Kris De Jaegher

A game-theoretic rationale for vagueness

This paper presents a game-theoretic rationale for vagueness, in showing how vagueness can assure that communication still takes place between a speaker and a listener with conflicting interests

The evolution of Horn's rule

Horns rule says that messages can be kept ambiguous if only a single interpretation is plausible. Speakers only perform costly disambiguation to convey surprising information. This paper shows that, while non‐cooperative game theory cannot justify Horns rule, evolutionary game theory can. In order to model the evolution of signalling, the pooling equilibrium needs to be ones starting point. But in such an equilibrium, the plausible interpretation is made, and the receiver is therefore already predisposed to interpret absence of a signal as referring to a plausible event. From there on, a marked signal referring to an implausible event can evolve. At the same time, the paper identifies an exception to Horns rule. If giving a plausible interpretation for an implausible event is very costly, then in the pooling equilibrium the implausible interpretation is always made. In this exceptional case, only an inefficient separating equilibrium disobeying Horns rule can evolve.Horn’s rule says that messages can be kept ambiguous if only a single interpretation is plausible. Speakers only perform costly disambiguation to convey surprising information. This paper shows that, while noncooperative game theory cannot justify Horn’s rule, evolutionary game theory can. In order to model the evolution of signalling, the pooling equilibrium needs to be one’s starting point. But in such an equilibrium, the plausible interpretation is made, and the receiver is therefore already predisposed to interpret absence of a signal as referring to a plausible event. From there on, a marked signal referring to an implausible event can evolve. At the same time, the paper identifies an exception to Horn’s rule. If giving a plausible interpretation for an implausible event is very costly, then in the pooling equilibrium the implausible interpretation is always made. In this exceptional case, only an inefficient separating equilibrium disobeying Horn’s rule can evolve.

Asymmetric Substitutability: Theory and Some Applications

Economists usually describe goods as being either (gross) complements or (gross) substitutes. Yet, what is less known is that one good may be a gross substitute for a second good, while the second good is a gross complement to the first good. This article develops a theory of asymmetric gross substitutability and suggests some potential examples and applications. (JEL D11)

Strategic vagueness, and appropriate contexts

This paper brings together several approaches to vagueness, and ends by suggesting a new approach. The common thread in these approaches is the crucial role played by context. In Section 2, we treat game-theoretic rationales for vagueness, and for the related concepts of ambiguity and generality. Common about these rationales is that they are based on the assumption of a conflict of interest between speaker and listener. We review this literature using a single example. We argue that the most plausible application to vagueness in natural language of these models is one where the listener only imperfectly observes the context in which the speaker makes her utterances. Yet, it is clear that not all vagueness can be accounted for by conflicts of interest. This is why the rest of the paper looks at the case of common interest. Section 3 argues that being vague by saying that someone is bald makes sense in a context where precision is of less importance; in a context where precision is of more importance, one can then refer to someone as completely bald. This make sense because the longer and therefore more costly to utter expression ‘completely bald’ is then used less often. Vagueness is thus seen as an application of Horn’s pragmatic rule that (un)marked states get an (un)marked expression. Section 4 tackles the Sorites paradox, which apparently leads to the violation of standard axioms of rational behaviour, and shows that this paradox arises from the use of vague predicates in an inappropriate context. If, as suggested by the Sorites paradox, fine-grainedness is important, then a vague language should not be used. Once vague language is used in an appropriate context, standard axioms of rational behaviour are no longer violated. Section 5 finally takes a different approach from the previous sections, and following prospect theory assumes that context directly enter agents’ utility functions in the form of reference points, with respect to which agents think in gains and losses. The rationale for vagueness here is that vague predicates allow players to express their valuations, without necessarily uttering the context, so that the advantage of vague predicates is that they can be expressed across contexts.

Error-proneness as a handicap signal

This paper describes two discrete signalling models in which the error-proneness of signals can serve as a handicap signal. In the first model, the direct handicap of sending a high-quality signal is not large enough to assure that a low-quality signaller will not send it. However, if the receiver sometimes mistakes a high-quality signal for a low-quality one, then there is an indirect handicap to sending a high-quality signal. The total handicap of sending such a signal may then still be such that a low-quality signaller would not want to send it. In the second model, there is no direct handicap of sending signals, so that nothing would seem to stop a signaller from always sending a high-quality signal. However, the receiver sometimes fails to detect signals, and this causes an indirect handicap of sending a high-quality signal that still stops the low-quality signaller of sending such a signal. The conditions for honesty are that the probability of an error of detection is higher for a high-quality than for a low-quality signal, and that the signaller who does not detect a signal adopts a response that is bad to the signaller. In both our models, we thus obtain the result that signal accuracy should not lie above a certain level in order for honest signalling to be possible. Moreover, we show that the maximal accuracy that can be achieved is higher the lower the degree of conflict between signaller and receiver. As well, we show that it is the conditions for honest signalling that may be constraining signal accuracy, rather than the signaller trying to make honest signals as effective as possible given receiver psychology, or the signaller adapting the accuracy of honest signals depending on his interests.

Collective action and the common enemy effect

How is collective defence by players affected when they face a threat from an intelligent attacker rather than a natural threat? This paper analyses this question using a game-theoretic model. Facing an intelligent attacker has an effect if players move first and visibly set their defence strategies, thereby exposing any players who do not defend, and if the attacker is, moreover, not able to commit to a random attack. Depending on the parameters of the game, the presence of an intelligent attacker either increases the probability that players jointly defend (where such joint defence either does or does not constitute a utilitarian optimum), or decreases the probability that players jointly defend (even though joint defence is a utilitarian optimum).

The Value of Private Patient Information in the Physician-Patient Relationship: A Game-Theoretic Account

This paper presents a game-theoretical model of the physician-patient relationship. There is a conflict of interest between physician and patient, in that the physician prefers the patient to always obtain a particular treatment, even if the patient would not consider this treatment in his interest. The patient obtains imperfect cues of whether or not he needs the treatment. The effect is studied of an increase in the quality of the patient’s private information, in the form of an improvement in the quality of his cues. It is shown that when the patient’s information improves in this sense, he may either become better off or worse off. The precise circumstances under which either result is obtained, are derived.

Physician incentives: Cure versus prevention

This paper distinguishes between two scenarios for the physician-patient encounter. In the cure scenario, the patient does not know whether a loss can be recovered. In the prevention scenario, the patient faces a threat but does not know whether this threat is real enough to justify preventive action. The patient wants to induce the physician both to give an accurate diagnosis and to put appropriate effort into cure or prevention. It is shown that in the cure scenario, a contingent fee solves both these incentive problems. In the prevention scenario, however, putting up with low effort makes it easier to get an accurate diagnosis, and the use of contingent fees should be limited. These results are interpreted as providing a rationale for observed exceptions to legal and ethical restrictions on the use of contingent fees. Indeed, such exceptions are often granted for cases that fit the cure scenario.

Game-Theoretic Grounding

Common knowledge plays a role in communication in two manners. First, as stressed by Lewis (1969), conversants need to have some degree of common knowledge (also referred to as common ground) about the meaning of signals. Second, as noted by Clark and Schaefer (1989), conversants will also try and achieve some degree of common knowledge about the fact that is being communicated, in a process that is known as grounding. Signals may get lost, or may be misunderstood, and conversants will seek confirmation that the communicated fact was understood.

Argumentation with (Bounded) Rational Agents

A major reason for our communication is to influence our conversational partners. This is so both if our preferences are aligned, and when they are not. In the latter case, our communicative acts are meant to manipulate our partners. We all know that attempts to manipulate are nothing out of the ordinary. Unfortunately, the standard theory of rational communicative behavior predicts that any such attempt will be seen through and is thus useless. The main aim of this chapter is to investigate which assumptions of the standard theory we have to give up to account for our communicative behavior, when preferences between partners are not aligned.