In this paper we use an experimental approach to investigate how linguistic conventions can emerge in a society without explicit agreement. As a starting point we consider the signaling game introduced by Lewis. We find that in experimental settings, small groups can quickly develop conventions of signal meaning in these games. We also investigate versions of the game where the theoretical literature indicates that meaning will be less likely to arise—when there are more than two states for actors to transfer (...) meaning about and when some states are more likely than others. In these cases, we find that actors are less likely to arrive at strategies where signals have clear conventional meaning. We conclude with a proposal for extending the use of the methodology of experimental economics in experimental philosophy. (shrink)

According to Bayesian epistemology, rational learning from experience is consistent learning, that is learning should incorporate new information consistently into one's old system of beliefs. Simon M. Huttegger argues that this core idea can be transferred to situations where the learner's informational inputs are much more limited than Bayesianism assumes, thereby significantly expanding the reach of a Bayesian type of epistemology. What results from this is a unified account of probabilistic learning in the tradition of Richard Jeffrey's 'radical probabilism'. Along (...) the way, Huttegger addresses a number of debates in epistemology and the philosophy of science, including the status of prior probabilities, whether Bayes' rule is the only legitimate form of learning from experience, and whether rational agents can have sustained disagreements. His book will be of interest to students and scholars of epistemology, of game and decision theory, and of cognitive, economic, and computer sciences. (shrink)

Signaling games provide basic insights into some fundamental questions concerning the explanation of meaning. They can be analyzed in terms of rational choice theory and in terms of evolutionary game theory. It is argued that an evolutionary approach provides better explanations for the emergence of simple communication systems. To substantiate these arguments, I will look at models similar to those of Skyrms (2000) and Komarova and Niyogi (2004) and study their dynamical properties. My results will lend partial support to the (...) thesis that evolution leads to communication. In general, states of partial communication may evolve with positive probability under standard evolutionary dynamics. However, unlike states of perfect communication, they are unstable relative to neutral drift. (shrink)

We explore the question of whether sustained rational disagreement is possible from a broadly Bayesian perspective. The setting is one where agents update on the same information, with special consideration being given to the case of uncertain information. The classical merging of opinions theorem of Blackwell and Dubins shows when updated beliefs come and stay closer for Bayesian conditioning. We extend this result to a type of Jeffrey conditioning where agents update on evidence that is uncertain but solid. However, merging (...) of beliefs does not generally hold for Jeffrey conditioning on evidence that is fluid. Several theorems on the asymptotic behavior of subjective probabilities are proven. Taken together they show that while a consensus nearly always emerges in important special cases, sustained rational disagreement can be expected in many other situations. (shrink)

Highly idealized models, such as the Hawk-Dove game, are pervasive in biological theorizing. We argue that the process and motivation that leads to the introduction of various idealizations into these models is not adequately captured by Michael Weisberg’s taxonomy of three kinds of idealization. Consequently, a fourth kind of idealization is required, which we call hypothetical pattern idealization. This kind of idealization is used to construct models that aim to be explanatory but do not aim to be explanations.

Recently there has been some interest in studying the explanation of meaning by using signaling games. I shall argue that the meaning of signals in signaling games remains sufficiently unclear to motivate further investigation. In particular, the possibility of distinguishing imperatives and indicatives at a fundamental level will be explored. Thereby I am trying to preserve the generality of the signaling games framework while bringing it closer to human languages. A number of convergence results for the evolutionary dynamics of our (...) models will be proved. (shrink)

Costly signalling theory has become a common explanation for honest communication when interests conflict. In this paper, we provide an alternative explanation for partially honest communication that does not require significant signal costs. We show that this alternative is at least as plausible as traditional costly signalling, and we suggest a number of experiments that might be used to distinguish the two theories.

I discuss two ways of justifying reflection principles. First, I propose that an undogmatic reading of dynamic Dutch book arguments provides them with a sound foundation. Second, I show also that minimizing expected inaccuracy leads to a novel argument for reflection principles. The required inaccuracy measures comprise a natural class of functions that can be derived from a generalization of a condition known as propriety or immodesty. This shows that reflection principles are an essential feature not just of consistent degrees (...) of belief but also of degrees of belief that approximate truth. (shrink)

It is well known that Rudolf Carnap’s original system of inductive logic failed to provide an adequate account of analogical reasoning. Since this problem was identified, there has been no shortage of proposals for how to incorporate analogy into inductive inference. Most alternatives to Carnap’s system, unlike his original one, have not been derived from first principles; this makes it to some extent unclear what the epistemic situations are to which they apply. This paper derives a new analogical inductive logic (...) from a set of axioms which extend Carnap’s postulates in a natural way. The key insights come from Bruno de Finetti’s ideas about analogy. The axioms of the new system capture epistemic conditions that call for a strong kind of analogical reasoning. The new system has a number of merits, but is also subject to limitations. I shall discuss both, together with some possible ways to generalize the approach taken in this paper. (shrink)

Game theory has a prominent role in evolutionary biology, in particular in the ecological study of various phenomena ranging from conflict behaviour to altruism to signalling and beyond. The two central methodological tools in biological game theory are the concepts of Nash equilibrium and evolutionarily stable strategy. While both were inspired by a dynamic conception of evolution, these concepts are essentially static—they only show that a population is uninvadable, but not that a population is likely to evolve. In this article, (...) we argue that a static methodology can lead to misleading views about dynamic evolutionary processes. We advocate, instead, a more pluralistic methodology, which includes both static and dynamic game theoretic tools. Such an approach provides a more complete picture of the evolution of strategic behaviour. 1 Introduction2 The Equilibrium Methodology3 Common Interest Signalling3.1 Lewis’s signalling game3.2 Static analysis3.3 Dynamic analysis4 The Sir Philip Sidney Game4.1 Static analysis4.2 Other equilibria4.3 Dynamic analysis5 Related Literature6 Static and Dynamic Approaches. (shrink)

The Bayesian theorem on convergence to the truth states that a rational inquirer believes with certainty that her degrees of belief capture the truth about a large swath of hypotheses with increasing evidence. This result has been criticized as showcasing a problematic kind of epistemic immodesty when applied to infinite hypotheses that can never be approximated by finite evidence. The central point at issue—that certain hypotheses may forever be beyond the reach of a finite investigation no matter how large one’s (...) reservoir of evidence—cannot be captured adequately within standard probability theory. As an alternative, I propose a nonstandard probabilistic framework that, by using arbitrarily small and large numbers, makes room for the type of fine-grained conceptual distinctions appropriate for a deeper analysis of convergence to the truth. This framework allows for the right kind of modesty about attaining truth in the limit. (shrink)

Generalized probabilistic learning takes place in a black-box where present probabilities lead to future probabilities by way of a hidden learning process. The idea that generalized learning can be partially characterized by saying that it doesn’t foreseeably lead to harmful decisions is explored. It is shown that a martingale principle follows for finite probability spaces.

One of the main contributions of Richard Bradley’s book is an elegant extension of Jeffrey’s Logic of Decision that countenances the evaluation of conditional prospects. This extension offers a promising new setting in which to model dynamic choice. In Bradley’s framework, plans can be understood as conditionals of an appropriate sort, while dynamic consistency can be viewed as providing a constraint on the evaluation of conditionals across time. In this paper, we study connections between planning conditionals and dynamic consistency.

We study the handicap principle in terms of the Sir Philip Sidney game. The handicap principle asserts that cost is required to allow for honest signalling in the face of conflicts of interest. We show that the significance of the handicap principle can be challenged from two new directions. Firstly, both the costly signalling equilibrium and certain states of no communication are stable under the replicator dynamics ; however, the latter states are more likely in cases where honest signalling should (...) apply. Secondly, we prove the existence and stability of polymorphisms where players mix between being honest and being deceptive and where signalling costs can be very low. Neither the polymorphisms nor the states of no communication are evolutionarily stable, but they turn out to be more important for standard evolutionary dynamics than the costly signalling equilibrium. (shrink)

In a recent paper, Belot argues that Bayesians are epistemologically flawed because they believe with probability 1 that they will learn the truth about observational propositions in the limit. While Belot’s considerations suggest that this result should be interpreted with some care, the concerns he raises can largely be defused by putting convergence to the truth in the context of learning from an arbitrarily large but finite number of observations.

Reflection and martingale principles are central to models of rational learning. They can be justified in a variety of ways. In what follows we study martingale and reflection principles in the con...

We study a low-rationality learning dynamics called probe and adjust. Our emphasis is on its properties in games of information transfer such as the Lewis signaling game or the Bala-Goyal network game. These games fall into the class of weakly better reply games, in which, starting from any action profile, there is a weakly better reply path to a strict Nash equilibrium. We prove that probe and adjust will be close to strict Nash equilibria in this class of games with (...) arbitrarily high probability. In addition, we compare these asymptotic properties to short-run behavior. (shrink)

The handicap principle is one of the most influential ideas in evolutionary biology. It asserts that when there is conflict of interest in a signaling interaction signals must be costly in order to be reliable. While in evolutionary biology it is a common practice to distinguish between indexes and fakable signals, we argue this dichotomy is an artifact of existing popular signaling models. Once this distinction is abandoned, we show one cannot adequately understand signaling behavior by focusing solely on cost. (...) Under our reframing, cost becomes one—and probably not the most important—of a collection of factors preventing deception. (shrink)

We consider the nature of quantum randomness and how one might have empirical evidence for it. We will see why, depending on one’s computational resources, it may be impossible to determine whether...

Formal spaces have become commonplace conceptual and computational tools in a large array of scientific disciplines, including both the natural and the social sciences. Morphological spaces are spaces describing and relating organismal phenotypes. They play a central role in morphometrics, the statistical description of biological forms, but also underlie the notion of adaptive landscapes that drives many theoretical considerations in evolutionary biology. We briefly review the topological and geometrical properties of the most common morphospaces in the biological literature. In contemporary (...) geometric morphometrics, the notion of a morphospace is based on the Euclidean tangent space to Kendall’s shape space, which is a Riemannian manifold. Many more classical morphospaces, such as Raup’s space of coiled shells, lack these metric properties, e.g., due to incommensurably scaled variables, so that these morphospaces typically are affine vector spaces. Other notions of a morphospace, like Thomas and Reif’s skeleton space, may not give rise to a quantitative measure of similarity at all. Such spaces can often be characterized in terms of topological or pretopological spaces. (shrink)

The spontaneous emergence of signaling has already been studied in terms of standard evolutionary dynamics of signaling games. Standard evolutionary dynamics is given by the replicator equations. Thus, it is not clear whether the results for standard evolutionary dynamics depend crucially on the functional form of the replicator equations. In this paper I show that the basic results for the replicator dynamics of signaling games carry over to a number of other evolutionary dynamics. ‡This research was supported by the Konrad (...) Lorenz Institute for Evolution and Cognition Research. †To contact the author, please write to: Konrad Lorenz Institute for Evolution and Cognition Research, Adolf Lorenz Gasse 2, A-3422 Altenberg, Austria; e-mail: [email protected]. (shrink)

This article surveys the main philosophical and formal ideas revolving around language as being conventional from the perspective of game theory. For very basic situations, this leads to a coherent view of conventions that offers interesting insights. Although there exist many open problems, this article will argue by outlining partial solution attempts that there is no principled reason for not applying methods from game theory to them.

We consider the Stag Hunt in terms of Maynard Smith’s famous Haystack model. In the Stag Hunt, contrary to the Prisoner’s Dilemma, there is a cooperative equilibrium besides the equilibrium where every player defects. This implies that in the Haystack model, where a population is partitioned into groups, groups playing the cooperative equilibrium tend to grow faster than those at the non-cooperative equilibrium. We determine under what conditions this leads to the takeover of the population by cooperators. Moreover, we compare (...) our results to the case of an unstructured population and to the case of the Prisoner’s Dilemma. Finally, we point to some implications our findings have for three distinct ideas: Ken Binmore’s group selection argument in favor of the evolution of efficient social contracts, Sewall Wright’s Shifting Balance theory, and the equilibrium selection problem of game theory. (shrink)

How can players reach a Nash equilibrium? I offer one possible explanation in terms of a low-rationality learning method called probe and adjust by proving that it converges to strict Nash equilibria in an important class of games. This demonstrates that decidedly limited learning methods can support Nash equilibrium play.

We study a simple game theoretic model of information transfer which we consider to be a baseline model for capturing strategic aspects of epistemological questions. In particular, we focus on the question whether simple learning rules lead to an efficient transfer of information. We find that reinforcement learning, which is based exclusively on payoff experiences, is inadequate to generate efficient networks of information transfer. Fictitious play, the game theoretic counterpart to Carnapian inductive logic and a more sophisticated kind of learning, (...) suffices to produce efficiency in information transfer. (shrink)

The concept of fitness is central to evolutionary biology. Models of evolutionary change typically use some quantity called “fitness” which measures an organism’s reproductive success. But what exactly does it mean that fitness is such a measure? In what follows, we look at the interplay between abstract evolutionary models and quantitative measures of fitness and develop a measurement-theoretic perspective on fitness in order to explore what makes certain measures of fitness significant.

There are decision problems in which rational deliberation fails to result in choosing a pure act. This phenomenon is known as decision instability and has been discussed in the literature on causal decision theory. In this paper we investigate another type of instability, called structural instability in dynamical systems theory. Structural instability indicates that certain qualitative features of the process of rational deliberation are under-determined in a decision situation. We illustrate some of the issues arising from structural instability with a (...) recent argument against causal decision theory proposed by Caspar Hare and Brian Hedden. We show that their argument is undermined by considerations arising from decision instability and structural instability. (shrink)

There are decision problems in which rational deliberation fails to result in choosing a pure act. This phenomenon is known as decision instability and has been discussed in the literature on causal decision theory. In this paper we investigate another type of instability, called structural instability in dynamical systems theory. Structural instability indicates that certain qualitative features of the process of rational deliberation are under-determined in a decision situation. We illustrate some of the issues arising from structural instability with a (...) recent argument against causal decision theory proposed by Caspar Hare and Brian Hedden. We show that their argument is undermined by considerations arising from decision instability and structural instability. (shrink)

In this paper we show that there are certain limits as to what applications of Maynard Smith’s concept of evolutionarily stable strategy can tell us about evolutionary processes. We shall argue that ESS is very similar in spirit to a particular branch of rational choice game theory, namely, the literature on refinements of Nash equilibrium. In the first place, ESS can also be viewed as a Nash equilibrium refinement. At a deeper level, ESS shares a common structure with other rational (...) choice equilibrium refinements. An equilibrium is evaluated according to whether it persists under specific kinds of perturbations. In the case of ESS, these perturbations are mutations. However, from a dynamical point of view, focusing exclusively on perturbations of equilibria provides only a partial account of the system under consideration. We will show that this has important consequences when it comes to analyzing game-theoretic models of evolutionary processes. In particular, there are non-ESS states which are significant for evolutionary dynamics. (shrink)