Lewis signalling games are often used to explain how it is possible for simple agents to develop systems of conventional semantic meaning. In these games, all players obtain identical payoffs in every outcome. This is an unrealistic payoff structure, but it is often employed because it is thought that semantic meaning will not emerge if interests conflict. Here it is shown that not only is conventional meaning possible when interests conflict, but it is the most likely outcome in a finite (...) population model of learning known as the Moran process. On the basis of this result it is suggested that evolutionary game theory’s standard models may yield results that are systematically distorted for a class of signalling games that have the abstract structure of social dilemmas. 1 Introduction2 The Seduction Game3 Imitation Dynamics with Small Mutations4 Dynamics with Unverifiable Message5 Analysis of a Related Three-Strategy Game6 Conclusion. (shrink)

Common wisdom holds that communication is impossible when messages are costless and communicators have totally opposed interests. This article demonstrates that such wisdom is false. Non-convergent dynamics can sustain partial information transfer even in a zero-sum signalling game. In particular, I investigate a signalling game in which messages are free, the state-act payoffs resemble rock–paper–scissors, and senders and receivers adjust their strategies according to the replicator dynamic. This system exhibits Hamiltonian chaos and trajectories do not converge to equilibria. This persistent (...) out-of-equilibrium behaviour results in messages that do not perfectly reveal the sender's private information, but do transfer information as quantified by the Kullback–Leibler divergence. This finding shows that adaptive dynamics can enable information transmission even though messages at equilibria are meaningless. This suggests a new explanation for the evolution or spontaneous emergence of meaning: non-convergent adaptive dynamics. (shrink)

Vague predicates, those that exhibit borderline cases, pose a persistent problem for philosophers and logicians. Although they are ubiquitous in natural language, when used in a logical context, vague predicates lead to contradiction. This paper will address a question that is intimately related to this problem. Given their inherent imprecision, why do vague predicates arise in the first place? I discuss a variation of the signaling game where the state space is treated as contiguous, i.e., endowed with a metric that (...) captures a similarity relation over states. This added structure is manifested in payoffs that reward approximate coordination between sender and receiver as well as perfect coordination. I evolve these games using a variation of Herrnstein reinforcement learning that better reflects the generalizing learning strategies real-world actors use in situations where states of the world are similar. In these simulations, signaling can develop very quickly, and the signals are vague in much the way ordinary language predicates are vague—they each exclusively apply to certain items, but for some transition period both signals apply to varying degrees. Moreover, I show that under certain parameter values, in particular when state spaces are large and time is limited, learning generalization of this sort yields strategies with higher payoffs than standard Herrnstein reinforcement learning. These models may then help explain why the phenomenon of vagueness arises in natural language: the learning strategies that allow actors to quickly and effectively develop signaling conventions in contiguous state spaces make it unavoidable. (shrink)

Vague predicates, those that exhibit borderline cases, pose a persistent problem for philosophers and logicians. Although they are ubiquitous in natural language, when used in a logical context, vague predicates lead to contradiction. This paper will address a question that is intimately related to this problem. Given their inherent imprecision, why do vague predicates arise in the first place? I discuss a variation of the signaling game where the state space is treated as contiguous, i.e., endowed with a metric that (...) captures a similarity relation over states. This added structure is manifested in payoffs that reward approximate coordination between sender and receiver as well as perfect coordination. I evolve these games using a variation of Herrnstein reinforcement learning that better reflects the generalizing learning strategies real-world actors use in situations where states of the world are similar. In these simulations, signaling can develop very quickly, and the signals are vague in much the way ordinary language predicates are vague—they each exclusively apply to certain items, but for some transition period both signals apply to varying degrees. Moreover, I show that under certain parameter values, in particular when state spaces are large and time is limited, learning generalization of this sort yields strategies with higher payoffs than standard Herrnstein reinforcement learning. These models may then help explain why the phenomenon of vagueness arises in natural language: the learning strategies that allow actors to quickly and effectively develop signaling conventions in contiguous state spaces make it unavoidable. (shrink)

Godfrey-Smith advocates for linking deception in sender-receiver games to the existence of undermining signals. I present games in which deceptive signals can be arbitrarily frequent, without this undermining information transfer between sender and receiver.

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)

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instance, a full appreciation of Axelrod's The Evolution of Cooperation requires that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questions we re-examine the very foundations of the evolutionary model. The results of this paper can be analytically separated into three parts. (...) The first part is conceptual: it identifies the evolutionary model's assumptions and shows how different assumptions imply different types of evolutionary stability. The second part is deductive: it establishes necessary and sufficient conditions for the types of evolutionary stability identified in the first part, and demonstrates in which games these kinds of stability can (and cannot) be attained. The third and final part is applied: it relates the general findings (which are independent of the specific payoffs of any particular evolutionary game) to the issue of the evolutionary stability of cooperation. Results on cooperation appear throughout the paper as they both exemplify and motivate the general results. These results essentially explain when cooperation is and is not stable, and why, thus shedding new light on the meaning and applicability of Axelrod's widely known claims. (shrink)

The mathematical theory of communication.

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.