The MaxMin value of stochastic games with imperfect monitoring

We study finite zero-sum stochastic games in which players do not observe the actions of their opponent. Rather, at each stage, each player observes a stochastic signal that may depend on the current state and on the pair of actions chosen by the players. We assume that each player observes the state and his/her own action. We prove that the uniform max-min value always exists. Moreover, the uniform max-min value is independent of the information structure of player 2. Symmetric results hold for the uniform min-max value. We deeply thank E. Lehrer, J.-F. Mertens, A. Neyman and S. Sorin. The discussions we had, and the suggestions they provided, were extremely useful. We acknowledge the financial support of the Arc-en-Ciel/Keshet program for 2001/2002. The research of the second author was supported by the Israel Science Foundation (grant No. 69/01-1).     

Radical catalyzed debromination of bromo-alkanes by formate in aqueous solutions via a hydrogen atom transfer mechanism

CO₂⁻ radicals catalyze the dehalogenation of bromo-alkanes by formate via a hydrogen atom transfer mechanism.     

Characterization of correlated equilibria in stochastic games

A general communication device is a device that at every stage of the game receives a private message from each player, and in return sends a private signal to each player; the signals the device sends depend on past play, past signals it sent, and past messages it received.  An autonomous correlation device is a general communication device where signals depend only on past signals the device sent, but not on past play or past messages it received.  We show that the set of all equilibrium payoffs in extended games that include a general communication device coincides with the set of all equilibrium payoffs in extended games that include an autonomous correlation device. A stronger result is obtained when the punishment level is independent of the history. Final version July 2001     

The Use of Index Numbers for Measuring Output of Multi-Product Systems

Measurement of output for a multi-product system often relies on revenue as a yardstick, but such an approach is inadequate for measures of physical output or aggregate price. Many alternative methods, based on the use of index numbers, are outlined and compared for a simple example. The strengths and weaknesses of these methods are discussed, and ways of overcoming difficulties due to discontinuities in the product range are suggested.     

An Algorithm for the Vehicle-dispatching Problem

The vehicle-scheduling problem involves the design of several vehicle tours to meet a given set of requirements for customers with known locations, subject to a capacity constraint for the vehicles and a distance (or time) constraint for vehicle tours. Three methods of solution are considered in this paper:

1. a
   A branch-and-bound approach.
    
2. b
   The "savings" approach.
    
3. c
   The 3-optimal tour method.
    

The excessive computation time and computer storage required for the first method renders it impracticable for large problems. Ten problems are examined and the results suggest that method C is superior to the other two methods.