(WP 2020-01) The Sea Battle Tomorrow: The Identity of Reflexive Economic Agents

This paper develops a conception of reflexive economic agents as an alternative to the standard utility conception, and explains individual identity in terms of how agents adjust to change in a self-organizing way, an idea developed from Herbert Simon. The paper distinguishes closed equilibrium and open process conceptions of the economy, and argues the former fails to explain time in a before-and-after sense in connection with Aristotle’s sea battle problem. A causal model is developed to represent the process conception, and a structure-agency understanding of the adjustment behavior of reflexive economic agents is illustrated using Merton’s self-fulfilling prophecy analysis. Simon’s account of how adjustment behavior has stopping points is then shown to underlie how agents’ identities are disrupted and then self-organized, and the identity analysis this involves is applied to the different identity models of Merton, Ross, Arthur, and Kirman. Finally, the self-organization idea is linked to the recent ‘preference purification’ debate in bounded rationality theory regarding the ‘inner rational agent trapped in an outer psychological shell,’ and it is argued that the behavior of self-organizing agents involves them taking positions toward their own individual identities

Superintegrable Calogero-type systems admit maximal number of Poisson structures

We present a general scheme for constructing the Poisson structure of super-integrable dynamical systems of which the rational Calogero-Moser system is one of the most interesting one. This dynamical system is $2N$ dimensional with $2N- 1$ first integrals and our construction yields $2N-1$ degenerate Poisson tensors that each admit $2(N-1)$ Casimirs. Our results are quite generally applicable to all super-integrable systems and form an alternative to the traditional bi-Hamiltonian approach

Automata and rational expressions

This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin