Symmetric two-stage contests with budget constraints

The impact of a budget constraint on individual expenditures is examined in two models of two-stage contests with homogenous and risk-neutral players competing to win a single, indivisible, commonly valued rent. The set of players is partitioned into equally sized groups. In the first model, one contestant from each group survives to compete on the second stage against the other survivors. In the second model, one group survives the first stage and its members compete against each other on the second stage. We derive and discuss the symmetric subgame perfect equilibrium solution for each model.