• Game Rules
• Nash Prediction for Self-Regarding Preferences
• Setup Overview
• Common Experimental Results
• Possible Explanations of Observed Behavior
• Examples of "Extreme" Behavior and Outcomes
• Further Readings
• Advanced Discussion on Separating Various Motives of Behavior in the Moonlighting Game

The moonlighting game is a sequential game that exhibits notions of fairness. In its structure it incorporates many motives of behavior present in everyday life, such as altruistic or inequality-averse other-regarding preferences, trust in positive reciprocity, and fear of negative reciprocity. The most important feature of the game is that both kind and unkind actions are feasible for both players.

The moonlighting game was first introduced by Abbink, Irlenbush, and Renner [2000]. It is an extension of the Investment game of Berg, Dickhaut, and McCabe [1995]. Consider an illegal moonlighter contracted to do some work. He has access to a homeowner's money in order to buy materials and is supposed to get paid after the work is finished. Neither the moonlighter's performance nor the homeowner's payment can be legally enforced because the transaction involves an illegal attempt to evade paying taxes. The moonlighter thus has several options: take the money for material and disappear; work at an arbitrary effort level (more effort is more costly to him and creates a higher homeowner's surplus) or not work at all. After the moonlighter finishes the work (or not), the homeowner may pay him the agreed amount, but also less than that or even nothing at all. However, if the moonlighter disappears without finishing the work, there is nothing the homeowner can do against him but go to court which will have negative consequences for both since the whole activity was forbidden by the law.

In the operationalized version of the game the endowment of both movers is $10. Unlike in the investment game the first mover can either give money to the second mover or take money from him/her. Maximum amount that can be passed is the whole endowment of the first player, maximum amount taken, however, is only $5, i.e. one-half of the second mover?s endowment. Money given is increased by a multiplicative factor greater than 1, say equal to 3, while any amount taken is not transformed. After the second mover learns about the outcome of stage 1 (i.e. about the tripled amount sent or the amount taken) he/she has an opportunity also to give or take money from the first mover. Each dollar given by the second mover to the first mover costs the second mover one dollar and each dollar taken by the second mover from the first mover costs the second mover 33 cents.

IMPORTANT OBSERVATION: Player 1, by choosing either to pass or take money changes the budget constraint of player 2, thus altering the set of available strategies (moves) to player 2.

Since the moonlighting game is a sequential game, the Nash equilibrium for self-regarding preferences can be solved for by using the backward induction method. Because of the fact that player 2 is concerned only with maximizing his own payoff, he will not pass nor take any money from the paired player 1. Player 1, who also maximizes own payoffs, realizes this and thus, in the first stage takes the maximum amount of $5 from player 2. This subgame perfect Nash equilibrium for selfish preferences is Pareto-inferior to some alternative feasible allocations when player 1 passes a positive amount of money to player 2 which increases the stake to be divided between them.

• There are 2 players participating in the two-stage game: player 1 and player 2.
• At the beginning of the game both players are endowed with $10.
• Stage 1: player 1 decides whether to pass some of his money to player 2, take away money from him or neither send nor take anything.
• Maximum amount that can be passed is $10, maximum amount that can be taken is $5.
• Any amount passed is tripled by the experimenter; any amount taken is not transformed.
• Stage 2: before making his/her move player 2 knows the outcome of stage 1
• Player 2 can now give or take money from player 1.
• Each dollar given by player 2 to player 1 costs player 2 one dollar and each dollar taken by player 2 from player 1 costs the second mover 33 cents.

Abbink, Irlenbush, and Renner [2000] run experiments with and without the option of making non-binding contracts beforehand. They found that such contracts, although non-binding, encourage trust between the players. Another finding of their study is that retribution (punishment for breaking the contract) is more compelling than reciprocity because the hostile actions are punished more often than friendly actions rewarded.

Cox, Sadiraj, and Sadiraj [2002] similarly observe that the behavior of players 1 is characterized by trust in positive reciprocity and they also notice that the first players are not afraid of negative reciprocity: 12 out of 30 players 1 took the maximum possible amount of 5, 1 player took 2, 3 players ?sent? zero and 14 players gave positive amounts to the paired player 2. However, their experiment produced a different kind of behavior of players 2 than in the Abbink, Irlenbush, and Renner [2000] no-contract study. In Cox et al. 13 out of 30 players 2 neither gave nor took money, 5 took and 12 gave money to first movers. The statistical analysis of the data reveals there was more positive reciprocity present in the behavior of players 2 than in Abbink et al. experiment. Cox, Sadiraj, and Sadiraj also find that although the second players are positively reciprocal, the evidence of negative reciprocity in their decisions is not significant. For more advanced and detailed discussion of separating motives behind the actions of players by using a moonlighting game triad, go here.

The first mover can pass money to the second mover because of:

• Altruistic other-regarding preferences.
• Trust that the second mover will return part of the tripled amount and thus make both better-off.

• Altruistic or inequality-averse other-regarding preferences.
• Fear that the second mover might retaliate by taking money from him/her in stage 2.

• Positive reciprocity (a costly action to benefit someone whose intentional behavior has benefited oneself).
• Altruistic or inequality-averse other-regarding preferences.

• Negative reciprocity (costly action to inflict harm on someone whose intentional behavior has inflicted harm on oneself.)
• Inequality-averse other-regarding preferences.
• Self-regarding own-regarding preferences.

To test for quantitative effects of altruistic or inequality-averse other-regarding preferences, trust in positive reciprocity, fear of negative reciprocity, and positive and negative reciprocity itself one can use a triadic design incorporating dictator controls. For descriptions of the Moonlighting Game Dictator Controls go to the Dictator Game section.

• First mover takes the maximum amount of money, i.e. $5, from the second mover, thus the allocation after stage 1 is ($15, $5). The second mover decides to reciprocate the behavior and uses the rest of the initial endowment to take away the $15 from the first mover. This action costs the second mover 1/3, i.e. $5. Thus both movers are left with $0 after stage 2.

• First mover gives the maximum amount of money, i.e. $10, to the second mover, thus the allocation after stage 1 is ($0, $40). The second mover can decide to reciprocate the behavior and give part or all $40 to the first mover (let this amount be x). Thus the two movers are left with the allocation ($x, $40-x) after the stage 2. The final allocation is Pareto superior to the endowment of ($10,$10) if x>=$10

• Abbink Klaus, Bernd Irlenbusch, and Elke Renner, ''The Moonlighting Game: An Empirical Study on Reciprocity and Retribution.'' Journal of Economic Behavior and Organization, 42, 2000, pp.265-77.
• Cox, James C., Daniel Friedman, and Steven Gjerstad, "A Tractable Model of Reciprocity and Fairness," University of Arizona discussion paper, 2004.
• Cox James C., Klarita Sadiraj, and Vjollca Sadiraj, ''Implications of Trust, Fear, and Reciprocity for Modelling Economic Behavior,'' University of Arizona discussion paper, 2004.
• Servátka, Maros, "Reciprocity and Reputation," University of Arizona discussion paper, 2003.