## Players go to their highest valued LTV: Ads are Beautiful Pareto Exchanges

Previously, I wrote about ads as a way to monetize non-payers, but there’s more to the ad exchange and what I’ll coin as ‘portfolio pumping’. It’s like portfolio theory, but not really.

These terms reference two growing phenomenon in F2P games. King is at the forefront of portfolio pumping, in which a given firm pushes a player from game to game within the firm’s portfolio.

Unlike portfolio pumping, ad exchanges push players to another firm’s games. Companies like Scopely are more fond of ad exchanges.

Frequently, the ads being served are for competitor games. Why would a company show ads for its competitors? In addition, why would firms want players to move from one game in their portfolio to another? I argue the underlying explanation is Pareto Efficiency which is just a fancy term for trade.

$churned player LTV < ad revenue$
$acquired player LTV > ad cost$

It tends to be the case that a given company will engage in both ad buying and selling. The outcome of these ad exchanges are migrations of players to the games in which they have the highest LTV; the initial allocation doesn’t matter. This process takes place in high-speed auctions where firms are constantly in the search for the maximizing the equations outlined above. The decision rule for portfolio pumping is similar, but we add some special conditions, mainly the probability of simultaneous play.

$P(rLTV_{i} + nLTV_{i}) + P(nLTV_{i}) > rLTV_{i}$

Where,
$P(rLTV_{i} + nLTV_{i})$ is the probability of playing both games simultaneously. We add up both of the LTVs in this case.
$rLTV_{i}$ is the remaining LTV in the old game for the ith player, while nLTV is the LTV for the new game for the ith player.

This must be bigger than $rLTV_{i}$ for profitability.

Of course, there are ways to play with this. Wooga tried altering portfolio game prompts during a player’s lifespan but found no effect.1 King continues to portfolio pump but dropped ads in Candy Crush Saga.

It’s a goddamn gorgeous process that should litter econ textbooks like lighthouses and lemons.