Signaling in Social Interactions:
a Multidisciplinary Approach

8-9 June 2022


Andreas Blume (University of Arizona): Meaning in Communication Games

This paper addresses two related questions: How can we model the strategic use of a pre-existing language? And, how should we capture different degrees of sharing that language? The paper proposes an iterative procedure, interpreted as a mental process on part of the sender, that associates a set of equilibria, which we dub language equilibria, with every combination of a sender-receiver game and a pre-existing language. Every sender-receiver game has a language equilibrium. Language equilibrium makes sharp predictions about joint distributions over types and actions in common-interest games, in games with sender-preferred equilibria, and in games with partial incentive alignment. This is the case when, as is frequently assumed, the language is rich, but also when the language is impoverished. Predictions are sensitive to the degree to which language is shared. Importantly, unlike earlier suggestions for how to invoke the role of a preexisting language in sender-receiver games, language equilibrium makes predictions about language use.

Alessandro Bonatti (MIT Sloan): Data, Platforms, and Competition

We propose a comprehensive model of digital commerce in which data and heterogeneity are defining features. A digital platform matches consumers and advertisers online. Each consumer has heterogenous preferences for each advertiser's brand, and the advertisers can tailor their product lines to the preferences of the consumer. Consumers can access each seller's products online or offline. The digital platform can improve the quality of the match through its data collection, and monetizes its data by selling digital advertising space to sellers.

We derive the equilibrium surplus sharing between consumer, advertisers, and the digital platform. We evaluate how different data-governance rules affect the creation and distribution of the surplus. We contrast the unrestricted use of data with contextual and cohort-restricted uses of data. We show that privacy-enhancing data-governance rules, such as those corresponding to federated learning, can increase competition among the advertisers and lead to welfare for the digital platform and for consumers.

Paul Egré and Benjamin Spector (Ecole Normale Superieure, with Adèle Mortier and Steven Verheyen): On the Optimality of Vagueness: "Around," "Between," and the Gricean Maxims

Why is ordinary language vague? We argue that in contexts in which a cooperative speaker is not perfectly informed about the world, the use of vague expressions can offer an optimal tradeoff between truthfulness (Gricean Quality) and informativeness (Gricean Quantity). Focusing on expressions of approximation such as "around", which are semantically vague, we show that they allow the speaker to convey indirect probabilistic information, in a way that can give the listener a more accurate representation of the information available to the speaker than any more precise expression would (intervals of the form "between"). That is, vague sentences can be more informative than their precise counterparts. We give a probabilistic treatment of the interpretation of "around", and offer a model for the interpretation and use of "around"-statements within the Rational Speech Act (RSA) framework. In our account the shape of the speaker's distribution matters in ways not predicted by the Lexical Uncertainty model standardly used in the RSA framework for vague predicates. We use our approach to draw further lessons concerning the semantic flexibility of vague expressions and their irreducibility to more precise meanings.

Sidartha Gordon (Paris Dauphine University, with Georg Nöldeke): Figures of Speech and Informative Communication

We study a communication game in which the sender has a conflict of interest with the receiver, who may be sophisticated (Bayesian) or naïve, in the sense that he interprets messages in a literal way. The receiver's naïveté makes distorting the truth risky for the receiver. The sender is also constrained by the inherent vagueness of the language she shares with the receiver. In equilibrium, the trade-off is resolved in an endogenous truth-distorting figure of speech (irony, exaggeration, understatement), which the sophisticated receiver is able to interpret. There can be multiple equilibria, unambiguously ranked in their informativeness. We characterize circumstances promoting the emergence and stability of particular figures of speech and obtain a number of comparative statics results. In particular, we find that a receiver may prefer a sender who is more dissimilar to him.

Olivier Gossner (Ecole Polytechnique, LSE): Rationalizable Outcomes in Games with Incomplete Information


Michael Greinecker (University of Graz, with Martin Meier and Konrad Podczeck): Sequential Equilibria in a Class of Infinite Extensive Form Games

Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form but is only defined for finite extensive-form games and is inapplicable whenever a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of a sequential equilibrium.

Takakazu Honryo (Doshisha University): Delegation in Teams

This paper considers the delegation of a decision to a team of informed agents and investigates whom to delegate the decision-making right. It shows that a trade-off arises between 1) improved communication within the team when an agent’s preference with the decision-making rights is closer to the average preference among other agents and 2) the cost from distorted decisions due to biased and misaligned preferences from the principal. In general, 1) gains importance as the size of the team increases.

Marie Laclau (HEC Paris, with Ludovic Renou and Xavier Venel): Communication on Networks and Strong Reliability

We consider sender-receiver games, where the sender and the receiver are two distant nodes on a communication network. We show that if the network has two disjoint paths of communication between the sender and the receiver, then we can replicate not only all equilibrium outcomes of the direct communication game (i.e., when the sender and the receiver communicate directly with each other), but also of the mediated game (i.e., when the sender and the receiver communicate with the help of a mediator).

Marcin Pęski (University of Toronto): Bargaining with Mechanisms

Two players bargain over a single indivisible good and a transfer, with one-sided incomplete information about preferences. Both players can offer arbitrary mechanisms to determine the allocation. We show that there is a unique perfect Bayesian equilibrium outcome. In the equilibrium, one of the players proposes a menu that is optimal for the uninformed player among all menus, such that each type of the informed player receives at least her payoff under complete information. The optimal menu can be implemented with at most three allocations. Under a natural assumption on the uninformed player’s beliefs, the optimal menu coincides with Myerson’s neutral solution to the bargaining problem in this environment.

Jérôme Renault (Toulouse School of Economics, with Eilon Solan and Nicolas Vielle): Strategic Experimentation with Private Payoffs


Karl Sigmund (University of Vienna, with Hannelore De Silva): Adaptive Dynamics for Signaling Games

Signaling games are used to investigate basic, nonverbal ways of conveying information. If the interests of senders and receivers are in conflict, this information is apt to be unreliable. We apply a single minimalistic framework to examples of frequently studied interactions, such as costly advertisements, ownership claims, and signals for help. We analyze their evolution within populations with the help of adaptive dynamics, a basic tool of evolutionary game theory describing a trial-and-error adjustment process. This new approach to signaling is particularly appropriate for investigating oscillations around partially revealing equilibria, communication failures, and paradoxical outcomes.

Dimitrios Xefteris (University of Cyprus): Information Aggregation by Councils

We consider a society of truth-seeking, yet, imperfectly and privately informed individuals who face a binary collective issue, and compare the informational efficiency of a council (i.e. a small deliberative body with the power to decide) to that of an electorate (i.e. a large non-deliberative body deciding by majority). We find that when an electorate aggregates information better than a council, it does so only slightly; while when a council aggregates information better than an electorate, the difference can be prodigious. This provides a novel rationale as to why most collective entities delegate decisions to councils rather than electorates.