The role of optimization in the human dynamics of tasks execution

In order to explain the empirical evidence that the dynamics of human activity may not be well modeled by Poisson processes, a model based on queuing processes were built in the literature \cite{bar05}. The main assumption behind that model is that people execute their tasks based on a protocol that execute firstly the high priority item. In this context, the purpose of this letter is to analyze the validity of that hypothesis assuming that people are rational agents that make their decisions in order minimize the cost of keeping non-executed tasks on the list. Therefore, we build and solve analytically a dynamic programming model with two priority types of tasks and show that the validity of this hypothesis depends strongly on the structure of the instantaneous costs that a person has to face if a given task is kept on the list for more than one step. Moreover, one interesting finding is that in one of the situations the protocol used to execute the tasks generates complex one dimensional dynamics

Nonzero-sum Stochastic Games

This paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete