Loss aversion equilibrium

The Nash equilibrium solution concept for games is based on the assumption of expected utility maximization. Reference dependent utility functions (in which utility is determined not only by an outcome, but also by the relationship of the outcome to a reference point) are a better predictor of behavior than expected utility. In particular, loss aversion is an important element of such utility functions.  We extend games to include loss aversion characteristics of the players. We define two types of loss-aversion equilibrium, a solution concept endogenizing reference points. The two types reflect different procedures of updating reference points during the game. Reference points emerge as expressions of anticipation which are fulfilled.  We show existence of myopic loss-aversion equilibrium for any extended game, and compare it to Nash equilibrium. Comparative statics show that an increase in loss aversion of one player can affect her and other players' payoffs in different directions. Received August 1998/Revised version February 2000     

Negotiation-proof Nash equilibrium

This paper defines “negotiation-proof Nash equilibrium', a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections; moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof Nash equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of coalition-proof Nash equilibrium. (2) The negotiation process is formalized by a “graph”, which serves as a natural extension to the approach that models preplay communication by an extensive game. Received: October 1998/Final version: May 2000     

Two-person repeated games with finite automata

We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An exogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player.  We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels. Received February 1997/revised version March 2000     

Player splitting in extensive form games

By a player splitting we mean a mechanism that distributes the information sets of a player among so-called agents. A player splitting is called independent if each path in the game tree contains at most one agent of every player. Following Mertens (1989), a solution is said to have the player splitting property if, roughly speaking, the solution of an extensive form game does not change by applying independent player splittings. We show that Nash equilibria, perfect equilibria, Kohlberg-Mertens stable sets and Mertens stable sets have the player splitting property. An example is given to show that the proper equilibrium concept does not satisfy the player splitting property. Next, we give a definition of invariance under (general) player splittings which is an extension of the player splitting property to the situation where we also allow for dependent player splittings. We come to the conclusion that, for any given dependent player splitting, each of the above solutions is not invariant under this player splitting. The results are used to give several characterizations of the class of independent player splittings and the class of single appearance structures by means of invariance of solution concepts under player splittings. Received: December 1996/Revised Version: January 2000     

Holomorphic automorphisms of continuous products of balls

We study continuous product domains in the space of all continuousE-valued functions on , where is a compact Hausdorff topological space and E is an arbitrary JB-triple, and discuss the group of holomorphic automorphisms of domains of that type. Received November 9, 1998; in final form March 23, 1999 / Published online May 8, 2000     

Cr_2O_7~(2-)/Cr~(3+)间接氧化环己醇合成己二酸

以Cr2O72-/Cr3+作为间接氧化剂电氧化环己醇制备己二酸.应用正交实验优化工艺条件,得出在原料比n(环己醇)∶n(Cr2O72-)=0.4∶1,t=35℃和CH2SO4=5mol.L-1条件下己二酸的收率可达70.29%.同时研究了Ag2SO4、(NH4)2SO4、H2SO4浓度、电流密度对Cr3+电氧化为Cr2O72-的影响,Cr3+的转化率可达82.52%.     

HARMONIC ANALYSIS ON THE QUOTIENT κ× ∝ κ \ A1 ∝ A

Let G be the semidirect product A¹ ∝ A of the adeles and the norm 1 ideles of a global field κ. Let Γ be the discrete subgroup κ^×∝ κ. In this paper the trace formula for this setting is established and used to give the complete decomposition of the G-representation on L²(Γ\G). It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.     

Semiconducting black phosphorus

Black phosphorus is a narrow-gap semiconductor newly attracting attention because of recent success in growing single crystals at a high temperature under a high pressure. This review covers recent research work on the preparation, the crystal structure, the band structure, the electrical and optical properties, and the superconductivity of black phosphorus.     

Improvements upon the Chevalley-Warning-Ax-Katz-type estimates

Let f be a polynomial over finite field Fq with q elements and let N(f=0) denote the number of zeros of f in Fq. The q-divisibility properties of N(f=0) have been studied by many authors, such as Chavelley, Warning, Ax, Katz, etc. In this paper, by reducing the degree of a given polynomial meanwhile remaining the number of its zeros unchanged, we present an improvement upon the Chevalley-Warning-Ax-Katz-type estimates in many cases. Furthermore, our result can improve Cao-Sun's reduction recently obtained on counting the number of zeros of general diagonal equations over finite fields.