If a player takes a stock from a company that the dummy player would control, the dummy player always accepts (it'll make things easier, I guess).
I think that would be pretty much like if you play with 2 players and both have 2 actions (taking turns: A-B-A-B --> City Round A-B-A-B --> End of round), because you can just get shares cheaply. Of course you dont get much money in the company either, but its a little bit to predictable perhaps...
Maybe you could roll a 10 sided-Die: If you bid 100, you have to roll a 1 to succeed. If you bid 200, you roll a 1 or 2 to succeed etc. (n100 = roll n/100 or lower to succed). If the dummy doesnt have enough money to pay for it, of course you dont need to roll.