Pure Strategy Equilibria of Multidimensional and Non-Monotonic Auctions
Humberto Moreira | Araujo, Aloisio | de Castro, Luciano
auctions | pure strategy equilibria | non-monotonic bidding functions | tie-breaking rules
We give necessary and suﬃcient conditions for the existence of symmetric equilibrium without ties in interdependent value auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and suﬃcient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results gives a new justification to the use of tournaments in practice.