Infinite Histories Research Articles

Utilitarian population ethics and births timing

Births postponement is a key demographic trend of the last decades. To examine its social desirability, we study how utilitarian criteria rank histories equal on all dimensions except the age at which individuals give birth to their children. We develop a T-period dynamic overlapping generations economy with a fixed living space, where individual welfare is increasing in the available space per head, and where agents have children in one out of two fertility periods. When comparing finite histories with an equal total number of life-periods, classical, average and critical-level utilitarian criteria select the same fertility timing, i.e. the one leading to the most smoothed population path. When comparing infinite histories with stationary population sizes, utilitarian criteria may select different birth timings, depending on individual utility functions. Those results are compared with the ones obtained when agents value coexistence time with their descendants. Finally, we identify conditions under which a shift from an early births regime to a late births regime is socially desirable.

Temporal Logics Specifications for Debit and Credit Transactions

Recently, with the emergence of mobile technology and mobile banking, debit and credit transactions have been the most common transactions that are widely spreading, using such technologies. In this research, we specify the concurrent debit and credit transactions in temporal logics such as CTL (Computational Tree Logic) and LTL (Linear-Time Temporal Logic). These specifications describe the infinite histories that may be produced by the iterations of such concurrent transactions infinitely many times. We represent the infinite histories as a model of temporal logics formulae. Then, model checkers, such as NuSMV or SPIN, can carry out exhaustive checks of the correctness of the concurrent debit and credit transactions. Moreover, in this paper, we presume that the serializability condition is too strict. Therefore, a relaxed condition has been suggested to keep the database consistent. Moreover, the relaxed condition is easier to encode into temporal logics formulae.

Learning in General Games with Nature’s Moves

This paper investigates simultaneous learning about both nature and others’ actions in repeated games and identifies a set of sufficient conditions for which Harsanyi’s doctrine holds. Players have a utility function over infinite histories that are continuous for the sup-norm topology. Nature’s drawing after any history may depend on any past actions. Provided that (1) every player maximizes her expected payoff against her own beliefs, (2) every player updates her beliefs in a Bayesian manner, (3) prior beliefs about both nature and other players’ strategies have a grain of truth, and (4) beliefs about nature are independent of actions chosen during the game, we construct a Nash equilibrium, that is, realization-equivalent to the actual plays, where Harsanyi’s doctrine holds. Those assumptions are shown to be tight.

Markov decision processes and regular events

Desirable properties of the infinite histories of a finite-state Markov decision process are specified in terms of a finite number of events represented as /spl omega/-regular sets. An infinite history of the process produces a reward which depends on the properties it satisfies. The authors investigate the existence of optimal policies and provide algorithms for the construction of such policies.

Infinite Histories and Steady Orbits in Repeated Games

We study a model of repeated games with the following features: (a) Infinite histories. The game has been played since days of yore, or is so perceived by the players: (b) Turing machines with memory. Since regular Turing machines coincide with bounded recall strategies (in the presence of infinite histories), we endow them with "external" memory; (c) Nonstrategic players. The players ignore complicated strategic considerations and speculations about them. Instead, each player uses his/her machine to update some statistics regarding the others′ behaviour, and chooses a best response to observed behaviour. Relying on these assumptions, we define a solution concept for the one shot game, called steady orbit. The (closure of the) set of steady orbit payoffs strictly includes the convex hull of the Nash equilibria payoffs and is strictly included in the correlated equilibria payoffs. Assumptions (a)–(c) above are independent to a large extent. In particular, one may define steady orbits without explicitly dealing with histories or machines.

A note on consistency in asynchronous multicaches

This note examines and contrasts the choice of finite versus infinite histories as the framework for analysing the behaviour of an asynchronous multicache scheme.

A fixed point approach to parallel discrete event simulation

Discrete event simulation is viewed as solving a fixed point problem whose unknowns are infinite histories or streams of event and time information. Stream domains provide two notions of convergence, which correspond to the usual categorization of simulation methods. Metric convergence leads to optimistic parallel simulation (the classic event list mechanism turns out to be a specialization), and convergence in the sense of partial orders leads to conservative parallel simulation.

Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes

Building on work of McLeish, we present a number of invariance principles for doubly indexed arrays of stochastic processes which may exhibit considerable dependence, heterogeneity, and/or trending moments. In particular, we consider possibly time-varying functions of infinite histories of heterogeneous mixing processes and obtain general invariance results, with central limit theorems following as corollaries. These results are formulated so as to apply to economic time series, which may exhibit some or all of the features allowed in our theorems. Results are given for the case of both scalar and vector stochastic processes. Using an approach recently pioneered by Phillips, and Phillips and Durlauf, we apply our results to least squares estimation of unit root models.

Countably additive gambling with a general expected reward

Optimal strategies and the optimal return function are characterized for a Borel gambling problem in which the utility of a strategy is the expectation under the strategy of a general, measurable function g defined on the space of all infinite histories. These results are based on a previous paper with Lester Dubins where g was assumed to be shift-invariant.