Common Knowledge and Consensus with Noisy Communication

Parikh and Krasucki (1990, JET 52) have suggested in an informal manner that a consensus does not require common knowledge. Weyers (1992, CORE DP 9228) has proved that their model does not permit such a conclusion, and that a more general one has to be constructed. Heifetz (1996, JET 70) has given an example with three agents, inspired by computer science works, which illustrates the intuition of the first authors, i.e. where a consensus is obtained without common knowledge of it. We propose a general setting of noisy communication to confirm this result. We show that for any non public and noisy communication, no event can become common knowledge if it was not at the beginning, but that under some assumptions a consensus and arbitrary high levels of interactive knowledge are achievable. A minimal example is given, with two agents and two states. Nevertheless, for public and noisy communication, some results on common knowledge are obtained, depending on the richness of available language. We apply our results to describe some conditions that ensure or prevent epistemic conditions for Nash equilibrium. In general, non public and noisy communication is not sufficient for the conjectures to form, during time, a Nash equilibrium, even if the game and mutual rationality are mutually known. However, with only two agents, or with a noisy and public communication protocol, sufficient conditions are given for the conjectures to form a Nash equilibrium in a finite number of communication periods.

Strategic Knowledge Sharing in Bayesian Games: Applications

This paper studies the properties of endogenous information structures in some classes of Bayesian games in which a first stage of strategic information revelation is added. Sufficient conditions for the existence of perfectly revealing or non-revealing equilibria are characterized. In particular, the existence of a perfectly revealing equilibrium is demonstrated for linear Bayesian games with an ordered information structure. Those games include, for example, Cournot games with incomplete information about the cost or the demand of industry, when firms may face any level of higher-order uncertainty. Several examples and different economic applications are examined to illustrate other results presented in the paper.Strategic information revelation; Bayesian games; Endogenous information structure; Certifiability.

Partial Certifiability and Information Precision in a Cournot Game

This paper examines strategic information revelation in a Cournot duopoly with incomplete information about firm~1\'s cost and information precision. Firm~2 relies on certifiable and ex post submissions of firm~1, without necessarily knowing whether firm~1 knows its cost or not. The sequential equilibria of the induced communication game are determined for different certifiability possibilities. A perfectly cevealing equilibrium in which information precision is irrelevant is obtained under full certifiability. On the contrary, it is shown that if only payoff-relevant (fundamental) events can be certified, then the equilibrium output and profit of firm~1 decreases with its average information precision if this firm is uninformed or if its cost is high. A consequence of this local effect is that information precision has, on average, no value for a firm.Strategic information revelation; Information precision; Cournot competition; Cost uncertainty; Higher order uncertainty.

Multidimensional communication mechanisms: cooperative and conflicting designs

This paper investigates optimal communication mechanisms with a two-dimensional policy space and no monetary transfers. Contrary to the one-dimensional setting, when a single principal controls two activities undertaken by his agent (cooperative design), the optimal communication mechanism never exhibits any pooling and the agent's ideal policies are never chosen. However, when the conflicts of interests between the agent and the principal on each dimension of the agent's activity are close to each other, simpler mechanisms that generalize those optimal in the one-dimensional case perform quite well. These simple mechanisms exhibit much pooling. When each activity of the agent is controlled by a different principal (non-cooperative design) and enters separately into the agent's utility function, optimal mechanisms under private communication take again the form of simple delegation sets, exactly as in the one-dimensional case. When instead the agent finds some benefits in coordinating actions, a one-sided contractual externality arises between principals under private communication. Under public communication instead, there does not exist any pure strategy Nash equilibrium with continuous and piecewise differentiable communication mechanisms. Relaxing the commitment ability of the principals restores equilibrium existence under public communication and yields partitional equilibria. Compared with private communication, public communication generates discipline or subversion effects among principals depending on the profile of their respective biases with respect to the agent's ideal policies.communication ; delegation ; mechanism design ; multi-dimensional decision ; common agency

Tie-breaking Rules and Informational Cascades: A Note

In Bikhchandani, Hirshleifer, and Welch\'s (1992) specific model, it is showed that conformist behaviors can emerge due to information externalities. In this note we establish that this result, based on `informational cascades\', heavily depends on the choice of a particular tie-breaking convention. Relaxing this assumption allows for other equilibria to exist, in which informational cascades are not necessarily observed. Our findings also have implications for the analysis of experimental data on informational cascades. In this respect, we argue that further experiments should be based on other experimental designs.Tie-breaking rules, informational cascades, experimental economics.

Strategic communication networks

In this paper, we consider situations in which individuals want to choose an action close to others' actions as well as close to a payoff relevant state of nature with the ideal proximity to the common state varying across the agents. Before this coordination game with heterogeneous preferences is played, a cheap talk communication stage is offered to players who decide to whom they reveal the private information they hold about the state. The strategic information transmission taking place in the communication stage is characterized by a strategic communication network. We provide a direct link between players' preferences and the strategic communication network emerging at equilibrium, depending on the strength of the coordination motive and the prior information structure. Equilibrium strategic communication networks are characterized in a very tractable way and compared in term of efficiency. In general, a maximal strategic communication network may not exist and communication networks cannot be ordered in the sense of Pareto. However, expected social welfare always increases when the communication network expands. Strategic information transmission can be improved when group or public communication is allowed, and/or when information is certifiable.cheap talk ; coordination ; partially verifiable types ; public and private communication

Multistage communication with and without verifiable types

We survey the main results on strategic information transmission, which is often referred to as ``persuasion" when types are verifiable and as ``cheap talk" when they are not. In the simplest ``cheap talk'' model, an informed player sends a single message to a receiver who makes a decision. The players' utilities depend on the sender's information and the receiver's decision, but not on the sender's message. Furthermore, the messages that are available to the sender do not depend on his true information. As is well-known, such a unilateral ``cheap talk" can affect the sender's decision at equilibrium. In a more general model, both players can exchange simultaneous costless messages during several stages before the final decision. The utility functions are unchanged. Multistage conversation allows the players to reach more equilibrium outcomes, which possibly Pareto dominate the original ones. More precisely, the set of equilibrium outcomes of long cheap talk games is fully characterized; it increases with the number of communication stages and can become even larger if no deadline is imposed. Concentrating on cheap talk is not appropriate if the informed player can influence the decision maker by producing unfalsifiable documents. In order to capture this possibility formally, one assumes that the informed player's set of messages depends on his private information. The literature has mostly dealt with unilateral persuasion. But multistage, bilateral communication enables the players to reach more equilibrium outcomes in the case of verifiable types as in the case of unverifiable ones. Equilibria of long persuasion games are fully characterized when information can be certified at any precision level.Cheap talk; certification; incomplete information; information transmission; jointly controlled lotteries; verifiable types

Strategic Communication Networks

We consider situations in which individuals would like to choose an action which is close to that of others, as well as close to a state of nature, with the ideal proximity to the state varying across agents. Before this coordination game is played, a cheap-talk communication stage is offered to the individuals who decide to whom they reveal their private information about the state. The information transmission occurring in the communication stage is characterized by a strategic communication network. We provide an explicit link between players' preferences and the equilibrium strategic communication networks. A key feature of our equilibrium characterization is that whether communication takes place between two agents not only depends on the conflict of interest between these agents, but also on the number and preferences of the other agents with whom they communicate. Apart from some specific cases, the equilibrium communication networks are quite complex despite our simple one-dimensional description of preference heterogeneity. In general, strategic communication networks cannot be completely Pareto-ranked, but expected social welfare always increases as the communication network expands.Cheap talk ; coordination ; incomplete information ; networks

Using or Hiding Private Information ? An Experimental Study of Zero-Sum Repeated Games with Incomplete Information

This paper studies experimentally the value of private information in strictly competitive interactions with asymmetric information. We implement in the laboratory three examples from the class of zero-sum repeated games with incomplete information on one side and perfect monitoring. The stage games share the same simple structure, but differ markedly on how information should be optimally used once they are repeated. Despite the complexity of the optimal strategies, the empirical value of information coincides with the theoretical prediction in most instances. In particular, it is never negative, it decreases with the number of repetitions, and it is nicely bounded below by the value of the infinitely repeated game and above by the value of the one-shot game. Subjects are unable to completely ignore their information when it is optimal to do so, but the use of information in the lab reacts qualitatively well to the type and length of the game being played.Concavification, laboratory experiments, incomplete information, value of information, zero-sum repeated games.

Communication equilibria with partially verifiable types.

This paper studies the set of equilibria that can be achieved by adding general communication systems to Bayesian games in which some information can be certified or, equivalently, in which players’ types are partially verifiable. Certifiability of information is formalized by a set of available reports for each player that varies with the true state of the world. Given these state-dependent sets of reports, we characterize canonical equilibria for which generalized versions of the revelation principle are valid. Communication equilibria and associated canonical representations are obtained as special cases when no information can be certified.Information privée; Théorie des jeux; Analyse bayésienne;