The zero-sum game theory states that, at any given time, the market consists of the cumulative holdings of all investors, and that the aggregate market return is equal to the asset-weighted return of all market participants.
For each position that outperforms the market, there must be a position that underperforms by the same amount, such that, in aggregate, the excess return of all invested assets equals zero.
The theory describes a theoretical cost-free market. In reality, however, investors are subject to costs to participate in the market. When costs are factored in, including management fees, bid-ask spreads, trading commissions and taxes, the aggregate performance of investors is less than zero sum, meaning there are more losing assets than winning assets.
Effectively, this means the more a fund manager charges investors the more they need to outperform simply to achieve the market average, putting costlier funds at an immediate disadvantage. This is at the heart of the ‘active vs. index’ conversation because active funds generally charge higher fees than index funds.