Charles Figuières

Theory of Conjectural Variations

We have witnessed in recent years a revival of Conjectural Variations in Game Theory. This reincarnation of an old idea, using a dynamic point of view, aims at combining the adequacy with facts to the requirements of a firmly grounded theory. This book presents, for the first time, a comprehensive account of conjectural variations equilibria in their static inceptions, featuring new comparative results of equilibria with regard to efficiency. It then describes several advances in Dynamic Game Theory, allowing to understand Conjectural Variations Equilibria as dynamic equilibria. The question of how conjectures evolve in strategic and learning situations with boundedly rational agents is also discussed.

The MBR intertemporal choice criterion and Rawls’ just savings principle

This paper provides general theorems about the control that maximizes the mixed Bentham–Rawls (MBR) criterion for intergenerational justice, which was introduced in Alvarez-Cuadrado and Long (2009). We establish sufficient concavity conditions for a candidate trajectory to be optimal and unique. We show that the state variable is monotonic under rather weak conditions. We also prove that inequality among generations, captured by the gap between the poorest and the richest generations, is lower when optimization is performed under the MBR criterion rather than under the discounted utilitarian criterion. A quadratic example is also used to perform comparative static exercises: it turns out, in particular, that the larger the weight attributed to the maximin part of the MBR criterion, the better-off the less fortunate generations. All those properties are discussed and compared with those of the discounted utilitarian (DU, Koopmans 1960) and the rank-discounted utilitarian (RDU, Zuber and Asheim, 2012) criteria. We contend they are in line with some aspects of the rawlsian just savings principle.