stochastic games: recent results (N. Vieille). Game theory and industrial organization (K. Bagwell, A. Wolinsky). Bargaining with incomplete information (L.M. Ausubel, P. Cramton, R.J. Deneckere). Inspection Games (R. Avenhaus, B.V. Stengel, S.Zamir). Economic history and game theory (A. Greif). The shapley value (E. Winter). Variations on the shapley value (D. Monderer, D. Samet). Values of non-transferable utility games (R. McLean). Values of games with infinitely many players (A. Neyman). Values of perfectly competitive economies (S. Hart). Some other economic applications of the value (J-F. Mertens). Strategic aspects of political systems (J. Banks). Game-theoretic analysis of legal rules and institutions (J-P. Benoit, L.A. Kornhauser). Implementation Theory (T. Palfrey). Game Theory and experimental Gaming (M. Shubik).

Handbook of game theory with economic applications

In this paper, we present an information propagation game on a network where the information is originated from a sponsor who is willing to pay a fixed total budget to the players who propagate the information. Our solution can be applied to real world situations such as advertising via social networks with limited budgets. The goal is to design a mechanism to distribute the budget such that all players in the social network are incentivized to propagate information to all their neighbours. We propose a family of mechanisms to achieve the goal, where propagating information to all neighbours is a dominant strategy for all players. Furthermore, we also consider the cases where the budget has to be completely shared.

Maximal Information Propagation with Budgets

We consider an auction design problem where a seller sells multiple homogeneous items to a set of connected buyers. Each buyer only knows the buyers she directly connects with and has a diminishing marginal utility valuation for the items. The seller initially only connects to some buyers who can be directly invited to the sale by the seller. Our goal is to design an auction to incentivize the buyers who are aware of the auction to further invite their neighbors to join the auction. This is challenging because the buyers are competing for the items and they would not invite each other by default. Thus, rewards need to be given to buyers who diffuse information, but the rewards should be carefully designed to guarantee both invitation incentives and the seller's revenue. Solutions have been proposed recently for the settings where each buyer requires at most one unit and demonstrated the difficulties of the design. We move this forward to propose the very first diffusion auction for the multi-unit demand settings to improve both the social welfare and the seller's revenue.

Diffusion Multi-unit Auctions with Diminishing Marginal Utility Buyers

We consider a fixed-price mechanism design setting where a seller sells one item via a social network, but the seller can only directly communicate with her neighbours initially. Each other node in the network is a potential buyer with a valuation derived from a common distribution. With a standard fixed-price mechanism, the seller can only sell the item among her neighbours. To improve her revenue, she needs more buyers to join in the sale. To achieve this, we propose the very first fixed-price mechanism to incentivize the seller's neighbours to inform their neighbours about the sale and to eventually inform all buyers in the network to improve seller's revenue. Compared with the existing mechanisms for the same purpose, our mechanism does not require the buyers to reveal their valuations and it is computationally easy. More importantly, it guarantees that the improved revenue is at least 1/2 of the optimal.

Fixed-price Diffusion Mechanism Design

This paper studies a double auction market where a set of sellers sell homogeneous items to a set of buyers and each buyer (seller) buys (sells) one item. Moreover, each buyer is linked to a set of other potential buyers via a network. The goal is to design a double auction such that the buyers are incentivized to invite their neighbours to join the auction to improve the allocation efficiency and the sellers' revenue, which is not achievable under the existing double auction mechanisms. Moreover, it is well-known that budget balance is not compatible with other desirable properties at the same time. Hence, we design double auction mechanisms that both incentivize buyers to invite their neighbours and guarantee budget balance. We first show that an extension of McAfee's trade reduction [8] cannot achieve this. Therefore, we propose a new mechanism called Double Network Auction (DNA) to guarantee the properties.

Double auction design on networks

This paper proposes an approach to design behaviour-based double auction mechanisms that are adaptive to market changes under the Trading Agent Competition Market Design platform. Because of the dynamics of the market environment, it is not feasible to test a mechanism in all kinds of environments. Since the strategies adopted by traders are well classified and studied, we will analyse and utilise the behaviour of traders with each kind of strategy, design specific (trader-dependent) mechanisms for attracting them, and finally integrate these trader-dependent mechanisms to achieve adaptive mechanisms.

Dengji Zhao

Papers

Maximal Information Propagation with Budgets

Diffusion Multi-unit Auctions with Diminishing Marginal Utility Buyers

Fixed-price Diffusion Mechanism Design

Double auction design on networks

How to Make Specialists NOT Specialised in TAC Market Design Competition? Behaviour-Based Mechanism Design