Date and time: 13 June 2025 (Friday), 11:30 a.m. – 12:30 p.m.
Venue: IEOR Seminar Room
Title: Maynard Smith & Price were almost right
Speaker: Reinoud Joosten, University of Twente
Abstract: Maynard Smith & Price [1973] came up with the evolutionarily stable strategy (ESS) in mathematical biology, and it can be demonstrated that each ESS is a Nash equilibrium. Several years later, Taylor & Jonker [1978] and Zeeman [1978.1979] showed that the ESS is an attractor for the replicator dynamics. This induced a veritable boom in evolutionary game theory to be used or at least inspire innovations in biology, economics, psychology, sociology, geography, law, traffic, industrial organization etc. Nowadays, evolutionary theorizing is applied across a wide range of scientific fields.
The interest of so many scientists was probably geared by an astonishing observation, a Nash equilibrium, thought of as requiring very high cognitive acumen, can be achieved by low cognitive beings under natural selection, or alternatively can be learned by unsophisticated agents by gradual improvement or adjustment processes. Unfortunately, the replicator dynamics lack authority outside mathematical biology and it is not guaranteed that adaptive dynamics empirically relevant to a certain field mentioned are able to preserve the dynamic properties of the ESS under the replicator dynamics.
So, the ESS is quite wrong, conceptually speaking. It is supposed to have properties which imply dynamic stability, but in fact, nothing in the definition of the concept contains any reference to any dynamics.
A similar problem ailed early day mathematical economics. The Walrasian equilibrium simply states that excess demand, the difference between demand and supply of a commodity, is non-positive. As such, a Walrasian equilibrium can be stable or unstable, and Hicks [1937] defined criteria which were to imply convergence of plausible price adjustment processes. However, Paul Samuelson’s critique was that conclusions about the stability or instability of equilibria should be based on an analysis of the dynamical system (nearby). This implies that the dynamics should be modeled as well.
Early in my work I discovered deep connections between concepts, ideas and developments in evolutionary game theory and mathematical economics. I recognized the need for some solution to the discrepancy between intent and definition of the ESS and I contributed to offer alternative yet rather similar concepts instead. After a long journey trying to reconcile the discrepancy mentioned, I came up with equilibrium refinements of various equilibrium concept in evolutionary game theory which reconcile static stability as incorporated by ESS and dynamic stability of its proposed alternatives for a wide class of evolutionary dynamics. The refinement criterion doing the trick is called attractive. Certain evolutionary equilibrium concepts satisfying attractiveness are DSC-stable which means dynamically stable, structurally stable and conceptually stable. The first should be not surprising as it should hold for any equilibrium concept in evolutionary theorizing, the second one implies that the system is robust to perturbations of the dynamics or the underlying payoff structure which is particularly useful in applications, the final one means that for a pair of concepts the discrepancy between static and dynamic stability is reconciled.
The actual adjustment to concepts is quite small, in the sense that generic ESS or its generic alternatives, satisfy the refinement as well. So, in retrospect, Maynard Smith & Price were almost right.