Dictator Controls for Investment Game

Nash Prediction for Self-Regarding Preferences

The unique Nash prediction for player 1 with self-regarding preferences is to pass zero money since any other action is costly.

Common Experimental Results

The action of player 1 in the Investment Game Dictator Control 1 is not motivated by trust because of the fact that the second mover cannot return anything. Thus the comparison of this treatment to the original treatment of the investment game enables one to discriminate between transfers that result from purely altruistic other-regarding preferences and transfers made because of trust in positive reciprocity of the second mover. The conclusions about whether first mover transfers in the investment game are to some extent motivated by trust depend on the difference between the resulting amounts sent by the first mover to the second mover in the investment game and in game with the above specified dictator control.

J. Cox (forthcoming) compares the behavior of players in the investment game and Investment Game Dictator Controls in "How to Identify Trust and Reciprocity” study. In the investment game 6 out of 32 players 1 sent zero, 7 sent exactly half of their endowments, 2 sent amounts that were greater than $5 and less than $10, and 13 players 1 sent all $10 of their endowments. In the Investment Game Dictator Control 1, 19 out of 30 players 1 (i.e. 63%) sent positive amounts of money and only 11 sent zero; thus there is substantial evidence of altruistic other-regarding preferences in these data. Further statistical analysis of the data that compares the amounts sent by players 1 in the Investment Game and Dictator Control 1 reveals that players 1 in the experiment also exhibited trust.

Investment Game Dictator Control 2

For the purposes of discriminating between positive reciprocity and unconditional other-regarding preferences of the second mover one can introduce a specially designed control: The first mover does not have a decision to make, the second mover is given an initial endowment (say, $10) plus additional money equal to the amount that he/she would receive in the investment game from the tripled amount sent by the paired first mover. This is done for all pairs of players. They are also informed about the relation between the additional amount they received and the endowment of the randomly and anonymously paired first mover. Since the first mover does not have an opportunity to send anything in this case, the second mover's action cannot be motivated by positive reciprocity. The difference between the resulting transfer sent by the second mover back to the first mover in the investment game treatment the control treatment enables one to make conclusions to what extent was this behavior motivated by positive reciprocity and not only by other-regarding preferences.

IMPORTANT OBSERVATION: The Investment Game Dictator Control 2 eliminates the possible motive of positive reciprocity that might be present in players’ behavior when playing the original investment game.

Overview

• There are 2 players participating in the game: player 1 and player 2.
• Player 1 is endowed with $10-A, player 2 with $10+3A and A>=0.
• Player 1 does not make a decision.
• Before making his/her move player 2 knows the endowments and the relation between the additional amount he/she received and the endowment of player 1.
• Player 2 can now give some money (or not) to player 1.
• Each dollar given by player 2 to player 1 costs player 2 one dollar.

Nash Prediction for Self-Regarding Preferences

The unique prediction for player 2 with self-regarding preferences is to pass zero money to player 1.

Common Experimental Results

In Cox’s (fortcoming) investment game 6 out of 6 players 2 who were passed zero money by players 1, returned zero (there were other 8 who also returned zero after being sent positive amounts). 2 out of 7 players 2 who received $15 kept all the money, one returned $3, and the remaining 4 players 2 returned more than they received. From among two players who received more than $15 but less than $30, one returned more than he/she received whereas the other returned nothing. Out of 13 players 2 who received $30, one returned $10, thus keeping all the profit from tripling of the amount sent, 4 returned zero, thus ending up with $40 and leaving paired players 1 without any money, 3 returned fairness focal point of $20, one returned $17, one $1, one $6, and finally one $9.

In the Investment Game Dictator Control 2, 13 out of 32 players 2 “returned” positive amounts of money to paired first movers, which provides substantial evidence of other-regarding preferences among players 2. Further statistical analysis of the data that compares amounts returned by the players 2 in the Investment Game and Dictator Control 2 reveals that players 2 in the experiment exhibit positive reciprocity.

Further Readings

• Berg, Joyce, John Dickhaut, and Kevin McCabe, "Trust, Reciprocity, and Social History." Games and Economic Behavior, July 1995, 10¹, pp. 122-42.
• Cox James C.,"Trust Reciprocity, and other-Regarding Preferences: Groups vs. individuals and Males vs. Females," in Rami Zwick and Amnon Rapoport(eds.), Advances in Experimental Business Research(Kluwer Academic Publishers,2002)
• Cox, James C., "How to Identify Trust and Reciprocity," Games and Economic Behavior,forthcoming.