On Rationality, Learning and Zero-Sum Betting - An Experimental Study of the No-Betting Conjecture

Sebenius and Geanakoplos (1983) prove that zero-sum betting is an irrational phenomenon. The current paper investigates the descriptive implications of this interesting result. For this sake, we have run six experiments (covering 21 different experimental conditions) in which human subjects played repeatedly the Sebenius and Geanakoplos betting game for 250 rounds. The results (for all 21 conditions) reveal a high initial betting rate that decreases very slowly with experience. Our experimental manipulations (that included changes in payoff information, game complexity, feedback system, incentive scheme, outside options and more) had a significant effect on the initial betting rates in some of the conditions, but did not affect the observed slow learning process. All together, the results demonstrate that human agents' behavior may persistently be very different from the one implied by "iterated removal of dominated strategies" even when it leads the agents into significant losses (up to 39% of the initial endowment). We show, however, that under the assumption that the learning speed decreases with payoff variability, simple 2parameters adaptive learning models can be used to approximate the observed adaptation processes in all 21 experimental conditions.

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