Appendix for Daniel Quint and Kenneth Hendricks , “ Indicative Bidding in Auctions With Costly Entry ” September 2015

We will show that for any (possibly mixed) strategy τ played in a symmetric equilibrium, if τ(s) puts positive probability on m and τ(s′) puts positive probability on m′, then s′ > s implies m′ ≥ m. As in the text, define vτ (m, si) as the expected payoff to a bidder with type si from sending message m (and then bidding si if selected), given that her opponents are all playing the strategy τ and bidding their types.28 If we let M−i denote the vector of messages (τ(sj))j 6=i sent by i’s opponents and F its probability distribution, we can write