Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

There are two projects, both evolutionary studies of behaviour. The first belongs to biology and concerns the nature and structure of the theoretical constructs we use in our attempt to understand behaviour of living organisms. The second belongs more to psychology and economics and has both theoretical and experimental components. It uses a new “signal” version of the much studied ultimatum game to help us understand human behaviour in economic decision making.

Project 1 continues my ongoing study of the inclusive fitness (IF) method for analyzing social behaviour. This concerns situations in which the behaviour of an actor affects the fitness of relatives and it has been realized for a long time that selective forces should modify behaviour to take account of such effects. Hamilton (F8) showed that evolution should maximize a simple weighted (by relatedness) sum of these fitness effects. This construct—the IF effect—is simple and intuitive (help your neighbours in proportion to their “closeness”) and under a wide set of assumptions (principally weak selection) its predictions match those of more-detailed genetic models.

My past work has been to discuss the predictions of IF models and establish precise equivalence results to other standard measures of fitness such as fixation probability. In this work I have discovered many elegant structural results. These include two general conditions for evolutionary stability; the first applies to all homogeneous population structures (F25) and the second to synergistic (non-additive) fitness effects in both finite and infinite populations (CCV10). It is certainly the case that the IF formulation was crucial to the discovery of these simple conditions.

Over the next five years I will continue this work, seeking simple general results, focusing on class-structured populations and non-additive fitness effects.

In the ultimatum game of Project 2, player 1 makes an offer to player 2 of how to split an available resource, but that is implemented only if player 2 accepts; otherwise both get nothing. Experiments show that humans play this game much more generously than the Nash equilibrium would predict. In our variation, player 2 makes an up-front demand: “I will accept no less than x,” which, however, he is not compelled to adhere to. This is analogous to the red patch on a male blackbird wing that appears to signal good paternity but might be dishonest. How is this, possibly empty, demand to affect player 1’s offer? It is known from biological studies that such signals of quality do not work unless they exact a cost on the signaler and for this reason we introduce and investigate a cost taken to be proportional to the difference between the demand and the “minaccept” below which the offer will fail.

This project has inspired the interest of my grad students and I will be able to involve them in the model building as well as the field work.