The Keynesian beauty contest revisited

Keynes’ beauty contest story (Keynes, 1936, p. 156) is a metaphor illuminating how speculators’ decisions on stock markets are guided by expectations’ expectations. Keynes’ idea has been implemented in laboratory experiments since the early nineties using a guessing game design with a contracting factor usually smaller than 1. That means that 1 is the unique Nash equilibrium if the choice space is given by the natural numbers from 1 to 100. In laboratory experiments it has been found out that a part of the participants learns to discover the theoretical equilibrium, but, having discovered it, not necessarily will choose it, taking into account the expected bounded rational behavior of the other participants. The theoretical equilibrium, however, plays the role of an anchor for those participants’ decisions. In our present study we pose the question what will happen in a guessing game if there is not a unique equilibrium, but a multiplicity of equilibria. Furthermore, we introduce (a)symmetric strategy space, with chosen numbers around the center of either zero, in the negative or positive interval. In our experimental setting, each integer of the choice set is an equilibrium of the guessing game if the contracting factor is chosen equal to 1. Since real stock market speculators also do not have a unique equilibrium anchor when deciding on selling or buying an asset, our procedure is in line with Keynes’ original idea. Game theory suggests that participants might use mixed strategies, leading to a stochastic sequence of choices in iterated experiments. In contrast, our exprimental evidence shows recurrent patterns in the time series of iterated choices instead. The aim of our study is to develop and to test hypotheses explaining this evidence.