[insickness]

There's nothing irrational about this. Choosing not to buy properties is not irrational. Choosing to buy Park Place and Boardwalk and then put houses on it as soon as possible is not irrational. In fact, my strategy when I play is to get a color set as quick as possible while saving my money by buying as few other properties as possible, then spending all that money on houses/hotels for those few properties I have.

[systoll]

Properties go up for auction if the player that lands on them chooses not to buy.

The losing player had the option to bid a total of $4 and get Electric company, Illinois Avenue, Pennsylvania Rail Road, and Baltic Avenue.

Mortgaging those properties would give them enough money to afford rent, and having a mortgaged property is still better than not having the property at all.

It is irrational to not bid up to the mortgage price.

[insickness]

The winning player can still bid to raise the cost to the losing player without winning the bid. In other words, the winning player can bid $100 for Electric Company, forcing the losing player to bid and pay $110 for Electric Company.

[systoll]

Right… but neither player made any bids, because doing so would make the game longer.

If we don’t care about players conspiring to shorten the game, player 2 can go bankrupt before making a move.

Player 1 lands on any property, and puts it up for auction.

Player 2 immediately bids $2000.

Player 2 wins the auction and bankrupts themselves.

[Kranar]

It's irrational not to buy properties for less than the mortgage price M (half the sticker price). You can buy a property at auction for Y <= M and immediately mortgage it to profit M - Y.