Workshop on Signaling in Markets, Auctions and Games:
a Multidisciplinary Approach

22-23 May 2019


Heather Burnett (Paris Diderot University): Signaling Games, Sociolinguistic Variation and the Construction of Style

In this presentation, I develop a formal model of the subtle meaning differences that exist between grammatical alternatives in socially conditioned variation (called variants) and how these variants can be used by speakers as resources for constructing personal linguistic styles. More specifically, this paper introduces a new formal system, called social meaning games (SMGs), which allows for the unification of variationist sociolinguistics and game-theoretic pragmatics, two fields that have had very little interaction in the past. Although remarks have been made concerning the possible usefulness of game-theoretic tools in the analysis of certain kinds of socially conditioned linguistic phenomena (Goffman, 1961, 1967, 1970; Bourdieu, 1977; Dror et al., 2013, 2014; Clark, 2014, among others), a general framework uniting game-theoretic pragmatics and quantitative sociolinguistics has yet to be developed. This paper constructs such a framework through giving a formalization of the Third Wave approach to the meaning of variation (see Eckert (2012) for an overview) using signalling games (Lewis, 1969) and a probabilistic approach to speaker/listener beliefs of the kind commonly used in the Bayesian game-theoretic pragmatics framework (see Goodman and Lassiter, 2014; Franke and Jäger, 2016, for recent overviews).

Francesc Dilme (Unviersity of Bonn): Skewed Information Transmission

This paper analyzes strategic information transition between skewed agents. More concretely, we study Crawford and Sobel's (1982) setting in which agents are not biased, but they differ on the relative importance they put on avoiding ''upward'' or ''downward'' mistakes. We show that even though agents can fully communicate when the state of the world is perfectly observed by the sender, their communication is significantly imprecise when there is an arbitrary small noise in the observation. Hence, contrary to what was previously thought, a small objective misalignment is not a sufficient condition for the existence of equilibria with precise information transmission. We illustrate the results through some applications.

Françoise Forges (Paris Dauphine Univesity, with Jérôme Renault): Strategic Information Transmission with Sender's Approval

- We consider a sender-receiver game in which the sender has a finite set of types, the receiver makes a decision in a compact convex set X and the (typically type- dependent) utility functions are continuous. We assume that, after the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject in favor of an outside option, and that the sender's approval is crucial to the receiver. We ask whether the game has a perfect Bayesian equilibrium (PBE).
- We construct a counter-example (with three types for the sender and type-dependent affine utility functions) in which there is no PBE, but there is a communication equilibrium.
- We show that a PBE in pure strategies exists if either (i) the sender only has two types or (ii) the receiver’s utility function does not depend on the sender’s type or (iii) the decision set X is a real interval and the sender’s utility function is monotonic, whatever his type or (iv) the decision set X is a real interval and the utility function have a standard quadratic form.
- We show that a communication equilibrium always exists when the sender has three types and the utility functions are affine.

Francesco Giovannoni (University of Bristol, with Miltiadis Makris): Auctions with External Incentives: Experimental Evidence

We consider auctions where bidders' valuations are positively correlated with their productivity in a second-stage aftermarket as in Giovannoni and Makris (2014). We test whether bidders recognize the incentives to signal their productivity through their bidding and, conditional on them doing so, whether disclosing different information about the auction further affects this behavior. Our results confirm that bidder recognize the signaling incentives they face and also react to differences in the way their bidding behavior is disclosed, although not always in a way that is consistent with theoretical predictions.

Josef Hofbauer (University of Vienna, with Christina Pawlowitsch): Evolutionary Dynamics of Costly Signaling Games

We study 5 classes of discrete costly-signaling games. We compute the index of the resulting equilibrium components and use it as a tool for equilibrium refinement. Furthermore, we study the replicator dynamics and the best response dynamics, in particular the question whether all solutions converge to equilibria.

Sander Onderstal (University of Amsterdam, with Olivier Bos, Francisco Gomez-Martinez and Tom Truyts): Signalling in Auctions: Experimental Evidence

We study the relative performance of the first-price sealed-bid auction and the second-price sealed-bid auction in a laboratory experiment where bidders can signal information through their bidding behaviour to an outside observer. We consider two different information settings: the auctioneer reveals either the identity of the winning bidder only, or she also reveals the winner’s payment to an outside observer. We find that the first-price sealed-bid auction in which the winner’s payment is revealed outperforms the other mechanisms in terms of revenue and efficiency. Our findings may have implications for the design of charity auctions, art auctions, and spectrum auctions.

Christina Pawlowitsch (Panthéon-Assas University): The Logic of Empty Forms

What is meaning-making in a costly-signaling game? What shall we do if multiplicity of equilibria persists notwithstanding refinements? Does this limit the explanatory potential of such models? I am going to address this and other questions related to applications of costly-signaling games.

Martin Pollrich (University of Bonn, with Olivier Bos, Nicolas Fugger, Vitali Gretschko and Tom Truyts): Mechanism Design with Signaling Agents

This presentation introduces mechanism design problems where agents care about the inference of outsiders. Agents derive utility from the alternative selected within the mechanism, and from the decisions taken by an outsider. The latter decisions depend on the outsider's beliefs about the agents' types. Upon devising a mechanism the designer takes into account the signaling motives of its agents. I outline a general setting encompassing most existing models and highlight the role of implicit assumptions on the designers ability to directly or indirectly communicate with outsiders through the mechanism. In two applications of auction design we illustrate how the presence of signaling concerns affect the optimal design of auctions.

Joel Sobel (University of California San Diego): Functional Language in Games

Game theoretic models of communication identify conditions under which strategic agents can use costless messages to exchange information. In the stylized models of communication, messages have no intrinsic meaning and so there is no necessary relationship between natural language and the way that players interpret messages within a game. I make the simple observation that these stylized models make it impossible to distinguish between different functions of language. I then propose ways in which one can distinguish between referential and conative functions and suggest criteria that predict when communication comes in the form of informational statements or commands.

Nora Szech (Karlsruhe Institute of Technology, with Thomas Mariotti, Nikolaus Schweizer and Jonas von Wangenheim): Information Nudges and Self-Control

We study the optimal design of information nudges for present-biased consumers who have to make sequential consumption decisions without exact prior knowledge of their long-term consequences. For arbitrary distributions of risk, there exists a consumer-optimal information nudge that is of cutoff type, recommending consumption or abstinence according to the magnitude of the risk. Under a stronger bias for the present, the target group receiving a credible signal to abstain must be tightened. We compare this nudge with those favored by a health authority or a lobbyist. When some consumers are more strongly present-biased than others, a traffic-light nudge is optimal.

Minus van Baalen (Ecole Normale Supérieure): On the Ecological and Evolutionary Feedbacks that Affect the Cost and Value of Information: the Evolution of Signals, Information Exchange, and Memes

In many cases the 'costs' of information transfer are quite low in terms of energy or biomass involved, but result more from behavioural, ecological or even evolutionary feedback processes. In my talk I will discuss the evolution of information transfer (communication sensu lato) within and between species, and what mechanisms may create but also erode information content. Information is not an objective quantity but results in the end from a complex interaction between potentially multiple signal producers and interpreters.

Robert van Rooij (University of Amsterdam): Signaling Games and the Semantics & Pragmatics of Natural Language

A number of authors have used signaling games to shed light on semantic and pragmatic aspects of natural language interpretation. Semantic is taken to be conventional meaning, while pragmatics takes care of what can be inferred from the use of a sentence on top of its conventional meaning, making use of rationality assumptions. In this talk I will give a (biased) overview of some of this work. First, I will indicate how by using standard game-theoretical tools signaling games can be used in pragmatics to account for various kinds of conversational implicatures (scalar implicatures, manner implicatures and quality implicatures). Second, I will sketch how by using an evolutionary perspective we can explain various conventional, or semantic, aspects of meaning, such as why language is compositional, why it gives rise to categories, or to vagueness, and why there is a semantic/pragmatic divide in the first place.

Péter Vida (Universty of Cergy-Pontoise, with Alessandro Ispano): Optimal Interrogations

We provide a model of interrogation where both the suspect and the police have private information. The police's information (if any) is a piece of evidence which determines the police's belief about the suspect. The police can also use this evidence to test the suspect's claim (if any) about her alibi. The suspect's type determines the probability that the police can prove his guiltiness. We find that the police benefits from committing to partially and gradually reveal information about the strength of her evidence so as to affect the suspect's belief and to maximize the probability of confession. Under the optimal mechanism: (1) the police interrogates even if she has no evidence, and (2) confessors obtain varying leniency depending on their confession.

Bernhard von Stengel (London School of Economics): Coordination with Noisy Signals

We consider a coordination game between an informed sender and an uninformed receiver who communicate over a noisy channel with given transmission errors. The sender's strategy, called a code, maps states of nature to signals. The receiver's best response is to decode the received channel output as the state with highest expected receiver payoff. Given this decoding, an equilibrium or "Nash code" results if the sender encodes every state as prescribed. We show two theorems that give sufficient conditions for Nash codes, such as a receiver-optimal code, or arbitrary (possibly bad) codes for binary channels. Compared to standard information theory, our game-theoretic approach requires that the code is also optimal for the sender. For further research, it may be of interest to study the evolution of such a Nash code as a model of language, to identify the sources and role of noise in this context, and to clarify the meaning of the communicated "states of nature".