Remarks on the application of statistical games to technological development forecasting

This work presents the probability of determining a quantitative forecast of technological development S(t) defined by a set m of parameters S⁽¹⁾(t),S⁽²⁾(t),…,S^(m)(t), based on statistical game theory. Assuming that the coordinates S⁽ⁱ⁾(t) (i = 1, 2,…,m) of a forecasted vector S(t) are stochastic processes with given probabilistic characteristics, a formula of a function forecasting the value of a coordinate S⁽ⁱ⁾(t) of this vector can be obtained. This formula permits to determine a vector of forecasts _τT(x) of technological development S(t) at a given moment t = τ+T.     

A leximin characterization of strategy-proof and non-resolute social choice procedures

Summary. We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality to k where . Received: November 8, 1999; revised version: September 18, 2001     

Cost-effectiveness analysis of disease modifiying drugs (interferons and glatiramer acetate) as first line treatments in remitting-relapsing multiple sclerosis patients

Abstract

Objective:

The aim of this study was to assess cost-effectiveness of the different Disease Modifying Drugs (DMD) used as first-line treatments (interferons IM IFNβ-1a, SC IFNβ-1a, SC IFNβ-1b, and glatiramer acetate, GA) in Remitting-Relapsing Multiple Sclerosis (RRMS) in Spain.

Methods:

A Markov model was developed to simulate the progression of a cohort of patients with RRMS, during a period of 10 years. Seven health states, defined by the Expanded Disability Status Scale (EDSS), were considered in the model. Patients with an EDSS score less than 6.0 were assumed to be treated with one of the DMD. In addition, all patients were assumed to receive symptomatic treatment. The monthly transition probabilities of the model were obtained from the literature. The analysis was performed from the societal perspective, in which both direct and indirect (losses in productivity) healthcare costs (€, 2010) were included. A discount rate of 3% was applied to both costs and efficacy results.

Results:

GA was the less costly strategy (€322,510), followed by IM IFNβ-1a (€329,595), SC IFNβ-1b (€ 333,925), and SC IFNβ-1a (€348,208). IM IFNβ-1a has shown the best efficacy results, with 4.176 quality-adjusted life years (QALY), followed by SC IFNβ-1a (4.158 QALY), SC IFNβ-1b (4.157 QALY), and GA (4.117 QALY). Incremental costs per QALY gained with IM IFNβ-1a were €?1,005,194/QALY, €?223,397/QALY, and €117,914/QALY in comparison to SC IFNβ-1a, SC IFNβ-1b, and GA, respectively.

Conclusions:

First-line treatment with GA is the less costly strategy for the treatment of patients with RRMS. Treatment with IM IFNβ-1a is a dominant strategy (lower cost and higher QALY) compared with SC IFNβ-1a and SC IFNβ-1b. However, IM IFNβ-1a is not a cost-effective strategy vs GA, because incremental cost per QALY gained with IM IFNβ-1a exceeds the €30,000 per QALY threshold commonly used in Spain.

Limitations:

The highly-restrictive inclusion criteria of clinical trials limits generalization of the results on efficacy to all patients with multiple sclerosis. Availability of data for head-to-head comparisons is associated with the use of information from clinical trials.     

Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities

This paper identifies a domain of payoff functions inno spillovernoncooperative games withPositive externalitywhich admit a pure strategy Nash equilibrium. Since in general a Nash equilibrium may fail to exist, in order to guarantee the existence of an equilibrium, we impose two additional assumptions,AnonymityandOrder preservation. The proof of our main result is carried out by constructing, for a given gameG, a potential function Ψ over the set of strategy profiles in such a way that the maximum of Ψ yields a Nash equilibrium in pure strategies ofG.Journal of Economics LiteratureClassification Numbers: C72, D62, H73.     

Stochastic stability in a double auction

In a k-double auction, a buyer and a seller must simultaneously announce a bid and an ask price respectively. Exchange of the indivisible good takes place if and only if the bid is at least as high as the ask, the trading price being the bid price with probability k and the ask price with probability (1−k). We show that the stable equilibria of a complete information k-double approximate an asymmetric Nash bargaining solution with the seller's bargaining power decreasing in k.Note that ceteris paribus, the payoffs of the seller of the one-shot game increase in k. Nevertheless, as the stochastically stable equilibrium price decreases in k, choosing the seller's favorite price with a relatively higher probability in individual encounters makes him worse off in the long run.     

Facilitating Consumer Learning in Insurance Markets: What Are the Welfare Effects?

We model a monopoly insurance market in which consumers can learn their accident risks at a cost c . We then examine the welfare effects of a policy that reduces c . If c is sufficiently small (c  < c ^*), the optimal contract is such that the consumer gathers information. For c  < c ^*, both the insurer and the consumer benefit from a policy that reduces c further. For c   >  c ^*, marginally reducing c hurts the insurer and weakly benefits the consumer. Finally, a reduction in c that is successful, meaning that the consumer gathers information after the reduction but not before it, can hurt both parties.     

A game of timing and visibility

We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x_i in the interval [0,1], and a player's payoff is the distance from its point x_i to the next larger point, or to 1 if x_i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games.     

No-envy in queueing problems

We explore the implications of no-envy(Foley 1967) in the context of queueing problems. We identify an easy way of checking whether a rule satisfies efficiencyand no-envy. The existence of such a rule can easily be established. Next, we ask whether there is a rule satisfying efficiency and no-envytogether with an additional solidarity requirement how agents should be affected as a consequence of changes in the waiting costs. However, there is no rule satisfying efficiency, noenvy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envyand backward/forward no-envy. Finally, we discuss whether three fairness requirements, no-envy, the identical preferences lower bound, and egalitarian equivalence, are compatible in this context.     

Validity of sustainability framework for China’s mining cities – a structural equation modelling approach

Many studies developed their framework for sustainability through indicator systems, but the interactions and relationships within these indicators have not been studied yet. In this article, based on indicator systems, we use a sample of 78 mining cities in China and employ structural equation modelling (SEM) method to explore the validity of sustainability framework. Our empirical results show that resources abundance positively affects urbanization level significantly but negatively affects cleaner production level and environmental protection level significantly; economic strength positively affects urbanization level significantly; cleaner production level has a significant effect on economic strength and non-mineral resources conversion efficiency. We also find that when economic strength is low, resources abundance might weaken the positive effect of economy on urbanization.     

Reciprocity and Giving in a Consecutive Three‐Person Dictator Game with Social Interaction

We study pure indirect reciprocity by setting up a modified dictator game with three players A, B, and C acting sequentially. Subject A takes a share of a pie and passes the rest to subject B, while B divides the rest between herself and C. We find that this consecutive three‐person dictator game increases generosity compared with the traditional two‐person dictator game. We analyze the influence of social interaction and uncertainty. In treatments with certainty we observe pure indirect reciprocity: B indirectly reciprocates for A's behavior in the decision on how generous to be to C.     

Designer path independent choice functions

Summary. This paper provides an algorithm for the construction of all PICFs on a finite set of alternatives, V, designed by an a priori given set I of initial choices as well as the determination of whether the initial set I is consistent with path independence. The algorithm is based on a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of the algorithm. The characterization result identifies two properties of a partition of the Boolean algebra as necessary and sufficient for a choice function C to be a PICF: (i): For every subset A of V the set is an interval in the Boolean algebra 2 ^V . (ii): If A/B is an interval in the Boolean algebra such that C(A) = C(B) and if M/N is an upper transpose of A/B then C(M) = C(N). The algorithm proceeds by expanding on the implications of these two properties.Received: 5 November 2003, Revised: 20 July 2004, JEL Classification Numbers: D00, D70.     

A class of multiattribute utility functions

A function u(z) is a utility function if u′(z) > 0. It is called risk averse if we also have u′′(z) < 0. Some authors, however, require that u ⁽ⁱ⁾(z) > 0 if i is odd and u ⁽ⁱ⁾(z) < 0 if i is even. The notion of a multiattribute utility function can be defined by requiring that it is increasing in each variable and concave as an s-variate function. A stronger condition, similar to the one in case of a univariate utility function, requires that, in addition, all partial derivatives of total order m should be positive if m is odd and negative if m is even. In this paper, we present a class of functions in analytic form such that each of them satisfies this stronger condition. We also give sharp lower and upper bounds for E[u(X ₁,... , X _s )] under moment information with respect to the joint probability distribution of the random variables X ₁,... , X _s assumed to be discrete and representing wealths. Partially supported by OTKA grants F-046309 and T-047340 in Hungary.     

Matching for teams

We are given a list of tasks Z and a population divided into several groups X _j of equal size. Performing one task z requires constituting a team with exactly one member x _j from every group. There is a cost (or reward) for participation: if type x _j chooses task z, he receives p _j (z); utilities are quasi-linear. One seeks an equilibrium price, that is, a price system that distributes all the agents into distinct teams. We prove existence of equilibria and fully characterize them as solutions to some convex optimization problems. The main mathematical tools are convex duality and mass transportation theory. Uniqueness and purity of equilibria are discussed. We will also give an alternative linear-programming formulation as in the recent work of Chiappori et al. (Econ Theory, to appear).     

What is macroeconomic causality?

The paper aims to develop an adequate account of macroeconomic causality. It discusses the definition that is central to Woodward’s interventionist account and the definitions that can be extracted from Hoover’s remarks on privileged parameterization and from the potential outcome approach that Angrist and Kuersteiner have introduced into macroeconomics more recently. The definition to be defended can be regarded as the gist that is common to all three definitions when they are relieved of overly restrictive conditions. It says (roughly) that X causes Y if and only if there is a possible intervention on X that changes Y, where X and Y stand for macroeconomic aggregates, where an intervention is understood as a manipulation of an intervention variable I that satisfies conditions requiring that I be a cause of X, and that there be no confounders of X and Y, and where an intervention variable is either a variable or a parameter.     

Identification of house price bubbles using user cost in a state space model

This article studies how much variation in house prices results from nonfundamental factors. We propose a relative valuation approach to quantifying a bubble in housing by incorporating the housing User Cost into a state space model. We find that UK house prices were undervalued from January 1995 to May 2001 and subsequently moved into a bubble over the period to October 2012. Our results support the bounded rationality hypothesis in the long run. However, we also find that the irrational and the rational expectation hypotheses can coexist in the short run when explosive bubbles are driven by price dynamics.     

Promotion and Coevolutionary Dynamics in Contemporary Capitalism

We characterize the dynamics of contemporary capitalist societies as emerging from the coevolution of five different subsystems: the intimate realm of individuals, the market, the state, civil society, and nature. We highlight a specific coevolution mechanism between some of these subsystems, which we call promotion. The insights from this coevolution approach are twofold. On one hand, from the ontological and heuristic perspectives, we argue that our proposal opens the possibility for constructing a general, interpretative framework in evolutionary economics. On the other hand, from a theoretical-explanatory perspective, we detect certain coevolution paths that may engender global pathologies in capitalist societies. We also suggest that future research may explore some normative implications of this approach, as well as alternative methodological strategies to develop it.     

COHERENCY AND COMPLETENESS OF STRUCTURAL MODELS CONTAINING A DUMMY ENDOGENOUS VARIABLE*

Let y be a vector of endogenous variables and let w be a vector of covariates, parameters, and errors or unobservables that together are assumed to determine y. A structural model y=H(y, w) is complete and coherent if it has a well‐defined reduced form, meaning that for any value of w there exists a unique value for y. Coherence and completeness simplifies identification and is required for many estimators and many model applications. Incoherency or incompleteness can arise in models with multiple decision makers, such as games, or when the decision making of individuals is either incorrectly or incompletely specified. This article provides necessary and sufficient conditions for the coherence and completeness of simultaneous equation systems where one equation is a binomial response. Examples are dummy endogenous regressor models, regime switching regressions, treatment response models, sample selection models, endogenous choice systems, and determining if a pair of binary choices are substitutes or complements.     

The relation between two different notions of direct and indirect input requirements

Ki-Jun Jeong (1982) proposed to distinguish between the notion of direct and indirect input requirements to support a unit of final demand (r_f) and that to produce a unit of gross output (r_g) in the open input-output model. In this note the two notions are related by the relation r_f = r_gc₁₁, where c₁₁ is direct and indirect output requirements to support a unit of final demand, or c₁₁ = 1 + r_f.     

Imitation processes with small mutations

This note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,” meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the absorbing states of the no-mutation process. The work of Freidlin and Wentzell [Random Perturbations of Dynamical Systems, Springer, New York, 1984] and its extensions provide a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a simpler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K×K Markov matrix on the K homogeneous states, where the probability of a transit from “all play i” to “all play j” is the probability of a transition from the state “all agents but 1 play i, 1 plays j” to the state “all play j”.     

Balanced Contributions Axiom in the Solution of Cooperative Games

In a gamevin characteristic function form, suppose the Banzhaf value ψ is used to pay a coalitionSalready formed. Then coalitionSno longer receivesv(S); instead it receivesR^ψ(S) = ∑_{i ∈ S}ψ_i(v_s), wherev_Sdenotes the subgame of coalitionS. Surprisingly, the Shapley value of this new game Sh(N, R^ψ) is equal to the Banzhaf value ofv. In this paper we establish a similar result for all values satisfying balanced contributions axiom. Additionally, we introduce player's weights to obtain the corresponding result in the nonsymmetric case.Journal of Economic LiteratureClassification Number: C71