Theoretical analysis for repeated trust game

I am studying trust game (Berg, 1995). There are 2 players in this game: A and B.

A moves first. A sends an amount between 0 and 10 to B. The amount is tripled in B's side. B sends back an amount between 0 and what she got to A.

Suppose A sent 5 to B. B receives 3*5 = 15. B sent back 9 to A. A receives 9.

In this case, the profit of A is 9 - 5 = 4, and the profit of B is 15 - 9 = 6.

(it is a turn-based game).

In fact, I am focusing on repeated trust game, i.e. A and B play again and again. In some rounds A moves first, and in some rounds, B moves first.

I wonder if there exist some studies that analyze the behavior of two players in this repeated game? I tried to look on Google Scholar, but I only found the analysis for repeated prisoner-dilemma or repeated sequential prisoner dilemma (i.e. A and B have only two choices: cooperate or deficit, and they play by turn).

I found a lot of studies that analyze the behavior of players in game empirically, but I did not find a study that analyzes the behavior theoretically, e.g. analyze the Nash equilibrium for two players.

I note that the game sometimes is called investment game.

I appreciate any help.

The sub-game Nash equilibrium (not really, but very close) can be found here: Finding subgame-perfect Nash equilibrium in the Trust game

It is easy to see, in one-shot game, the Nash equilibrium is both players send 0. However, I could not find any information about repeated trust game.

References:

 Berg, Joyce, John Dickhaut, and Kevin McCabe. "Trust, reciprocity, and social history." Games and economic behavior 10.1 (1995): 122-142.

• As long as the game is repeated a finite a number of times, I suspected the always send zero and always send zero back are the only subgame perfect strategies. If the game is repeated an infinite number of times, you would probably have an infinite number of subgame perfect eq. as in the spirit of the folk theorem. – Sergio Parreiras Aug 3 '17 at 19:23