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