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Trust Game

Game Description

Can trust and trustworthiness lead to better outcomes than predicted under standard behavioral assumptions?

Players are placed in pairs: one player is the Investor, and the other is the Responder. The Investor chooses how much of her money to invest with the Responder. The investment amount is multiplied (i.e., the investment is successful), and the Responder chooses how much of this multiplied amount to return to the Investor.

Learning Objective 1: Trust and Trustworthiness

Preferences for trustworthiness (positive reciprocity) or fairness may lead a Responder to return positive amounts. Anticipating this, and perhaps also motivated by altruism or fairness, Investors may choose to invest. Investment increases total surplus, and may make both better off if the Responder returns more than the amount invested.

Learning Objective 2: Backward Induction

Under standard assumptions, in the unique subgame-perfect Nash equilibrium, the Responder always returns zero, and therefore the Investor invests zero.

Brief Instructions

The default parameters (a one-shot game where each player’s Endowment=100 and the Multipler=3) implement the canonical game and will satisfy the majority of instructors. As choices are restricted to integers, an instructor may want to avoid small values for Player 1 Endowment. Setting the Multipler>1 ensures that investment increases total surplus.

To remove strategic incentives, play a one-period game (Periods=1). Typically, most investors choose to invest, which is consistent with trust, although most do not invest all of their endowment. Many, but not all, Responders will return more than the amount originally invested. This is consistent with trustworthy behavior and positive reciprocity. It is common that those who invested most or all of their endowment are more likely to have their original investment returned than those who invest relatively little. This is because players tend to be more willing to return positive amounts to investors who are seen as trusting (by investing larger amounts initially).

There are alternative explanations for non-equilibrium play. For example, an investor who is risk seeking, or even just curious, might choose to invest. This can be the case even if the expected return is smaller than the investment, but greater than zero. Alternatively, if there is a disparity in initial endowments, fairness considerations might prompt investment (akin to positive offers in a Dictator game).

For the Responder, while positive returns are consistent with trustworthiness (i.e. positive reciprocity), they are also consistent with altruism and and a preference for fairness.

Key Treatment Variations

The Trust game can be paired with the Dictator game to gain insights into the motivations of Responders who return money. From the default game, change Player 2 Endowment to 0. In this case, the Investor who invests all her endowment puts her Responder in the same position as the Dictator in a Dictator game where the amount to be split equals Player 1 Endowment × Multipler. The increase from Dictator game offers to Trust game responses can be attributed to positive reciprocity as opposed to altruism or fairness.

Repeat interaction (Periods=1), especially indefinite repetition (Ending Probability<100%), provides strategic incentives for Responders to return more than the original investment, thus providing Investors with an incentive to invest.

Results

The results start with a table (Figure 1) displaying the parameters you selected: each player's endowment and the investment multiplier.

Figure 1: Parameters

Next, we show per-group outcomes. First, we present a table (Figure 2) displaying for each group the amounts invested, and returned, as well as the resulting payoff for each player. Click a column’s header to sort.

Figure 2: Per-group Outcome Table

In the graph (Figure 3), we depict this information graphically. With amount invested on the horizontal axis and amount returned on the vertical, we mark each outcome, and provide two lines to help interpret group outcomes. The first line shows amount returned equal to amount invested, meaning observations above the line show investments ex post profitable for the Investor. Second, we show the best-fit line. In most instances, the ratio of returns to investment increases in investment, meaning you should expect the best-fit line to be steeper than the investment=return line.

Figure 3: Per-group Outcome Graph
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