Garbling of signals and outcome equivalence

In a game with incomplete information players receive stochastic signals about the state of nature. The distribution of the signals given the state of nature is determined by the information structure. Different information structures may induce different equilibria.Two information structures are equivalent from the perspective of a modeler, if they induce the same equilibrium outcomes. We characterize the situations in which two information structures are equivalent in terms of natural transformations, called garblings, from one structure to another. We study the notion of ‘being equivalent to’ in relation with three equilibrium concepts: Nash equilibrium, agent normal-form correlated equilibrium and the belief invariant Bayesian solution.     

Low information nash equilibria for oligopolistic markets

This paper deals with an infinite horizon n firm oligopoly in which firms are assumed to have incomplete information about one another's actions and profit functions. An equilibrium concept is defined that is similar to the Nash non-cooperative equilibrium, but is suitable for the information assumptions of the model. The equilibrium uses a type of bounded rationality which makes firms' computations relatively easy. This is due to an implicit assumption that computation is costly and a Bayesian approach is prohibitively costly. This low information Nash equilibrium is proved to exist, and, in addition, an adaptive expectations decision process is described which, if followed by all firms, leads to the low information Nash equilibrium.     

Signaling and mediation in games with common interests

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a means of correlation.Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.     

COGNITIVE EMPATHY IN CONFLICT SITUATIONS

Two individuals are involved in a conflict situation in which preferences are ex ante uncertain. Although they eventually learn their own preferences, they have to pay a small cost if they want to secretly learn their opponent's preferences. We show that there is an interval with an upper bound less than 1 and lower bound greater than zero such that, for sufficiently small positive costs of information acquisition, in any Bayesian Nash equilibrium of the resulting game of incomplete information the probability of acquiring information about the opponent's preferences is within this interval.     

On Non-Nash Equilibria

I consider generalisations of the Nash equilibrium concept based on the idea that in equilibrium the players' beliefs should not be contradicted, even if they could possibly be incorrect. This possibility depends on the information about opponents' behaviour available to the players in equilibrium. Therefore the players' information is crucial for this notion of equilibrium, called Conjectural Equilibrium in general and Rationalizable Conjectural Equilibrium (Rubinstein-Wolinsky 1994) when the game and the players' Bayesian rationality are common knowledge. In this paper I argue for a refinement of Rationalizable Conjectural Equilibrium showing by propositions and by examples how this equilibrium notion works and how the suitable equilibrium concept depends on the players' information.Journal of Economic LiteratureClassification Numbers: C72, D83, D82.     

Incentives and incomplete information

The problem of incentives for correct revelation in a collective decision model is presented as a game with incomplete information. Two approaches to incomplete information are used, a first where the individual beliefs are not introduced and a second where they are. In the first approach it is recalled that the mechanisms for which the solution to the incentive problem is in dominant strategies lead in general to a budgetary problem for the central agency. For these mechanisms a uniqueness property is demonstrated. In the second approach it is shown that if a compatibility condition is imposed on the individual beliefs and if a Bayesian solution is given to the incentive problem, then it is possible to avoid the budgetary problem.     

Reciprocal relationships and mechanism design

We study an incomplete information game in which players can coordinate their actions by contracting among themselves. We model this relationship as a reciprocal contracting procedure where each player has the ability to make commitments contingent on the other players' commitments. We differ from the rest of the literature on reciprocal contracting by assuming that punishments cannot be enforced in the event that cooperation breaks down. We fully characterize the outcomes that can be supported as perfect Bayesian equilibrium outcomes in such an environment. We use our characterization to show that the set of supportable outcomes with reciprocal contracting is larger than the set of outcomes available in a centralized mechanism design environment in which the mechanism designer is constrained by his inability to enforce punishments against non‐participants. The difference stems from the players' ability in our contracting game to convey partial information about their types at the time they offer contracts. We discuss the implications of our analysis for modelling collusion between multiple agents interacting with the same principal.     

Fishermen's Discount Rates in ITQ Systems

In this paper the fishermen's planning and investment horizon is investigated using their discount rates. It is shown that one might calculate the implicit discount rate in an ITQ regulated fishery from the available information from the quota market. This gives information about how well the system is working. In particular, discount rates where ITQ systems are in operation initially were very high, before they started to decrease. This implies that it take some time to reap the full benefits of an ITQ system. It also gives arguments for not letting ITQs be perpetual property rights, and hence, enables more flexibility in the management system.     

Inefficient policies and incumbency advantage

We present a model of (re)elections in which an incumbency advantage arises because the incumbent can manipulate issue salience by choosing inefficient policies in the policy dimension in which he is the stronger candidate. The voters are uncertain about the state of the world and the incumbent's choice of policy. Under complete information they would reelect the incumbent if and only if the state is sufficiently high. Undesirable policy outcomes may be due to either a bad state or the incumbent's choice of inefficient policies. The incumbent uses inefficient policies in intermediate states, whereby he creates uncertainty about the true state in such a way that voters are better off in expectation reelecting him. Hence the equilibrium exhibits an incumbency advantage that stems from asymmetric information and the use of inefficient policies.     

Forecasting Time Series Subject to Multiple Structural Breaks

This paper provides a new approach to forecasting time series that are subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks occurring over the forecast horizon, taking account of the size and duration of past breaks (if any) by means of a hierarchical hidden Markov chain model. Predictions are formed by integrating over the parameters from the meta-distribution that characterizes the stochastic break-point process. In an application to U.S. Treasury bill rates, we find that the method leads to better out-of-sample forecasts than a range of alternative methods.     

The veil of public ignorance

A theory of cooperative choice under incomplete information is developed in which agents possess private information at the time of contracting and have agreed on a utilitarian “standard of evaluation” governing choices under complete information. The task is to extend this standard to situations of incomplete information. Our first main result generalizes Harsanyi's (J. Polit. Econ. 63 (1955) 309) classical result to situations of incomplete information, assuming that group preferences satisfy Bayesian Coherence and Interim Pareto Dominance. These axioms are mutually compatible if and only if a common prior exists. We argue that this result partly resolves the impossibility of Bayesian preference aggregation under complete information.     

A General Approach to Rational Learning in Games

This paper provides a general framework for analysing rational learning in strategic situations in which the players have private priors and private information. The author analyses the behaviour of Bayesian rational players both in a repeated game and in a recurrent game when they are uncertain about opponents' behaviour and the game they are playing. The aim of the paper is to explain how Bayesian rational agents learn by playing and to characterize the outcome of this learning process. By studying the concept of 'conjectural equilibrium' and analysing the process of convergence of players' behaviour, the roles played by the notions of merging and of consistency are demonstrated.     

Learning Under Ambiguity

This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extreme—it models agents who are implausibly ambitious about what they can learn in complicated environments. The paper then provides a generalization of the Bayesian model that accommodates the intuitive choices in the thought experiments. In particular, the model allows decision-makers' confidence about the environment to change—along with beliefs—as they learn. A portfolio choice application compares the effect of changes in confidence under ambiguity vs. changes in estimation risk under Bayesian learning. The former is shown to induce a trend towards more stock market participation and investment even when the latter does not.     

Information Sharing and Cooperative Search in Fisheries

We present a dynamic game of search and learning about the productivity of competing fishing locations. Perfect Bayesian Nash equilibrium search patterns for non-cooperating fishermen and members of an information sharing cooperative are compared with first-best outcomes. Independent fishermen do not internalize the full value of information, and do not replicate first-best search. A fishing cooperative faces a free-riding problem, as each coop member prefers that other members undertake costly search for information. Pooling contracts among coop members may mitigate, but are not likely to eliminate free-riding. Our results explain the paucity of information sharing in fisheries and suggest regulators use caution in advocating cooperatives as a solution to common pool inefficiencies in fisheries.     

The Ramsey Discounting Formula for a Hidden-State Stochastic Growth Process

The long term discount rate is critically dependent upon projections of future growth rates that are fuzzier in proportion to the remoteness of the time horizon. This paper models such increasing fuzziness as an evolving hidden-state stochastic process. The underlying trend growth rate is an unobservable random walk hidden by noisy transitory shocks and recoverable only as a probability distribution via Bayesian updating. A simple expression is derived for the time-declining Ramsey discount rate. The components of this hidden-state Ramsey discounting formula are then analyzed, followed by a few remarks about possible implications and applications.     

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.     

Collective decisions with interdependent valuations

Many collective decision problems have in common that individuals’ desired outcomes are correlated but not identical. This paper studies collective decisions with private information about desired policies. Each agent holds private information which mainly concerns his own bliss point, but private information also affects all other agents. We concentrate on two specific mechanism, the median and mean mechanisms establish the existence of symmetric Bayesian Nash equilibria of the corresponding games and compare the performance of the mechanisms for different degrees of interdependencies. Applications of our framework include the provision of public goods and the design of decision processes in international organizations.     

Robust implementation in general mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.     

Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate

Consider a decentralized, dynamic market with an infinite horizon and incomplete information in which buyers and sellers' values for the traded good are private and independently drawn. Time is discrete, each period has length δ, and each unit of time a large number of new buyers and sellers enter the market. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, the seller and winning buyer exit with their realized utility. Traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate. We show that in all steady state, perfect Bayesian equilibria, as δ approaches zero, equilibrium prices converge to the Walrasian price and realized allocations converge to the competitive allocation.     

Measuring the Impact of Asymmetric Information: An Example from Energy Conservation

Asymmetric information has occupied a central role in theoretical microeconomics for almost two decades, but little has been done to ascertain when it matters in practice. The regulatory problem of promoting energy conservation offers an opportunity to ascertain if asymmetric information mattered and to what extent it altered outcomes. Regulators encouraged utilities to promote conservation, and while the regulators could observe conservation prices, they could not observe utilities' promotional efforts. A theoretical model of the regulatory asymmetric information problem yields propositions about the levels of conservation, prices and utility effort, and simulations with realistic parameters are used to determine asymmetric information's impact on these levels.