Evolution: Selection For Positive Illusions

Everybody knows that overconfidence can be foolhardy. But a study reveals that having an overly positive self-image might confer an evolutionary advantage if the rewards outweigh the risks.MathematicsOrganismic and Evolutionary Biolog

Repeated games with endogenous separation

Producción CientíficaWe consider repeated games with endogenous separation – also known as voluntarily separable or voluntary partnership games – and their evolutionary dynamics. We formulate the replicator dynamics for games with endogenous separation, and provide a definition of neutral stability that guarantees Lyapunov stability in the replicator dynamics. We also provide existence results for monomorphic neutrally stable states in games with endogenous separation.Organización de Empresas y CI

Altruism, Fairness and Evolution: the Case for Repeated Stochastic Games

This paper is an effort to convince the reader that using a stochastic stage game in a repeated setting - rather than a deterministic one - comes with many advantages. The first is that as a game it is more realistic to assume that payoffs in future games are uncertain. The second is that it allows for strategies that make an evolutionary approach possible, while folk theorem strategies do not allow for such an analysis. But the most important feature is that such a setting allows for equilibrium strategies that look very much like human behaviour; altruism and fairness will be shown to feature in a natural way in equilibrium.

But Some Neutrally Stable Strategies are More Neutrally Stable than Others

For games in which there is no evolutionarily stable strategy, it can be useful to look for neutrally stable ones. In extensive form games for instance there is typically no evolutionary stable strategy, while there may very well be a neutrally stable one. Such strategies can however still be relatively stable or unstable, depending on whether or not the neutral mutants it allows for - which by definition do not have a selective advantage themselves - can open doors for other mutants, that do have a selective advantage. This paper defines robustness against indirect invasions in order to be able to discern between those two very different situations. Robustness against indirect invasions turns out to come with a very natural setwise generalisation of evolutionary stability; we prove that if a strategy is robust against indirect invasions, then this strategy and its (indirect) neutral mutants form a set that is asymptotically stable in the replicator dynamics.Robustness against indirect invasions, neutrally stable strategy, evolutionarily stable strategy, extensive form game

The apples and oranges theorem for price indices

The question is whether or not there is a generally meaningful way to compute price indices. I explore the duality between price and quantity indices, and present an impossibility result that is analogous to the one for quantity indices.Price index True index Homothetic utility functions Impossibility theorem