I use a mixture of bidding quickly at the start of each round to make it seem as though I have a load of tokens, and sniping players by bidding at the last second when the other player is 'winning but not qualified for the next round'.

Using this strategy I haven't been involved in any bidding wars bar one, where I went 35 rounds and paid 2x the cash value for a DC against a Vietnamese chap that ironically has been put in the same League as me.