Persuasion Games with Higher Order Uncertainty

In persuasion games, it is well known that a perfectly revealing equilibrium may fail to exist when the decision maker is uncertain about the interested party\'s payoff-relevant information. However, by explicitly integrating higher order uncertainty into the information structure, this paper shows that a perfectly revealing equilibrium does exist when disclosures are not restrained to intervals of the payoff-relevant state space. On the contrary, when payoff-irrelevant disclosures are impossible, a perfectly revealing equilibrium fails to exist as long as there is a strictly positive probability that the decision maker does not know whether the interested party is informed or not. In this case, a partially revealing equilibrium and associated inferences are characterized.Strategic information revelation; Persuasion games; Higher order uncertainty; Provability

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.

Common Knowledge and Interactive Behaviors: A Survey

This paper surveys the notion of common knowledge taken from game theory and computer science. It studies and illustrates more generally the effects of interactive knowledge in economic and social problems. First of all, common knowledge is shown to be a central concept and often a necessary condition for coordination, equilibrium achievement, agreement, and consensus. We present how common knowledge can be practically generated, for example, by particular advertisements or leadership. Secondly, we prove that common knowledge can be harmful, essentially in various cooperation and negotiation problems, and more generally when there are con icts of interest. Finally, in some asymmetric relationships, common knowledge is shown to be preferable for some players, but not for all. The ambiguous welfare effects of higher-order knowledge on interactive behaviors leads us to analyze the role of decentralized communication in order to deal with dynamic or endogenous information structures.Interactive knowledge, common knowledge, information structure, communication.

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.

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.

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

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.