Two-stage contests with budget constraints: An experimental study

We report the results of an experiment on two-stage contests with budget-constrained agents competing to win an exogenously determined prize. In stage 1, agents first compete within their own groups by expending resources, and then in stage 2 the winners of each group compete with one another to win the prize by expending additional resources subject to the budget constraint. Winners in each stage are determined by Tullock's proportional contest success function. We present the subgame perfect equilibrium solution for this model, derive predictions for our experiment, and then test them experimentally. In agreement with previous experimental research on single-stage contests, the equilibrium model is flatly rejected due to over-expenditure in stage 1. A descriptive model that extends the equilibrium solution by allowing for (1) non-pecuniary utility of winning and (2) misperception of the probability of winning better accounts for some, but not all, of the behavioral regularities. Taking an alternative approach, we then turn to an adaptive learning model that accounts for several features of the dynamics of play but still significantly under-predicts the stage 1 expenditures.