The standard analysis of repeated games assumes that the payoff of a player from a repeated game is a sum (or arithmetic mean, or discounted sum) of the payoffs in the basic games.
But what if the players have decreasing marginal returns?
For example, suppose the basic game is Matching Pennies. In each basic game, a player can either win 1 or lose 1. However, the average utility of a player from winning e.g. 10 times, is not 1 - it may be less than 1 if the player has decreasing marginal returns.
Are there references that deal with such repeated games?