Impermanent types and permanent reputations

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.     

When is reputation bad?

In traditional reputation models, the ability to build a reputation is good for the long-run player. In [Ely, J., Valimaki, J., 2003. Bad reputation. NAJ Econ. 4, 2; http://www.najecon.org/v4.htm. Quart. J. Econ. 118 (2003) 785–814], Ely and Valimaki give an example in which reputation is unambiguously bad. This paper characterizes a class of games in which that insight holds. The key to bad reputation is that participation is optional for the short-run players, and that every action of the long-run player that makes the short-run players want to participate has a chance of being interpreted as a signal that the long-run player is “bad.” We allow a broad set of commitment types, allowing many types, including the “Stackelberg type” used to prove positive results on reputation. Although reputation need not be bad if the probability of the Stackelberg type is too high, the relative probability of the Stackelberg type can be high when all commitment types are unlikely.     

Information asymmetry and reentry

We model a reputation game, in which a sequence of short-run players chooses if to interact with a long-run player. Although beliefs may be identical, choices may be different, as not-interacting can lead the long-run player to improve on effort.     

Imitation and selective matching in reputational games

This paper investigates imitation and selective matching in reputational games with an outside option. We identify two classes of such games, ultimatum and trust games. By selective matching we mean that short-run players have the possibility of selecting the long-run player they play against. We find that selective matching (unlike random matching) favors the equilibrium associated to reputation in the ultimatum game, but not in the trust game.     

A learning-based model of repeated games with incomplete information

This paper tests a learning-based model of strategic teaching in repeated games with incomplete information. The repeated game has a long-run player whose type is unknown to a group of short-run players. The proposed model assumes a fraction of ‘short-run’ players follow a one-parameter learning model (self-tuning EWA). In addition, some ‘long-run’ players are myopic while others are sophisticated and rationally anticipate how short-run players adjust their actions over time and “teach” the short-run players to maximize their long-run payoffs. All players optimize noisily. The proposed model nests an agent-based quantal-response equilibrium (AQRE) and the standard equilibrium models as special cases. Using data from 28 experimental sessions of trust and entry repeated games, including 8 previously unpublished sessions, the model fits substantially better than chance and much better than standard equilibrium models. Estimates show that most of the long-run players are sophisticated, and short-run players become more sophisticated with experience.     

One-sided patience with one-sided communication does not justify stackelberg equilibrium

The theory of games (with complete information) in which a single patient longrun player faces a succession of short-run opponents cannot plausibly be used to justify the Stackelberg solution concept, because if that player can select which subgame-perfect equilibrium is to be played then she can presumably also change her selection. Consequently, while she can choose among one-shot Nash outcomes, she cannot achieve the Stackelberg outcome.     

Continuous time limits of repeated games with imperfect public monitoring

In a repeated game with imperfect public information, the set of equilibria depends on the way that the distribution of public signals varies with the players' actions. Recent research has focused on the case of “frequent monitoring,” where the time interval between periods becomes small. Here we study a simple example of a commitment game with a long-run and short-run player in order to examine different specifications of how the signal distribution depends upon period length. We give a simple criterion for the existence of efficient equilibrium, and show that the efficiency of the equilibria that can be supported depends in an important way on the effect of the player's actions on the variance of the signals, and whether extreme values of the signals are “bad news” of “cheating” behavior, or “good news” of “cooperative” behavior.     

Fractional cointegration,low frequency dynamics and long-run purchasing power parity: an analysis of the Australian dollar over its recent float

A relatively new but generalized concept of fractional cointegration is applied to shed some light on the validity of purchasing power parity (PPP) as a long-run equilibrium condition, by examining the long-run relationship between quarterly consumer price indices and bilateral exchange rates of the Australian dollar and seven major OECD trading partners, over Australia's recent float. The paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a I(0) process, provides a wide range of cases of parity-reversion with processes that are CI(1,d) with 0 < d < 1. Findings tend to suggest that, while standard tests of cointegration fail to support cointegration between nominal exchange rates, domestic and foreign prices, and thus the empirical favour for PPP as a long-run phenomenon, the fractional cointegration analysis permits deviations from equilibrium to follow a fractionally integrated process and hence captures a much wider class of parity or mean-reversion behaviour. Results are mainly supportive of long-run PPP. Furthermore, an analysis of the short-run dynamics propelling the long-run relationship (through a VECM) reveals that domestic prices are consistently the initial receptor of an exogenous shock to the equilibrium and the long-run equilibrium is restored through the short-run adjustment of the nominal exchange rates. These findings are shown to hold clear policy implications.     

Second Mover Disadvantages in a Three-Player Stackelberg Game with Private Information

I consider a three-player Stackelberg. game where each player has its private signal concerning stochastic demand. I show that at a perfectly revealing equilibrium, the second mover earns the lowest and the third mover the highest expected profit of the three. I characterize this result by the strategic substitutes or complements relationships among three firms at the equilibrium. Journal of Economic Literature Classification Numbers: C72, D82, and L13.     

Adaptive behavior and the existence of Weizsäcker's long-run indifference curves

Suppose that past consumptions of the first r commodities (r < n) influence present consumption. Then, the long-run demand function to which demand converges maximizes the equilibrium short-run utility function only under very restrictive conditions. The long-run demand functions can be rationalized by a utility function, different from the equilibrium short-run utility function, if and only if the short-run utility function is such that past consumptions of any good that experience, learning, or taste changes is separable from all other goods. The class of such utility functions has been found.     

Short-run and long-run dynamic linkages among international stock markets

This paper investigates the dynamic linkages among the U.S., Japan, U.K. and German stock market indices using daily data for the April 1, 1984 to May 31,91 period. In contrast to previous studies, a vector error correction model of cointegrated variables as developed by Johansen (1988, 1991) and Johansen and Juselius (1990) is employed to examine both short-run and long-run intermarket relationships among these four stock markets. Significant evidence is found in support of both short-run and long-run relationships among these four stock market indices. The U.S. stock market leads other stock markets in short-run in the pre and post October 1987 crash, but leads all other markets in the long-run in all periods examined. The presence of a one long-run cointegrating equilibrium relationship among the four stock market indices implies a limited role of international diversification for investors with long holding periods. However, because the US-Japan-Germany stock market indices, and Japan-UK-Germany indices are not cointegrated with each other, these indices may yield international portfolio diversification in the long-run. Finally, the conflicting results from multivariate cointegration tests found in this study can not be used to provide conclusive evidence on international stock market efficiency.     

Adaptive behavior,demand and preferences

This paper extends the work on endogenous change of tastes of Von Weizsäcker to the n-commodity framework and for a general adaptive behavior process. The paper examines the relation between the effect of taste changes to income and price changes. It provides sufficient conditions for stability of the underlying dynamic process, establishes uniqueness of the equilibrium demand vector and some useful relations between the long-run demand functions and the equilibrium short-run demand functions. It is also shown that the long-run demand functions can be rationalized by a utility function if and only if the short-run utility function is such that any good that experiences learning or taste change is separable from all other goods.     

Purchasing power parity in the short and long run: a reappraisal of the post-1973 evidence

In this paper, an attempt is made to separate the short-run and long-run aspects of the purchasing power parity (PPP) relationship, using the techniques of band-spectral regression and cointegration for eight industrialized countries. The long-run PPP is first tested for all the eight countries, with reference to their nominal bilateral exchange rates vis-à-visthe US dollar. For five European currencies, the analysis is repeated with respect to the Deutschmark, with a separate consideration of the post-EMS period. In the concluding sections, possible reasons for PPP deviations are examined.     

Minimum Memory for Equivalence between Ex Ante Optimality and Time-Consistency

I give a necessary and sufficient condition on memory of a player in an extensive game for equivalence between ex ante optimality and time-consistency (for all payoff assignments). The condition is called A-loss recall and requires that each loss of a player's memory can be traced back to some loss of memory of his own action. A-loss recall is also shown to be a necessary and sufficient condition for the existence of a time-consistent strategy (for all payoff assignments) if the player is conscious-minded. Journal of Economic Literature Classification Numbers: C72, D80.     

The Game Model Analysis between the Individual and the Group

This paper analyses the game model between the individual and the group that has the characteristics of Stackelberg model in traditional game theory and replicator dynamic model in evolutionary game theory. In the first phase of game, the bounded rationality group players adopt the replicator dynamic behavior. Secondly, the full rationality individual player decides the own response function by the strategies distribution of group players. The shortsighted individual player will take the risk-dominant strategy. This model has some unique characteristics.     

Nominal uniqueness and money non-neutrality in the limit-price exchange process

We define continuous-time dynamics for exchange economies with fiat money. Traders have locally rational expectations, face a cash-in-advance constraint, and continuously adjust their short-run dominant strategy in a monetary strategic market game involving a double-auction with limit-price orders. Money has a positive value except on optimal rest-points where it becomes a ??veil?? and trade vanishes. Typically, there is a piecewise globally unique trade-and-price curve both in real and in nominal variables. Money is not neutral, either in the short-run or long-run and a localized version of the quantity theory of money holds in the short-run. An optimal money growth rate is derived, which enables monetary trade curves to converge towards Pareto optimal rest-points. Below this growth rate, the economy enters a (sub- optimal) liquidity trap where monetary policy is ineffective; above this threshold inflation rises. Finally, market liquidity, measured through the speed of real trades, can be linked to gains-to-trade, households?? expectations, and the quantity of circulating money.     

To Commit or Not to Commit: Endogenous Timing in Experimental Duopoly Markets

In this paper we experimentally investigate the extended game with action commitment of Hamilton and Slutsky (1990, Games Econ. Behavior2, 29–46). In their duopoly game firms can choose their quantities in one of two periods before the market clears. If a firm commits to a quantity in period 1, it does not know whether the other firm also commits early. By waiting until period 2, a firm can observe the other firm's period-1 action. Hamilton and Slutsky predicted the emergence of endogenous Stackelberg leadership. Our data, however, do not confirm the theory. While Stackelberg equilibria are extremely rare, we often observe endogenous Cournot outcomes and sometimes collusive play. This is partly driven by the fact that endogenous Stackelberg followers learn to behave in a reciprocal fashion over time, i.e., they learn to reward cooperation and to punish exploitation. Journal of Economic Literature Classification Numbers: C72, C92, D43.     

σ: The long and short of it

Research on the elasticity of substitution between capital and labor – σ – has been proceeding for 75 years. While there is clearly a strong case for the importance of σ in the analysis of growth and other economic issues, much less agreement exists on the value of σ. This paper offers some perspectives on prior estimates of σ, emphasizing the fundamental tension between the short-run data that are available and the long-run parameter that is required. Estimates of σ based on various short-run and long-run models are discussed and, while the estimates range widely, the weight of the evidence suggests a value of σ in the range of 0.40–0.60. There is little evidence to sustain the assumption of a Cobb–Douglas production function.     

Time series explanations of merger activity: some econometric results

Existing papers which have attempted to test explanations of time series patterns in merger behaviour suffer from the defects that, first, they usually consider only one hypothesis and, secondly, none use a moderm econometric methodology. Consequently, their results may be subject to the spurious correlation problem. In this paper we argue that four well-known approaches to explaining time series data in acquisitions (Gort's disturbance theory, King's Trapped Equity model, disequilibrium hypotheses and ad hoc approaches) can all be nested within a capital budgeting decision-making framework. Using a co-integration methodology, a long-run relationship was found between the quarterly number of acquisitions and the growth rate of GDP, Tobin's Q, the balance of payments, the unemployment rate and share prices. Some of the previously proposed theories were found to explain the short-run dynamic variation in acquisition activity. No support was found for Gort's disturbance theory or for King's Trapped Equity model. Conclusions for antitrust policy are suggested.     

Pricing decisions in a dual channels system with different power structures

This paper investigates the effect of product substitutability and relative channel status on pricing decisions under different power structures of a dual exclusive channel system where each manufacturer distributes its goods through a single exclusive retailer but two goods are substitute. A linear demand based on the utility function of a representative consumer is assumed, and three game scenarios(Manufacturer Stackelberg, Retailer Stackelbeg and Vertical Nash) are examined under symmetric and asymmetric related channel status. It is shown that no power structure is always the best for the entire supply chain though all members on supply chain have incentive to lead the Stackelberg game. Meanwhile, the vertical Nash game is an equilibrium for the members, however, a Prisoner's dilemma necessarily incurs for the entire supply chain because the Retailer Stackelberg or the Manufacturer Stackelberg can gain the better performance than that in vertical Nash for the entire supply chain when the product substitutability is moderate or higher and the asymmetric relative channel status is moderate, while consumers always get the most welfare from the vertical Nash game.