Deriving Nash equilibria as the supercore for a relational system

In this paper, under a binary relation that refines the standard relation which only accounts for single profitable deviations, we obtain that the set of NE strategy profiles of every finite non-cooperative game in normal form coincides with the supercore (Roth, 1976) of its associated abstract system. Further, under the standard relation we show when these two solution concepts coincide.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Coalitional games with veto players: Consistency, monotonicity and Nash outcomes

Following Dagan et al. [Dagan, N., Volij, O., Serrano, R. (1997). A non-cooperative view on consistent bankruptcy rules, Games Econ. Behav. 18, 55–72], we construct an extensive form game for veto-balanced TU games in which a veto player is the proposer and the other players are responders. The set of Nash outcomes of this extensive form game is described, and compared to solutions of TU games such as the nucleolus, kernel and egalitarian core. We find necessary and sufficient conditions under which the nucleolus of the game is a Nash outcome.     

Network formation with sequential demands

This paper introduces a non-cooperative game-theoretic model of sequential network formation, in which players propose links and demand payoffs. Payoff division is therefore endogenous. We show that if the value of networks satisfies size monotonicity, then each and every equilibrium network is efficient. The result holds not only when players make absolute participation demands, but also when they are allowed to make link-specific demands.     

Extreme points of two digraph polytopes: Description and applications in economics and game theory

In this paper, we introduce two polytopes that respect a digraph in the sense that for every vector in the polytope every component corresponds to a node and is at least equal to the component corresponding to each successor of this node. The sharing polytope is the set of all elements from the unit simplex that respect the digraph. The fuzzy polytope is the set of all elements of the unit cube respecting the digraph. The main results are characterizations of the extreme points of the above described two digraph polytopes. We also give an economic application of the result on the sharing polytope and a game-theoretical application for the fuzzy polytope.     

The joint continuity of the expected payoff functions

Glicksberg [Glicksberg, I.L., 1952. A further generalization of the Kakutani fixed point theorem, with applications to Nash equilibrium points. In: Proceedings of the American Mathematical Society 3, pp. 170–174] generalized the Kakutani fixed point theorem to the setting of locally convex spaces and used it to prove that every k-person strategic game with action sets convex compact subsets of locally convex spaces and continuous payoff functions has a Nash equilibrium. He subsequently used this result to establish the following fundamental theorem of game theory: Every k-person strategic game with action sets metrizable compact topological spaces and continuous payoff functions has a mixed strategies equilibrium. However, in his proof of the latter result, Glicksberg did not show that the expected payoff functions were jointly continuous, something that was required for the existence of a mixed strategies equilibrium.     

A central limit theorem for endogenous locations and complex spatial interactions

We provide a new central limit theorem (CLT) for spatial processes under weak conditions that are plausible for many economic applications in which location is endogenous. In particular, our CLT is designed for problems that have some, but not necessarily all, of the following features: (i) Agents choose the locations of observations to maximize profits, welfare, or some other objective. (ii) The objects that are chosen (e.g., stores or brands) interact with one another. For example, they can be substitutes or complements. (iii) Interaction can be complex. In particular, interaction between i and j need not depend only on the distance between the locations of i and j, but can also depend on distance to or location of other observations k, or possibly on the number of other such observations.     

Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player i is a best response to the distribution of strategies of his opponents (when they face i) in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.     

基于博弈的闭环供应链非合作模型分析

对基于单一制造商和单一零售商构成的闭环供应链进行了研究,应用博弈理论对闭环供应链的定价策略进行了分析,分别得出两个非合作博弈的均衡解(Stackelberg均衡和Nash均衡),并进一步对各种定价策略的效率进行了分析。     

Cross-sectional dependence robust block bootstrap panel unit root tests

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectional dependence including (but not exclusive to) the popular common factor framework. We consider block bootstrap versions of the group-mean (Im et al., 2003) and the pooled (Levin et al., 2002) unit root coefficient DF tests for panel data, originally proposed for a setting of no cross-sectional dependence beyond a common time effect. The tests, suited for testing for unit roots in the observed data, can be easily implemented as no specification or estimation of the dependence structure is required. Asymptotic properties of the tests are derived for T going to infinity and N finite. Asymptotic validity of the bootstrap tests is established in very general settings, including the presence of common factors and cointegration across units. Properties under the alternative hypothesis are also considered. In a Monte Carlo simulation, the bootstrap tests are found to have rejection frequencies that are much closer to nominal size than the rejection frequencies for the corresponding asymptotic tests. The power properties of the bootstrap tests appear to be similar to those of the asymptotic tests.     

Mixtures of t-distributions for finance and forecasting

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. Particularly desirable for econometric applications are closed-form expressions for antiderivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-of-sample, than density forecasts obtained using normal or standard t-distributions. In the second application, we replicate the option-pricing exercise of Abadir and Rockinger [Density functionals, with an option-pricing application. Econometric Theory 19, 778–811.] and obtain comparably good results, while gaining analytical tractability.     

An exact non-cooperative support for the sequential Raiffa solution

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two-person bargaining games. Based on an approximate foundation due to Myerson (1991) for any two-person bargaining game (S, d) an extensive form game G^S,d is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game.By a modification of G^S,d the analogous result is provided for subgame perfect equilibria. These results immediately extend to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.     

Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models

This paper analyzes the higher-order properties of the estimators based on the nested pseudo-likelihood (NPL) algorithm and the practical implementation of such estimators for parametric discrete Markov decision models. We derive the rate at which the NPL algorithm converges to the MLE and provide a theoretical explanation for the simulation results in Aguirregabiria and Mira [Aguirregabiria, V., Mira, P., 2002. Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519–1543], in which iterating the NPL algorithm improves the accuracy of the estimator. We then propose a new NPL algorithm that can achieve quadratic convergence without fully solving the fixed point problem in every iteration and apply our estimation procedure to a finite mixture model. We also develop one-step NPL bootstrap procedures for discrete Markov decision models. The Monte Carlo simulation evidence based on a machine replacement model of Rust [Rust, J., 1987. Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica 55, 999–1033] shows that the proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations.     

Uniqueness conditions for strongly point-rationalizable solutions to games with metrizable strategy sets

This paper introduces the iterative solution concept of strong point-rationalizability as a strengthening of standard point-rationalizability by stipulating that any two players have identical beliefs about the strategy choices of their common opponents. By adopting and generalizing the contraction-property approach of Moulin [Moulin, H., 1984. Dominance solvability and cournot stability. Mathematical Social Sciences 7, 83–102] and Bernheim [Bernheim, B.D., 1984. Rationalizable strategic behavior. Econometrica 52, 1007–1028] we derive sufficient conditions for the existence of unique strongly point-rationalizable strategies in strategic games with best response functions. These uniqueness results are derived under fairly general assumptions and are especially useful for complete and bounded, as well as finite strategy sets. For games with monotonic individual best response functions, equivalence between a unique strongly point-rationalizable and a unique point-rationalizable solution in the standard sense is established. Furthermore, the existence of unique fixed points is proven under conditions that generalize for bounded metric spaces an established fixed point theorem by Bonsall [Bonsall, F.F., 1962. Lectures on Some Fixed Point Theorems of Functional Analysis. Tata Institute of Fundamental Research, Bombay] and Smart [Smart, D.R., 1974. Fixed Point Theorems. Cambridge University Press, Cambridge, London]. Possible extensions of our findings to games with multi-valued best response correspondences are discussed.     

Identification of peer effects through social networks

We provide new results regarding the identification of peer effects. We consider an extended version of the linear-in-means model where interactions are structured through a social network. We assume that correlated unobservables are either absent, or treated as network fixed effects. We provide easy-to-check necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although identification may fail for some particular structures. We use data from the Add Health survey to provide an empirical application of our results on the consumption of recreational services (e.g., participation in artistic, sports and social activities) by secondary school students. Monte Carlo simulations calibrated on this application provide an analysis of the effects of some crucial characteristics of a network (i.e., density, intransitivity) on the estimates of peer effects. Our approach generalizes a number of previous results due to Manski [Manski, C., 1993. Identification of endogenous social effects: The reflection problem. Review of Economic Studies 60 (3), 531–542], Moffitt [Moffitt, R., 2001. Policy interventions low-level equilibria, and social interactions. In: Durlauf, Steven, Young, Peyton (Eds.), Social Dynamics. MIT Press] and Lee [Lee, L.F., 2007. Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics 140 (2), 333–374].     

Inequality and catching-up under decreasing marginal impatience

This paper examines how endogenous time preference interacts with inequalities in economic development. We consider two distinct groups of households with intrinsic inequality (e.g., capitalists and workers), and show that (i) under decreasing marginal impatience (DMI), an unequal society may be preferable for poor households than an egalitarian one in which every household owns an equal share of asset; (ii) poor households tend to benefit more under DMI than CMI (constant marginal impatience) from positive shocks; (iii) inequality exhibits a sharp inverted-U shape as more people become rich, which should be good news for developing countries in catching up; and (iv) a tax on capital income reduces poor households’ income when the fraction of the rich is sufficiently small. We also examine immigration and discuss capital mobility.     

非线性需求下两层供应链的定价策略及协调机制研究

对基于单一制造商和单一零售商构成的供应链,在非线性需求函数的前提下,应用博弈理论对供应链系统的定价策略进行了分析,分别得出非合作博弈和合作博弈的均衡解,进一步对各种定价策略的效率进行了分析。另外,给出了便于实际操作的协调方法。     

Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

Detecting big structural breaks in large factor models

Time invariance of factor loadings is a standard assumption in the analysis of large factor models. Yet, this assumption may be restrictive unless parameter shifts are mild (i.e., local to zero). In this paper we develop a new testing procedure to detect big breaks in these loadings at either known or unknown dates. It relies upon testing for parameter breaks in a regression of one of the factors estimated by Principal Components analysis on the remaining estimated factors, where the number of factors is chosen according to Bai and Ng’s (2002) information criteria. The test fares well in terms of power relative to other recently proposed tests on this issue, and can be easily implemented to avoid forecasting failures in standard factor-augmented (FAR, FAVAR) models where the number of factors is a priori imposed on the basis of theoretical considerations.