The partially cursed and the analogy-based expectation equilibrium

Recent literature has established a link between the fully cursed equilibrium and the analogy-based expectation equilibrium. In this note, even the partially cursed equilibrium is shown to correspond to an analogy-based expectation equilibrium.     

Sampling equilibrium, with an application to strategic voting

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.     

Bounded rationality: static versus dynamic approaches

Summary. Two kinds of theories of boundedly rational behavior are possible. Static theories focus on stationary behavior and do not include any explicit mechanism for temporal change. Dynamic theories, on the other hand, explicitly model the fine-grain adjustments made by the subjects in response to their recent experiences. The main contribution of this paper is to argue that the restrictions usually imposed on the distribution of choices in the static approach are generically not supported by a dynamic adjustment mechanism. The genericity here is understood both in the measure theoretic and in the topological sense.Received: 29 April 2002, Revised: 11 February 2004, JEL Classification Numbers: C0, D7.I thank Peter Bardsley and Rabee Tourky for useful suggestions. Special thanks are due to an anonymous referee.     

A spectrum of equilibration processes in game theory

In game theory, four dynamic processes converging towards an equilibrium are distinguished and ordered by way of agents' decreasing cognitive capacities. In the eductive process, each player has enough information to simulate perfectly the others' behavior and gets immediately to the equilibrium. In epistemic learning, each player updates his beliefs about others' future strategies, with regard to their sequentially observed actions. In behavioral learning, each player modifies his own strategies according to the observed payoffs obtained from his past actions. In the evolutionary process, each agent has a fixed strategy and reproduces in proportion to the utilities obtained through stochastic interactions. All along the spectrum, longer term dynamics makes up for weaker rationality, and physical relations substitute for mental interactions. Convergence, if any, is towards an always stronger equilibrium notion and selection of an equilibrium state becomes more sensitive to context and history. The processes can be mixed if associated to different periods, agents or mechanisms and deepened if obtained by formal reasoning principles.     

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     

Learning by trial and error

A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is conditional on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium.     

Policy Consequences of Multiple Equilibria and the Indeterminacy of Economic Outcomes in a Boundedly Rational World: Closing the System with Non-Economic Variables1

In the conventional economic wisdom, the notion of unique equilibria that are efficient and Pareto optimal dominates the modeling discourse. Hebert Simon proposed an alternative analytical framework where the notion of multiple and sustainable equilibria is critical. Multiple equilibrium is the crucial stylized fact of economic life that requires better understanding and modeling. Of particular significance, Simon touched on the importance of institutions and differential power relationships in affecting economic outcomes. But this modeling approach was not well developed by Simon. Following from his contributions, further develop the notion of multiple equilibria especially in the realm of production with an emphasis on x-efficiency theory. I bring to bear the importance of institutional parameters (including power relationships), culture, norms, ethics, and moral sentiments to the determination of economic outcomes. In the model developed here, boundedly rational decision-makers’ choices are contextualized and constrained by complex environmental factors. No one choice is either inevitable or economically efficient. A multiplicity of outcomes is possible and sustainable inclusive of those that are suboptimal. Much depends on individual preferences and institutional design. This has significant implication for institutional design and policy.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

Does local and Euro area sentiment matter for sovereign debt markets? Evidence from a bailout country

Does sentiment impact the sovereign debt markets? This article investigates whether lagged domestic and Euro area irrational sentiment (optimism or pessimism unwarranted by fundamentals) predicts future sovereign bond spreads, in Portugal, between January 2000 and December 2013. We find that domestic and Euro area sentiment negatively forecasts total return spreads and that this effect is stronger during the bailout period. Also, we find that the business sentiment is even most noticed. Therefore, Portuguese sovereign debt market is prone to the influence of investors’ sentiment.     

IPO发行价溢价异象与投资者情绪研究

以2003—2011年沪深两市所有A股作为样本进行研究可以发现,IPO发行价与IPO溢价之间存在显著的负相关关系,IPO发行价越低,IPO溢价现象越明显,称之为“发行价溢价异象”。采用受限因变量Tobit模型对投资者结构进行分析又可发现,IPO发行价越低,个人投资者持股比例越高,机构投资者持股比例越低．由此表明,正是由于低发行价股票投资以个人投资者为主,个人投资者易于受到投资者情绪影响,高估股票价值,增加非理性投资需求,寸导致了“发行价溢价异象”产生。     

Noisy Directional Learning and the Logit Equilibrium

We specify a dynamic model in which agents adjust their decisions toward higher payoffs, subject to normal error. This process generates a probability distribution of players’ decisions that evolves over time according to the Fokker–Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studied games. In equilibrium, the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs. This “logit equilibrium” forms a stochastic generalization of the Nash equilibrium and provides a possible explanation of anomalous laboratory data.     

A model of noisy introspection

We present a theoretical model of noisy introspection designed to explain behavior in games played only once. The model determines layers of beliefs about others' beliefs about …, etc., but allows for surprises by relaxing the equilibrium requirement that belief distributions coincide with decision distributions. Noise is injected into iterated conjectures about others' decisions and beliefs, which causes the predictions to differ from those of deterministic models of iterated thinking, e.g., rationalizability. The paper contains a convergence proof that implies existence and uniqueness of the outcome of the iterated thought process. In addition, estimated introspection and noise parameters for data from 37 one-shot matrix games are reported. The accuracy of the model is compared with that of several alternatives.     

Investor sentiment,variance risk premium and delta-hedged gains

Delta-hedged gains are supposed to be negative and represent a volatility risk premium. Using a sample of Standard & Poor 500 index options from 2006 to 2009, this study documents two anomalies that cannot be explained by the volatility risk premium. First, delta-hedged gains are more negative for out-of-money options than for at-the-money options. Second, delta-hedged gains are significantly positive during financial crisis period. We propose a behavioural explanation in which both option prices and stock prices are affected by investor’s sentiment, but pessimistic sentiment has a greater impact on stock market than option market. This asymmetric response to pessimistic mood in turn affects the relative expensiveness of option prices.     

Ricardian equivalence with uninformed consumers?

Empirical studies have shown that the majority of people are poorly informed about the size of government debts and deficits. This paper investigates whether it is nevertheless possible for households to mimic Ricardian behavior on the basis of those variables that they actually observe. In a simple two-period model, it is shown that imperfect information about government debt can lead to departures from Ricardian equivalence even if the households' estimates of debt are unbiased. The paper discusses why households face difficulties in obtaining relevant information about government debt.