Arising out of the author's lifetime fascination with the links between the formal language of mathematical models and natural language, this short book comprises five essays investigating both the economics of language and the language of economics. Ariel Rubinstein touches the structure imposed on binary relations in daily language, the evolutionary development of the meaning of words, game-theoretical considerations of pragmatics, the language of economic agents and the rhetoric of game theory. These short essays are full of challenging ideas for (...) social scientists that should help to encourage a fundamental rethinking of many of the underlying assumptions in economic theory and game theory. As a postscript two economists, Tilman Borgers and Bart Lipman, and a logician, Johan van Benthem offer comments. (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 are concerned here with explaining how successful rule-following behavior might evolve and how an old evolved rule might come to be successfully used in a new context. Such rule-following behavior is illustrated in the transitive judgments of pinyon and scrub-jays (Bond et al., Anim Behav 65:479–487, 2003). We begin by considering how successful transitive rule-following behavior might evolve in the context of Skyrms–Lewis sender–receiver games (Lewis, Convention. Harvard University Press, Cambridge, 1969; Skyrms, Philos Sci 75:489–500, 2006). We then consider (...) two ways that an agent might come to use an old evolved rule in a new context. The first involves the agent evolving successful dispositions for one concrete type of experience, then associating a new type of experience with the old evolved dispositions. The second involves the agent evolving dispositions that represent a general inferential schema, then composing these dispositions with others in a way that allows the agent to make inferences concerning a new concrete type of experience. (shrink)

This paper concerns how rule-following behavior might evolve in the context of a variety of Skyrms–Lewis signaling game, how such rules might subsequently evolve to be used in new contexts, and how such appropriation allows for the composition of evolved rules. We will also consider how the composition of simpler rules to form more complex rules may be significantly more efficient than evolving the complex rules directly. And we will review an example of rule following by pinyon and scrub jays (...) as an illustration of the appropriation of a rule to a new context :142–150, 2013a; Barrett, Philos Sci, 2014). The proposal here is that the composition of rules might occur in a way that is precisely analogous to such simple appropriation. Finally, we will briefly consider how any finite truth-functional operation might evolve by the sequential appropriation of simpler rules. (shrink)

This article concerns how rule-following behavior might evolve, how an old evolved rule might come to be appropriated to a new context, and how simple concepts might coevolve with rule-following behavior. In particular, we consider how the transitive inferential rule-following behavior exhibited by pinyon and scrub jays might evolve in the context of a variety of the Skyrms-Lewis signaling game, then how such a rule might come to be appropriated to carry out inferences regarding stimuli different from those involved in (...) the original evolution of the rule, and how this appropriation involves a step toward the evolution of basic ordinal concepts. (shrink)

Skyrms-Lewis sender-receiver games with invention allow one to model how a simple mathematical language might be invented and become meaningful as its use coevolves with the basic arithmetic competence of primitive mathematical inquirers. Such models provide sufficient conditions for the invention and evolution of a very basic sort of arithmetic language and practice, and, in doing so, provide insight into the nature of a correspondingly basic sort of mathematical knowledge in an evolutionary context. Given traditional philosophical reflections concerning the nature (...) and preconditions of mathematical knowledge, these conditions are strikingly modest. (shrink)

Lewis sender‐receiver games illustrate how a meaningful term language might evolve from initially meaningless random signals (Lewis 1969; Skyrms 2006). Here we consider how a meaningful language with a primitive grammar might evolve in a somewhat more subtle sort of game. The evolution of such a language involves the co‐evolution of partitions of the physical world into what may seem, at least from the perspective of someone using the language, to correspond to canonical natural kinds. While the evolved language may (...) allow for the sort of precise representation that is required for successful coordinated action and prediction, the apparent natural kinds reflected in its structure may be purely conventional. This has both positive and negative implications for the limits of naturalized metaphysics. (shrink)

Amodel for inventing newsignals is introduced in the context of sender–receiver games with reinforcement learning. If the invention parameter is set to zero, it reduces to basic Roth–Erev learning applied to acts rather than strategies, as in Argiento et al. (Stoch. Process. Appl. 119:373–390, 2009). If every act is uniformly reinforced in every state it reduces to the Chinese Restaurant Process—also known as the Hoppe–Pólya urn—applied to each act. The dynamics can move players from one signaling game to another during (...) the learning process. Invention helps agents avoid pooling and partial pooling equilibria. (shrink)

"This reviewer had to be restrained from stopping people in the street to urge them to read it: They would learn something of the way science is done,...

Lewis signaling games illustrate how language might evolve from random behavior. The probability of evolving an optimal signaling language is, in part, a function of what learning strategy the agents use. Here we investigate three learning strategies, each of which allows agents to forget old experience. In each case, we find that forgetting increases the probability of evolving an optimal language. It does this by making it less likely that past partial success will continue to reinforce suboptimal practice. The learning (...) strategies considered here show how forgetting past experience can promote learning in the context of games with suboptimal equilibria. (shrink)

To coordinate action, information must be transmitted, processed, and utilized to make decisions. Transmission of information requires the existence of a signaling system in which the signals that are exchanged are coordinated with the appropriate content. Signaling systems in nature range from quorum signaling in bacteria [Schauder and Bassler, Kaiser ], through the dance of the bees [Dyer and Seeley ], birdcalls [Hailman, Ficken, and Ficken, Gyger, Marler and Pickert, Evans, Evans, and Marler, Charrier and Sturdy ], and alarm calls (...) in many species [Seyfarth and Cheney, Green and Maegner,Manser, Seyfarth and Cheney ], up to human language. Information processing includes filtering – that is discarding irrelevant information and passing along what is important – and integration of multiple pieces of information. Integration includes logical inference and voting. Finally, the information must be used to make decisions with consequences for payoffs that drive evolution or learning. (shrink)

We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1’s play and plays from the set {1, 2}. Both players win if Player 2’s play equals Nature’s play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as (...) follows. Each node of the desicion tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination. (shrink)