A Model of Evolutionary Drift

Laburpena

It is common place to observe that the equilibrium selected by a theory depends on the manner in which perturbations are handled (see, for example, Selten�s (1975) perfect equilibrium and Myerson�s (1978) proper equilibrium ). Binmore et al.(1995) and Binmore and Samuelson (1999) also emphasize the importance of perturbations, but they place these in the dynamic process that takes the players to equilibrium rather than perturbing the game itself (like Selten or Myerson). It is in modelling such perturbations realistically that the present paper is concerned. The important work of Binmore and Samuelson (1999), �B & S, from now on�, studies the limiting behaviour of perturbed systems, but little insight is given into what perturbations one should expect. The implicit message of B & S is the need of an explicit microeconomic model of psychologically observed human choice behaviour that originates the drift that perturbs a selection dynamics. B & S have opened a possible application for perception theory wit the introduction of a decreasing and Lipschitz continuous drift function in the expected payoffs differences (Assumption 4). This means that when the payoffs at stake increase, the player�s efforts for a better perception of the game are increased and as a consequence of his more careful moves the mistakes will decrease (the assumption is related to Myerson�s (1978) proper equilibrium). Perception theory is precisely at the heart of our model of drift. The model derives explicitly from the similarity theory developed first by Tversky (1977) in psychology and later applied to choice theory by Rubinstein (1988) and Aizpurua et al. (1993). The present paper extends the theory developed in Uriarte (1999), by building a similarity compatible choice model valid for a dynamic setting. We shall use the same methodology as B & S to study the stability properties of Nash equilibria specifying different out-of-equilibrium path appearing in connected components of stationary states. Thus, we start with a continuous, deterministic selection dynamic model (in the present paper, the model will be the popular replicator dynamics model,- RD). Then, for a better approximation to an underlying stochastic strategy-adjustment process that governs the players� behaviour, the selection model will be completed by adding perturbations that incorporates some of the real-life imperfections or �anomalies� of the human choice behaviour which are excluded by the model. These appear in the model as drift. In the present paper drift is not derived from the behaviour of agents who misread the game.