Students / Subjects

# Trust Game

In the investment game each player is endowed with the same amount of money. The first mover decides whether she wants to pass amy of her endowment to the paired second mover; any amount passed is tripled by the experimenter; the second mover decides whether he wants to return any part of the amount received. The trust game is a truncation of the investment game with the following structure.

Player 1 can either decide to keep her \$5 which choice ends the game and both players get a payoff of \$5 or can pass the entire \$5 to player 2. If she chooses to pass the money to player 2 it is tripled by the experimenter and player 2 can then decide to keep the additional \$15 for himself or can return \$7.50 to player 1, what results in (\$0, \$20) and (\$7.5, \$12.5) payoffs respectively.

The strategies can be given the following names: in the first stage player 1 chooses either to Exit or to Engage. If player 1 chooses Engage, then player 2 in the second stage chooses between Cooperate and Defect.

### Overview of the Trust Game

• There are 2 players participating in the two-stage game: player 1 and player 2.
• At the beginning each player is endowed with \$5.
• Stage 1: player 1 decides whether to Exit and keep his endowment, which results in (\$5, \$5) payoffs or to Engage and pass his money to player 2.
• Money sent is tripled by the experimenter.
• Stage 2: before making his/her move player 2 knows the decision of player 1.
• If player 1 decided to Exit, player 2 has no decision to make.
• If player 1 decided to Engage, player 2 can either Cooperate and reciprocate player 1?s behavior which results in payoffs (\$7.5, \$12.5) or Defect and keep all the money, which yields payoffs (\$0, \$20).

### Nash Prediction for Self-Regarding Preferences

The subgame perfect Nash equilibrium of the trust game for the self-regarding preferences model can be solved for by using backward induction. In the second stage the payoff maximizing player 2 prefers strategy Defect over Cooperate. Realizing this, player 1 prefers strategy Exit over Engage. Thus, the NE is given by (Exit, Defect) which leads to (\$5, \$5) equilibrium payoffs.

The trust game incorporates motives of trust in positive reciprocity and positive reciprocity itself. To test for quantitative effects of these motives one can use a triadic design incorporating dictator controls for trust and for positive reciprocity. For the descriptions of Trust Dictator Controls go to Dictator Game section.

### Other set-ups

The truncation of the strategy set of the investment game makes the trust game simple in structure and allows for an easy exploration of the dependence of observed behavior on the level of payoffs. One might for example investigate the effects of halving and doubling the payoffs on players? choices. Another interesting alternation of the experimental design is varying the social distance from double-blind to single- and zero-blind.

### Common experimental results

In Cox and Deck (2002), 13 out of 30 players 1 decided to Exit while 17 others chose to Engage. Out of 17 players 2 who were sent money by paired players 1, 13 Defected and left players 1 with zero and only 4 Cooperated. As Cox and Deck note, these experimental results imply that trust game is not a very cooperative environment. When comparing the data from the Trust game with the data from Trust Game Dictator Controls, they conclude that the choices of first movers are motivated by trust and that positive reciprocity does not explain behavior of the second movers. From further investigations of the Trust game they observe that it is differences in the level of social distance in the experiment payoff protocol (double-blind vs. single-blind), not differences in the monetary payoff level that accounts for behavioral differences between their data and data from other Trust game experiments.