Mindreading and endogenous beliefs in games

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs.     

Gurus and belief manipulation

We analyze a model with two types of agents: standard agents and gurus, i.e. agents who have the ability to influence the other investors. Gurus announce their beliefs and act accordingly. Gurus are strategic: they take into account the impact of their announced beliefs on the other agents, hence on prices. Standard agents observe gurus' performances, choose a guru and follow her/his recommendations. Prices are determined through a classical Walras mechanism. The competition among gurus for attracting followers among standard agents is governed by the level of accuracy of their predictions. The strategic behavior leads to belief subjectivity and heterogeneity among the gurus even when gurus' initial beliefs coincide with the objective belief. Optimism as well as pessimism can both emerge. We find a positive correlation across the agents between pessimism and risk tolerance. The representative agent belief, or the consensus belief is pessimistic. As a consequence of the pessimistic bias at the aggregate level, the risk premium is greater than in the standard rational expectations equilibrium. We show on an example that this impact is significative. In a multi-asset framework, the impact is stronger on the riskier assets.     

An Equilibrium Approach to the Aggregation of Beliefs

This paper presents a new answer to the old question of how to aggregate individual beliefs. We construct a model which allows agents to take arbitrage opportunities against the aggregated belief by making contingent claims against the states, and the aggregator (market maker) regulates the probability of states. When all claims from the agents are mutually covered for every realization of the state, an aggregation of individual beliefs is thus obtained. We prove the existence and uniqueness of the equilibrium aggregation, and also show that the aggregate belief lies in the convex hull of individual beliefs. This model allows us to address some important problems such as how individual agent’s attitude toward risk and wealth endowment affect the outcome of the aggregation process, and whether the aggregate belief satisfies the well-known properties like equal treatment.     

How does the diversity of investors’ beliefs affect stock price informativeness?

A growing number of studies have investigated the role of stock prices in aggregating private information and guiding resource reallocation. However, this article may be the first attempt to study how the diversity of beliefs affects stock price informativeness. The framework of the noisy rational expectations model shows that stock informativeness is determined by both the precision and use of private information in trading. If private beliefs about the value are highly diverse, the aggregate average opinion revealed in a stock’s price will be more accurate and, thus, more informative. As the price becomes more informative, however, individual investors will rely less on their private information. When this occurs, less private information will be absorbed in price, which, in turn, reduces price informativeness. Our model shows that the relationship between belief diversity and price informativeness is U-shaped in equilibrium.     

Resolving Indeterminacy in Coordination Games: A New Approach Applied to a Pay-as-you-go Pension Scheme

This paper shows that when players ignore what outcome will emerge because of the presence of multiple equilibria, they can coordinate their expectations by forming an initial belief based on the principle of indifference followed by a process of reasoning that updates this belief. Since this procedure describes a natural way to form beliefs under indeterminacy, it is reasonable for every agent to conjecture that all the others form their beliefs according to the same logic. Exactly the fact that agents are aware that they form their beliefs following the same procedure allows them to successfully coordinate their expectations.      

Utility from anticipation and personal equilibrium

I develop a dynamic model of individual decisionmaking in which the agent derives utility from physical outcomes as well as from rational beliefs about physical outcomes (“anticipation”), and these two payoff components can interact. Beliefs and behavior are jointly determined in a personal equilibrium by the requirement that behavior given past beliefs must be consistent with those beliefs. I explore three phenomena made possible by utility from anticipation, and prove that if the decisionmaker’s behavior is distinguishable from a person’s who cares only about physical outcomes, she must exhibit at least one of these phenomena. First, the decisionmaker can be prone to self-fulfilling expectations. Second, she might be time-inconsistent even if her preferences in all periods are identical. Third, she might exhibit informational preferences, where these preferences are intimately connected to her attitudes toward disappointments. Applications of the framework to reference-dependent preferences, impulsive behaviors, and emotionally difficult choices are discussed.     

Belief in Mean Reversion and the Disposition Effect: An Experimental Test

The disposition effect refers to investors' tendency to disproportionately sell more winning than losing assets. The literature mostly offered indirect evidence regarding its cause. Using a lab experiment, the author directly evaluates the two competing behavioral mechanisms for this effect: belief in mean reversion and dual risk attitudes of prospect theory. The participants were endowed with some hypothetical assets, observed price charts, and made selling decisions. Sixty-one percent of them exhibited significant disposition effect. The author elicited the participants' risk attitude parameters and beliefs about price movements, and found that beliefs, especially those in the loss domain, but not the dual risk attitudes, significantly contributed to the between-subject variation of the disposition effect. The results from a goodness-of-fit test also favor the belief mechanism.     

Random belief equilibrium in normal form games

In defining random belief equilibrium (RBE) in finite, normal form games we assume a player's beliefs about others' strategy choices are randomly drawn from a belief distribution that is dispersed around a central strategy profile, the focus. At an RBE: (1) Each chooses a best response relative to her beliefs. (2) Each player's expected choice coincides with the focus of the other players' belief distributions. RBE provides a statistical framework for estimation which we apply to data from three experimental games. We also characterize the limit-RBE as players' beliefs converge to certainty. When atoms in the belief distributions vanish in the limit, not all limit-RBE (called robust equilibria) are trembling hand perfect Nash equilibria and not all perfect equilibria are robust.     

Are more risk averse agents more optimistic? Insights from a rational expectations model

We analyse a model of partially revealing, rational expectations equilibrium with diverse information, endogenous beliefs formation and uncertain distribution of risk aversion. More risk averse agents are then more optimistic. Such a positive correlation is important for collective decision analysis.     

DOES NEAR‐RATIONALITY MATTER IN FIRST‐ORDER APPROXIMATE SOLUTIONS? A PERTURBATION APPROACH

This paper studies first‐order approximate solutions to near‐rational dynamic equilibrium models. Under near‐rationality, agents' subjective beliefs are distorted away from rational expectations via a change of measure process which fulfills some regularity conditions. In most applications, the beliefs distortion process is also directly observed by (a subset of) the decision‐makers – e.g., ambiguity‐averse households or policy‐makers with a concern for robustness – and therefore included into their optimization problems. We investigate conditions for existence and local uniqueness of solutions under endogenous distortions, as well as the relation with their rational expectations counterparts. We show that linearly perturbed solutions may well be affected by the presence of distorted beliefs, depending on the underlying model economy. In particular, while directly affecting first‐order decision rules, near‐rationality may also induce failure of the certainty equivalence principle. Moreover, the martingale representation of distorted beliefs might prove non‐unique, pointing to a subtle form of equilibrium indeterminacy.     

The Risk Premium, Exchange Rate Expectations, and the Forward Exchange Rate: Estimates for the Yen–Dollar Rate

The hypothesis that the forward rate is an unbiased predictor of the future spot rate has been rejected in many empirical studies. The rejection of this hypothesis could occur because market behavior is inconsistent with rational–expectations or because there exists a risk premium. Equations describing the forward premium and the change in the exchange rate are estimated jointly, and tests of both the rational–expectations and no–risk–premium hypotheses are conducted. Empirical estimates, obtained using quarterly data for the yen–dollar exchange rate, reject the rational–expectations hypothesis and suggest that there exists a time–varying risk premium.     

Does the Lucas critique apply during hyperinflation?: empirical evidence from four hyperinflationary episodes

Farmer (Review of Economic Studies, 58, 321–32, 1991) suggests that in a model in which there are multiple rational expectations equilibria agents may find it useful to coordinate their expectations in a unique rational expectations equilibrium which is supported by a self-fulfilling forecast rule having the property of being immune to the Lucas Critique. In this paper, Farmer's hypothesis is tested using data from hyperinflationary episodes. It is believed that those episodes are suitable for testing this hypothesis because an agent who lives in a hyperinflationary environment usually faces frequent changes in policy regime. The agent may thus choose a selffulfilling forecast rule which is immune to the Lucas Critique as a way of hedging against unanticipated policy regime switches. The empirical results show mixed evidence on Farmer's hypothesis during the hyperinflationary episodes studied.     

Tests of real interest parity in international currency markets

The purpose of this paper is to examine the behavior of real bilateral exchange rates for major currencies and test the hypothesis of real uncovered interest parity with risk premia, and forward looking expectations. It is plausible that the hypothesis of rational expectations cannot be rejected given the unit root nonstationarity of real exchange rates but it is not unlikely that unit root nonstationarity may be due to rational expectations in foreign exchange markets.     

Rationalizability, Strong Rationality, and Expectational Stability

We examine the connection between two stability concepts of rational expectations equilibria: expectational stability, based on the convergence of iterations of expectations, and strong rationality, based on uniqueness of the rationalizable solutions of an associated game with restrictions on beliefs. To compare the concepts we embed a standard expectations model in a game-theoretic framework. It is shown that the two stability concepts coincide when agents are homogeneous. For the general case of heterogeneous agents we show that expectational stability is a necessary condition for strong rationality and we provide a sufficient condition for the latter. Journal of Economic Literature Classification Numbers: C72, C62.     

Dominated choices in a simple game with large stakes

This paper examines data from the Norwegian television game show Joker, where contestants make well-specified choices under risk. The game involves very large stakes, randomly drawn contestants, and ample opportunities for learning. Central models of risk choice, including expected utility theory, give a simple prediction of choice under weak conditions, as one decision is always first-order stochastically dominating. We document frequent, systematic and costly violations of dominance. Many contestants appear to have a systematic expectation bias that can be related to Tversky and Kahneman’s (Cogn. Psychol. 5(2):207–232, 1973) “availability heuristic”. In addition, contestants seem to make systematic calculation errors that are well captured by the so-called Fechner model.     

Stated Beliefs and Play in Normal-Form Games

Using data on one-shot games, we investigate whether players' actions can be viewed as responses to underlying expectations about their opponent's behaviour. In our laboratory experiments, subjects play a set of 14 two-person 3×3 games and state beliefs about which actions they expect their opponents to play. The data sets from the two tasks are largely inconsistent. Rather, we find evidence that the subjects perceive the games differently when they (i) choose actions and (ii) state beliefs—their stated beliefs reveal deeper strategic thinking than their actions. On average, they fail to best respond to their own stated beliefs in almost half of the games. The inconsistency is confirmed by estimates of a unified statistical model that jointly uses the actions and the belief statements. There, we can control for decision noise and formulate a statistical test that rejects consistency. Effects of the belief elicitation procedure on subsequent actions are mostly insignificant.     

The effect of heterogeneous beliefs on mergers and acquisitions

This article investigates the effect of heterogeneous beliefs on firms’ mergers and acquisitions (M&A) decisions. Using data of China’s financial market, which is featured with great heterogeneity of belief, we find that heterogeneous beliefs are positively associated with the occurrence of M&A transactions, and firms with greater heterogeneous beliefs are more likely to pay the transactions with stock. Moreover, we show that government intervention, measured by state ownership, weakens the effect of heterogeneous beliefs on firms’ M&A decisions.     

Efficient allocations under ambiguity

Important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief, then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the consumption plans are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications.     

Money demand, the Cagan model, testing rational expectations vs adaptive expectations: The case of Turkey

This paper estimates the Cagan type demand for money function for Turkish economy during the period 1986:1–1995:3 and tests whether Cagan's specification fits the Turkish data using an econometric technique assuming that forecasting errors are stationary. This paper also tests the hypothesis that monetary policy was implemented in aiming to maximize the inflation tax revenue. Finally, the Cagan model is estimated with the additional assumption of rational expectations for Turkey for the considered period. First version received: March 1998/final version received: October 1998     

Rational expectations and monopolistic trades

We argue that the use of rational expectations in monopolistic markets, as typically done, is overly restrictive because the rationale of this approach is not met in those markets. In a model that encompasses a general equilibrium framework, we consider a monopolist (a producer) with subjective beliefs that endogenously hedges against fluctuations in input prices in a complete market. We introduce a notion of entropy of beliefs, and we characterize long-run optimal rational investments with this entropy. For irrational beliefs, we show that long-run profits are a decreasing function of this entropy. However, long-run profits always remain positive as long as the entropy remains finite despite the Market Selection Hypothesis that would predict long-run 0-profit.