 Dr. Stephen Woodcock is a mathematics lecturer at the University of Technology, Sydney, who uses game theory to show how negative gearing can have some other, more surprising outcomes. Game theory is a branch of mathematics that models how rational players work within systems. It's all theoretical, but it can tell us a lot about how systems and policies are likely to play out. So let's play a game to show how this actually works. But remember, this is a game, so first we have to start off with a few rules. One, there is a limited supply of homes and the selling price of each house is decided by the market, which means any one buyer will spend what they can afford to own a house and competes with other players to set the price. Two, the maximum amount players can borrow from the bank is about a thousand times their weekly wage. This is roughly equivalent to an 80% mortgage at 4% interest per annum, a healthy mortgage at the current rate. Three, players can add any income from rental properties to their budget to buy or rent other property. And four, when there's a market for other players to rent, the most a player can make on rent each week is three quarters of the weekly mortgage cost. This is equivalent to a 4% yield. If no other player can afford the rent, the house is let for the highest price a tenant can pay. Now, remember this is a game, so much like in life itself, everyone is going to act rationally and get the most out of the system for themselves. So let's play. Without negative gearing, there's no immediate financial incentive for players to purchase additional homes as investments. The mortgage costs for a second property, not including things like maintenance, means the priority for all players, even the most wealthy, is to become an owner-occupier, so there's a relatively even distribution of homes across the market. Player one, the richest player, gets the best house. Player five gets the worst. Oh, and player six? Well, every game has a loser. Unfortunately, they're left out of the market, but they help to set a floor price on the market by competing with player five. In this version of the game, we make negative gearing available, but it's limited to one property per player, so the priority for all players is to be both an owner-occupier and to try and purchase one other property as an investment. Player one uses their stash of money to jump in and buy the best two houses. One to live in, one to rent. Players two, three, and four can still buy houses, but they're now in worse houses for the same cost, because the market is higher. But player five? Because the market is tapped out, remember there's a limited supply, they have no option but to rent from player one. Sure, they're living in a nicer house, but they can't afford to compete. In this scenario, players still focus on buying a house and being an owner-occupier, and they still have the ability to buy a single investment property, but now there's a greater incentive to live in the best house available, even if they can own a cheaper property as an investment. Player one still buys the first two houses, but because all players have a desire to rent the best house available, player two uses the first move to rent from player one and then buy house number three. Player three then rents from player two and buys house four, and so on. Player five is again left paying rent, but this time it's for a house that's worse than in the previous scenario. And they're paying almost as much rent as they were for the good house. This is how our current negative gearing system works. The priority for all players is to live in the best possible home, whether owner-occupiers or renters, and this time there's no cap on the amount of investment properties anyone player can own, or the negative gearing on each. So with no restrictions on the number of homes player one can negatively gear and the ability to buy in all markets at once, they start buying up the first two properties. Player two wants to buy a house, but they also want to live in the best home for their family, which forces them to rent the second house, which gives player one the money to buy house three. The same happens for player three and so on and so on until player one owns the whole board and everyone else is just paying rent. Now the last scenario doesn't completely mirror the real world. No one person in Australia's property market owns everything, but investors with large property portfolios are not uncommon.