No Speculation under Expectations in Awareness Ken Horie 1 and Takashi Matsuhisa 2⋆ 1 Advanced Course of Electronic and Computer Engineering, Ibaraki National College of Technology 2 Department of Liberal Arts and Sciences, Ibaraki National College of Technology, Nakane 866, Hitachinaka-shi, Ibaraki 312-8508, Japan. mathisa@ge.ibaraki-ct.ac.jp Abstract. We present the extended notion of pure exchange eco- nomy under uncertainty, called an economy with awareness structure, where each trader makes decision under his/her awareness and belief and has strictly monotone preferences. We show the no specula- tion theorem: If the initial endowment is ex-ante Pareto optimal then there exists no other expectations equilibrium in awareness for any price. Keywords: Pure exchange economy, Awareness, Belief, No spe- culation, Expectations equilibrium, Ex-ante Pareto optimum. 1 Introduction This article relates economies and distributed knowledge. The purposes are the two points: First we present an extended notion of economy under uncertainty, called an economy with awareness structure, where each trader makes decision in his/her awareness and belief under incomplete information. Secondly we show the following ‘no trade theorem’ under generalized expectations equilibrium in the extended economy: No speculation theorem. In a pure exchange economy under uncertainty, the traders are assumed to have an awareness structure and to have strictly monotone preferences. If the initial endowment is ex-ante Pareto optimal then there exists no other expectations equilibrium in awareness. Recently researchers in such fields as economics, AI, and computer science have become interested in reasoning of belief and knowledge. There are pragmatic concerns about the relationship between knowledge (belief) and actions. Of most interest to us is the emphasis on situations involving the distributed knowledge (belief) of a group of agents rather than that of a single agent. At the heart of any analysis of such situations as a conversation, a bargaining session or a ⋆ Corresponding author. Partially supported by the Grant-in-Aid for Scientific Rese- arch(C)(2)(No.14540145) in the Japan Society for the Promotion of Sciences. Dedi- cated to Professor Shoji Koizumi on the occasion of his 80th birthday M. Bubak et al. (Eds.): ICCS 2004, LNCS 3039, pp. 915–922, 2004. c  Springer-Verlag Berlin Heidelberg 2004