Computationally restricted unmediated talk under incomplete information

Summary. We show the role of unmediated talk with computational complexity bounds as both an information transmission and a coordination device for the class of two-player games with incomplete information and rational parameters. We prove that any communication equilibrium payoff of such games can be reached as a Bayesian-Nash equilibrium payoff of the game extended by a two phase universal mechanism of interim computationally restricted pre-play communication. The communication protocols are designed with the help of modern cryptographic tools. A familiar context in which our results could be applied is bilateral trading with incomplete information.Received: 9 September 2002, Revised: 14 March 2003, JEL Classification Numbers: C72. Correspondence to: Amparo UrbanoWe wish to thank financial aid from the Valencian Institute of Economic Research (IVIE) and partial support by DIGCYT under project PB95 - 1074. A previous version of this work appears as IVIE Working Paper WP-AD 99-07, under the title: "Unmediated talk under incomplete information".     

Cheap talk in games with incomplete information

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_i of each player i the expected payoff of t_i in q is larger than the expected payoff of t_i in s.     

Fairness, errors and the power of competition

In this paper, we investigate the effects of competition on bargained outcomes. We show that the neglect of either fairness concerns or decision errors will prevent a satisfactory understanding of how competition affects bargaining. We conducted experiments which demonstrate that introducing a small amount of competition to a bilateral ultimatum game – by adding just one competitor – induces large behavioral changes among responders and proposers, causing large changes in accepted offers. Models that assume that all people are self-interested and fully rational do not adequately explain these changes. We show that a model which combines heterogeneous fairness concerns with decision errors correctly predicts the comparative static effects of changes in competition. Moreover, the combined model is remarkably good at predicting the entire distribution of offers in many different competitive situations.     

DISCRETE CHOICE AND RATIONAL INATTENTION: A GENERAL EQUIVALENCE RESULT

This article establishes a general equivalence between discrete choice and rational inattention models. Matějka and McKay (2015) showed that when information costs are modeled using the Shannon entropy, the choice probabilities in the rational inattention (RI) model take the multinomial logit form. We show that, for one given prior over states, RI choice probabilities may take the form of any additive random utility discrete choice model (ARUM) when the information cost is a Bregman information, a class defined in this article. The prior information of the rationally inattentive agent is summarized in a constant vector of utilities in the corresponding ARUM.     

Does risk aversion explain behavior in a lemon market?

Siegenthaler proposes an ingenious solution to the lemon market adverse selection problem. He incorporates ‘‘cheap talk’’ in which sellers send out costless and nonbinding messages informing potential buyers of the quality of their goods; these messages could be true or false. This segments the market into several submarkets. Potential buyers need to decide which submarket to enter and what price to bid for the goods. Sellers then decide whether to accept the bid or not. He experimentally tests his model and finds that the comparative static results align with his theory, although the data do not exactly fit the model. Indeed, he does not fit the model to the data. His theory assumes risk-neutral decision-makers (DMs). Two reasons why the fit is not perfect may be that the DMs are not risk neutral and not perfectly rational. In this note, we report the results of fitting an asymmetric risk averse quantal response equilibrium (QRE) extension of his model to his data, and we find that the extension fits well. We show that the results are consistent with the market evidence and shed light on future research on lemon markets.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

Tacit Coordination in a Decentralized Market Entry Game with Fixed Capacity

We focus on a class of market entry games in which a newly emergent market opportunity may be fruitfully exploited by no more than a commonly known, exogenously determined number of firms. Our results show significant effects of the parameters manipulated in the study, namely, the market capacity, entry fee, and method of subject assignment to groups (fixed vs. random). In contrast to previous market entry games with linear payoff functions, we find no evidence of convergence to equilibrium play on the aggregate level. Shifting the focus of the analysis from the aggregate to the individual level, four clusters of subjects are identified. The patterns are: (1) choice of the same action that is independent of the parameters of the game or the outcome of previous presentations of the same game; (2) random choices with probabilities prescribed by the equilibrium solution for risk-neutral players; (3) random choices with probabilities equal to the individual observed overall proportion of entry; and (4) sequential dependencies that violate any model that assumes randomization. Subjects in the fourth and largest category are shown to adjust their choices in accordance with a simple principle of strategic reasoning.     

One-Shot Public Mediated Talk

We show that any correlation device with rational coefficients can be generated by a mechanism, where each player sends a private message to a mediator who in turn makes a public deterministic announcement. It is then shown that the mechanism can be adapted also to situations with differential information, where the correlation device itself depends on the players' private messages that may vary with their realized types. All the mechanisms suggested are immunized against individual deviations. Therefore, by using them, players can implement any correlated or communication equilibrium.Journal of Economic LiteratureClassification Number: C72.     

Can people learn rational expectations?

In this note the stability of the rational expectations equilibrium for the Foster and Frierman (1990) version of the Blume and Easley (1982) model is investigated under the assumption that the learning mechanism used by economic agents is based on a selection mechanism on a class of competing models having a physical meaning for the agent and not on the interpolation of models having no clear physical meaning, as it is often the case in the literature on learning rational expectations. It is found that, under the standard assumption that the rational expectations model is in the information set of the uninformed trader no matter his degree of rationality, convergence to it is less likely the higher the uninformed agent's degree of rationality, in a sense to be specified in the paper. Some comments on the result are also provided.     

ANTICIPATED UTILITY AND RATIONAL EXPECTATIONS AS APPROXIMATIONS OF BAYESIAN DECISION MAKING*

We study a Markov decision problem with unknown transition probabilities. We compute the exact Bayesian decision rule and compare it with two approximations. The first is an infinite‐history, rational‐expectations approximation that assumes that the decision maker knows the transition probabilities. The second is a version of Kreps' anticipated‐utility model in which decision makers update using Bayes' law but optimize in a way that is myopic with respect to their updating of probabilities. For several consumption‐smoothing examples, the anticipated‐utility approximation outperforms the rational expectations approximation. The rational expectations approximation misrepresents the market price of risk.     

Reputational cheap talk with misunderstanding

We consider a cheap talk game with a sender who has a reputational concern for an ability to predict a state of the world correctly, and where receivers may misunderstand the message sent. When communication between the sender and each receiver is private, we identify an equilibrium in which the sender only discloses the least noisy information. Hence, what determines the amount of information revealed is not the absolute noise level of communication, but the extent to which the noise level may vary. The resulting threshold in transmission noise for which information is revealed may differ across receivers, but is unrelated to the quality of the information channel. When information transmission has to be public, a race to the bottom results: the cut-off level for noise of transmitted information now drops to the lowest cut-off level for any receiver in the audience.     

Communication in games of incomplete information: Two players

We study the effect of communication in two-person games of incomplete information. We show that for any two-player game of incomplete information, any rational mediated communication mechanism outcome (satisfying a Nash domination condition) can be implemented as the perfect Bayesian equilibrium of a cheap-communication extension of the original game.     

Competitive equilibrium hyperinflation under rational expectations

This paper shows that a competitive equilibrium model, where a representative agent maximizes welfare, expectations are rational and markets are in equilibrium can account for several hyperinflation stylized facts. The theory is built by combining two hypotheses, namely, a fiscal crisis that requires printing money to finance an increasing public deficit and a predicted change in an unsustainable fiscal regime.We thank an anonymous referee for very helpful comments. A. B. Cunha acknowledges financial support from the Brazilian Council of Science and Technology (CNPq).     

PROBLEMS IN MODELING COMPLEX DYNAMIC INTERACTIONS: THE POLITICAL REALIGNMENT OF THE 1850s*

This paper argues that a model of sequential choice is superior to the standard rational choice model in explaining a process as complex and dynamic as the political realignment of the 1850s. Part 1 sketches the facts and processes that need to be encompassed by a model and identifies key branching points. Part 2 describes an appropriate model of sequential choice and discusses procedures for estimating transition probabilities and the impact of key variables on these transition probabilities. Part 3 identifies implicit assumptions of rational choice theory that limit its usefulness.     

Macroeconomic equilibrium and welfare under simple monetary and switching fiscal policy rules

Using a standard forward-looking New Keynesian model, this paper investigates rational expectation equilibrium determinacy and macroeconomic performance of simple monetary policy rules under exogenous versus endogenous tax policies when there is tax uncertainty. Under the endogenous tax framework, we found: 1. responding to tax allows monetary policy to have control on the determinacy region, hence higher policy flexibility with respect to the fiscal policy conduct; 2. welfare improvement may come at the expense of cycling. The risk minimizing monetary policy behavior may become problematic since loss function values display huge variations depending on the probabilities given to future tax policy outcomes.     

Finite allocation mechanisms: approximate Walrasian versus approximate Direct Revelation

Summary. This paper obtains finite counterparts of previous results that showed the informational efficiency of the Walrasian mechanism among all mechanisms yielding Pareto-optimal individually rational trades in exchange economies while using a continuum of possible messages. In particular, we develop finite counterparts of the superiority, with respect to message-space dimension, of the Walrasian mechanism over Direct Revelation (DR). We measure a finite mechanism's cost by the number of its (equilibrium) messages. Our two main results are as follows: (1) For exchange economies we find that the overall (maximum) error of a (sufficiently fine) approximate Walrasian mechanism is less than the overall error of a not-more-costly approximate DR mechanism whose equilibrium outcomes are trades that are (approximately) Pareto optimal and individually rational; more generally, approximate Walrasian mechanisms are superior, in the same sense, to approximations of any continuum mechanism whose outcomes are Pareto optimal individ ually rational trades and whose message space has higher dimension than that of the Walrasian mechanism. (2) As we increase without limit the dimension of the set of environments (characteristics) defining our class of exchange economies, the extra cost of DR approximations relative to Walrasian approximations, when both achieve the same overall error, also grows without limit. Thus the informational superiority of the Walrasian mechanism emerges again when we approximate it and take the finite number of messages in the approximation as our cost measure. Received: June 16, 2002; revised version: July 22, 2002 RID="*" ID="*" The second author is grateful for support from National Science Foundation grant #IIS-0118600. Correspondence to: T. Marschak     

Public policies as specification errors

Treating public policies as computable dynamic general equilibrium model specification errors offers computational and conceptional advantages for comparing models with data. The set of policies calculated to rationalize observed behaviors raises the substantive economic question whether, in any particular market, actual public policies sufficiently coincide with the model's behavior-rationalizing policies, or whether the model offers correct hypotheses about the determinants of demand and supply. As illustrations, public policies are calculated to rationalize, with respect to the stochastic neoclassical growth model, capital market behavior since WWII and labor market behavior in 1929–1950. One conclusion is that capital taxation drives a wedge between consumption growth and the expected pre-tax capital return, in the direction and amount predicted by the theory, and that capital taxation is the major intertemporal distortion in the postwar capital market. Second, a good theory of the Great Depression labor market must explain why measured MRS and MPL diverged so dramatically in 1929–1933 and why the wedge persisted.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Shunning uncertainty: The neglect of learning opportunities

Financial, managerial, and medical decisions often involve alternatives whose possible outcomes have uncertain probabilities. In contrast to alternatives whose probabilities are known, these uncertain alternatives offer the benefits of learning. In repeat-choice situations, such learning brings value. If probabilities appear favorable (unfavorable), a choice can be repeated (avoided). In a series of experiments involving bets on the colors of poker chips drawn from bags, decision makers often prove to be blind to the learning opportunities offered by uncertain probabilities. They forgo significant expected payoffs when they shun uncertain alternatives in favor of known ones. Worse, when information is revealed, many make choices contrary to learning. Priming with optimal strategies offers little improvement. Such decision makers violate identified requirements for making rational decisions.     

Preliminary results from a five-sector flow of funds model of the United Kingdom, 1972–77

This paper provides a preliminary report on a five sector twelve asset flow of funds model estimated on monthly data for the period 1972–77. The model follows the general equilibrium approach in including a complete set of asset demands and supplies. It distinguishes between long-run and short-run demands and in some cases between short-run national and effective demands. It allows for variable adjustment speeds and, apart from the five forcing variables which are the sector's net surpluses, it does not contain any shift variables to serve as proxies for private or public behaviour. This report outlines the structure of the model and summarizes the initial parameter estimates. Some simulations are reported for comparison with related models.