Existence of perfect equilibria: a direct proof

We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game.     

Stochastic evolutionary stability in extensive form games of perfect information

Nöldeke and Samuelson [Games Econ. Behav. 5 (1993) 425] investigate a stochastic evolutionary model for extensive form games and show that even for games of perfect information with a unique subgame perfect equilibrium, non-subgame perfect equilibrium-strategies may well survive in the long run even when mutation rates tend to zero. In a different model of evolution in the agent normal form of these games Hart [Games Econ. Behav. 41 (2002) 227] shows that under suitable limit-taking, where small mutation rates are accompanied by large population sizes in a particular way, the unique prediction is again the subgame perfect equilibrium. This paper provides a proof of a similar result for the model of Nöldeke and Samuelson.     

Determinacy and Stability under Learning of Rational Expectations Equilibria

This paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied. Journal of Economic Literature Classification Numbers: E32, D83.     

The local best response criterion: An epistemic approach to equilibrium refinement

The standard refinement criteria for extensive form games, including subgame perfect, perfect, perfect Bayesian, sequential, and proper, reject important classes of reasonable Nash equilibria and accept many unreasonable Nash equilibria. This paper develops a new refinement criterion, based on epistemic game theory, that captures the concept of a Nash equilibrium that is plausible when players are rational. I call this the local best response (LBR) criterion. This criterion is conceptually simpler than the standard refinement criteria because it does not depend on out-of-equilibrium, counterfactual, or passage to the limit arguments. The LBR is also informationally richer because it clarifies the epistemic conditions that render a Nash equilibrium reasonable. The LBR criterion appears to render the traditional refinement criteria superfluous.     

Effects of uncertain lifetime and annuity insurance on capital accumulation and growth

Summary.  This paper studies the effects of uncertain lifetime on capital accumulation and growth and also the sensitivity of those effects to the existence of a perfect annuities market. The model is an overlapping generations model with uncertain lifetimes. The technology is convex and such that the marginal product of capital is bounded away from zero. A contribution of this paper is to show that the existence of accidental bequests may lead the economy to an equilibrium that exhibits asymptotic growth, which is impossible in an economy with a perfect annuities market or with certain lifetimes. This paper also shows that if individuals face a positive probability of surviving in every period, they may be willing to save at any age. This effect of uncertain lifetime on savings may also lead the economy to an equilibrium exhibiting asymptotic growth even if there exists a perfect annuities market. Received: April 17, 1996; revised version: December 9, 1997     

Capital controls and welfare

This paper computes welfare levels under different degree of capital controls and compares them with the welfare level under perfect capital mobility by using the methodology of Schmitt-Grohé and Uribe (2007). We show that perfect capital mobility is not always optimal and that capital controls may enhance an economy’s welfare level. There exists an optimal degree of capital-account restriction that achieves a higher level of welfare than that under perfect capital mobility, if the economy has costly financial intermediaries. The results of our analysis imply that as the domestic financial intermediaries are less efficient, the government should impose stricter capital controls in the form of a tax on foreign borrowing.     

The capital gain lock-in effect and perfect substitutes

This paper analyses the effect of investors' accrued capital gains on optimal portfolio composition and equilibrium returns under the assumption that investors are able to re-balance with perfect substitute securities. No-dominance arguments are used to show that pricing differences because of accrued capital gains do not arise among securities which are perfect substitutes. These arguments are insufficient, however, to prevent pricing differences because of accrued capital gains among securities which are not perfect substitutes. Trading rules are developed which outline the conditions necessary for the realisation of accrued capital gains and the deferral of capital losses. These trading rules also provide guidance on which securities investors should sell, given their tax basis, when re-balancing their portfolios.     

Selective Acceptance and Inefficiency in a Two-Issue Complete Information Bargaining Game

This paper explores the effects of a “selective acceptance” rule on the outcome of two-issue negotiations. The alternating-offer game introduced here allows for the possibility that settlement may be reached on one issue while negotiation continues about the other. This model captures features of laws that are generally believed to increase efficiency. The analysis shows that if one issue is indivisible, there are inefficient subgame perfect equilibria with no Pareto-improving alternative equilibria. With opposing valuations, rapid communication guarantees inefficiency. These are unique examples of this strong form of inefficiency in an alternating-offer bargaining game with complete (and perfect) information. Journal of Economic Literature Classification Numbers: C72, J30.     

进一步完善我国现行增值税的思考

本文首先对现行增值税在实践中存在问题产生的不利于创造公平税收环境、不能体现宏观经济政策、造成税源流失的负面效应进行分析。进而进一步明确了完善现行增值税票要解决的认识问题。在此基础上提出了完善增值税的总体设想和具体措施, 即由生产型增值税向消费型增值税过渡、分阶段扩大增值税范围、减少增值税税收优惠、建立健全增值税征管制度。     

Perfect and Proper Equilibria of Large Games

This paper deals with the existence and other related issues of perfect and proper equilibria of games with a continuum of players. A sufficient condition for the existence of a perfect (proper) equilibrium as an almost everywhere limit of a sequence of ε-perfect (ε-proper) equilibria is given. An example shows that almost everywhere convergence need not obtain if the condition is violated. Extension to the case where the set of actions available to the players can differ is discussed.Journal of Economic LiteratureClassification Number: C79.     

Existence of Nash equilibria in finite extensive form games with imperfect recall: A counterexample

This paper provides an example showing that for finite extensive form games without perfect recall existence of Nash equilibria in behaviour strategies is not guaranteed in general.     

Global convergence of adaptive learning in models of pure exchange

Summary. This paper develops an adaptive learning scheme for a standard version of the OLG model with pure exchange. Perfect forecasting rules which generate perfect foresight orbits are approximated by cubic spline functions. These approximations are successively constructed using historical data only. Trajectories generated by this scheme converge to perfect foresight orbits globally for all initial conditions. This result holds for all parameterizations guaranteeing the existence of a monetary steady state and hence is independent of consumers' savings behavior. It generalizes to all one-dimensional models of the Cobweb type. Received: October 5, 2000; revised version: February 15, 2001     

Product differentiation,price discrimination and collusion

The existing literature which analyses the relationship between the product differentiation degree and the sustainability of a collusive agreement on price assumes that firms cannot price discriminate, and concludes that there is a negative relationship between the product differentiation degree and the critical discount factor. This paper, in contrast, assumes that firms are able to price discriminate. Within the Hotelling framework, three different collusive schemes are studied: perfect collusion on discriminatory prices; perfect collusion on a uniform price; collusion not to discriminate. We obtain that the critical discount factor of the first and the third collusive scheme does not depend on the product differentiation degree, while the critical discount factor of the second collusive scheme depends positively on the product differentiation degree. Moreover, we show that imperfect collusion is more difficult to sustain than perfect collusion.     

Bonding and the enforcement of labor contracts

Bonded contracts are a perfect substitute for legally enforceable contracts, if capital markets are perfect. This idea is applied to labor market contracts involving specific training.     

A characterisation of the perfect equilibria of infinite horizon games

This paper builds on the work of Fudenberg and Levine (J. Econ. Theory31 (1983), 251–268). It shows that the perfect equilibria of any game in which events become uniformly unimportant as their distance into the future increases can be characterised as limits of sequences of perfect approximate equilibrium points of finite horizon approximations to the game. The result holds both for a strong and for a weak topology. The topologies are tractable, and the nature of convergence relative to them is transparent. Finally, the weak topology is probably the weakest tractable topology in which the result holds.     

Finitely repeated games with social preferences

A well-known result from the theory of finitely repeated games states that if the stage game has a unique equilibrium, then there is a unique subgame perfect equilibrium in the finitely repeated game in which the equilibrium of the stage game is being played in every period. Here I show that this result does in general not hold anymore if players have social preferences of the form frequently assumed in the recent literature, for example in the inequity aversion models of Fehr and Schmidt (Quartely Journal of Economics 114:817–868, 1999) or Bolton and Ockenfels (American Economic Review 100:166–193, 2000). In fact, repeating the unique stage game equilibrium may not be a subgame perfect equilibrium at all. This finding should have relevance for all experiments with repeated interaction, whether with fixed, random or perfect stranger matching.     

Non-trivial subgame perfect duopoly equilibria can be supported by continuous reaction functions

This paper demonstrates that non-trivial subgame perfect duopoly equilibria can be supported by continuous reaction functions when previous-period actions of both firms are arguments of reaction functions. Continuity imposes essentially no restrictions on the set of equilibria.     

On the limit perfect public equilibrium payoff set in repeated and stochastic games

This paper provides a dual characterization of the existing ones for the limit set of perfect public equilibrium payoffs in a class of finite stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg et al. (1994), Kandori and Matsushima (1998) and Hörner et al. (2011) obtain. As a second corollary, it is shown that this limit set of payoffs is a convex polytope when attention is restricted to perfect public equilibria in pure strategies. This result fails for mixed strategies, even when attention is restricted to two-player repeated games.     

Capital income taxation and perfect foresight

This paper develops a perfect foresight model of capital income taxation in a representative household neoclassical one-sector framework. The household sector is based on intertemporal utility maximization. The main result is the equivalence of a perfect foresight solution and an artificial central planning solution; if there is no tax, this is the equivalence of a market equilibrium and social optinum. The equivalence result is used to deduce the implications of a partial tax reform policy. It is shown that a partial reform increases capital at each time following the initial period of the program.     

Growth and equilibrium indeterminacy: the role of capital mobility

Summary. The paper presents a human capital driven endogenous growth model which, in general, permits a multiplicity of equilibrium balanced growth paths. It is shown that allowing for perfect capital mobility across countries increases the range of parameter values for which the model permits equilibrium indeterminacy. As opposed to the closed capital markets case, simple restrictions on preferences are no longer sufficient to eliminate the indeterminacy. Intuitively, under perfect capital mobility agents are able to smooth consumption completely. This induces an economy with open capital markets to behave like a closed economy with linear preferences thereby increasing the possibility of equilibrium indeterminacy. Received: 18 November 1998; revised version: 10 August 1999