Evolution of Strategies in Repeated Games with Discounting

In repeated games there is in general a large set of equilibria. We also know that in the repeated prisoners dilemma there is a profusion of neutrally stable strategies, but no strategy that is evolutionarily stable. This paper investigates whether and how neutrally stable strategies can be upset in a process of mutation and selection. While neutral stability excludes that mutants have a selective advantage themselves, it does not rule out the possibility that mutants that are neutral can enter a population and create a selective advantage for a second mutant. This will be called an indirect invasion and the central results show that, for high enough continuation probability, there is no strategy that is robust against indirect invasions. Such stepping stone paths out of equilibrium generally exist both in the direction of more and in the direction of less cooperation

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

Inclusive Fitness

This paper reviews and addresses a variety of issues relating to inclusive fitness. The main question is: are there limits to the generality of inclusive fitness, and if so, what are the perimeters of the domain within which inclusive fitness works? This question is addressed using two well known tools from evolutionary theory: the replicator dynamics, and adaptive dynamics. Both are combined with population structure. How generally Hamilton's rule applies depends on how costs and benefits are defined. We therefore consider costs and benefits following from Karlin & Matessi's (1983) "counterfactual method", and costs and benefits as defined by the "regression method" (Gardner et al., 2011). With the latter definition of costs and benefits, Hamilton's rule always indicates the direction of selection correctly, and with the former it does not. How these two definitions can meaningfully be interpreted is also discussed. We also consider cases where the qualitative claim that relatedness fosters cooperation holds, even if Hamilton's rule as a quantitative prediction does not. We furthermore find out what the relation is between Hamilton's rule and Fisher's Fundamental Theorem of Natural Selection. We also consider cancellation effects - which is the most important deepening of our understanding of when altruism is selected for - and we discuss preference evolution. Finally we also explore the remarkable (im)possibilities for empirical testing with either definition of costs and benefits in Hamilton's rule

In and Out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs

We explore evolutionary dynamics for repeated games with small, but positive complexity costs. To understand the dynamics, we extend a folk theorem result by Cooper (1996) to continuation probabilities, or discount rates, smaller than 1. While this result delineates which payoffs can be supported by neutrally stable strategies, the only strategy that is evolutionarily stable, and has a uniform invasion barrier, is All D. However, with sufficiently small complexity costs, indirect invasions - but now through 'almost neutral' mutants - become an important ingredient of the dynamics. These indirect invasions include stepping stone paths out of full defection

The generalized price equation

The main ingredient of this paper is the derivation of the Generalized Price equation. This generalizes the original Price equation in the sense that it produces a set of Price-like equations, one for every different underlying model that one could assume has generated the data. All of these different Price-like equations are identities, and all of them only have a meaningful interpretation if the data are indeed generated by the model they presuppose. The criteria for choosing between these different Price-like equations are the exact same as the criteria that standard statistics uses when choosing the right statistical model, based on the data. The original Price equation in regression form is the generalized Price equation that goes with the simplest linear model. The problem with the widespread misuse of the Price equation is caused by the fact that it loses its meaning if the data are not generated by this model - in the same way that any of the other Price-like equations lose their meaning if the data are not generated by the model they presuppose