Dictator Controls for Punishment-MUG Game

Nash Prediction for Self-Regarding Preferences

The unique Nash prediction for player 1 with selfish preferences is to choose “Take” since it leads to higher monetary payoffs.

Common Experimental Results

The comparison of players’ 1 decisions in the punishment-MUG game and the decisions in the Punishment Dictator Control 1 discriminates between choices of Share that are motivated by fear of negative reciprocity and choices that are motivated by non-reciprocal other-regarding preferences.

In Cox and Deck [2002] 64% of players 1 chose Take in the original Punishment-MUG game and 70% chose Take in PDC1. This means that more participants of the experiment decided to chose the unequal decision when the paired player 2 did not have a chance to punish them than when this opportunity existed. From comparison of data one can conclude that first movers’ behavior in the Punishment-MUG game is not characterized by fear of negative reciprocity.

Punishment-MUG Dictator Control 2

Punishment-MUG Dictator Control 2 is a dictator game in which player 1 does not make a decision. The choice is determined by a random process when the strategies Take and Share can be selected with an equal probability. Since the situation player 2 is in was not chosen by player 1, player 2 has no reason to punish him. Thus the difference between player 2’s decision in the punishment-MUG game and Punishment Dictator Control 2 game discriminates between player 2’s choices of ($0, $0) outcome motivated by negative reciprocity and choices motivated by non-reciprocal inequality-averse preferences.

The Punishment-MUG Dictator Control 2 eliminates the possible motive of negative reciprocity that might be present in players’ behavior when playing the original Punishment-MUG game.

The Game

• There are 2 players participating in the two-stage game: player 1 and player 2.
• $10 is to be divided between them.
• Player 1 has no decision to make
• Stage 1: Nature decides with a probability of ½ whether player 2 will find himself in the “Share node” of the game tree corresponding to an equal split of ($5, $5) or in the “Take node” corresponding to an unequal split of ($8, $2) when both outcomes are equally likely to occur (both with a probability of ½.)
• Stage 2: before making his/her move player 2 knows the outcome of stage 1.
• If in the “Share node” of the game tree, player 2 can either Accept what results in payoffs ($5, $5) or Reject ($0, $0).
• If in the “Take node,” player 2 can choose to either Tolerate ($8, $2) or Punish ($0, $0).

Nash Prediction for Self-Regarding Preferences

Player 2 with self-regarding preferences prefers the strategies Tolerate to Punish when in the “Take node” and Accept to Reject when in the “Share node”.

Common Experimental Results

Let’s again look at Cox and Deck [2002] results. After being offered an unequal split only 21% of players 2 chose punish. This behavior can be described as negative reciprocity only if it is the case that players 2 prefer the outcome ($8, $2) to ($0, $0) when players 1 have not made any decision that would harm players 2. Only 3 out of 13 (23%) players 2 in PCD2 who hade to decide whether to Tolerate or Punish because of the outcome of the coin flip chose Punish. The difference in the behavior of players 2 in the Punishment-MUG game and PCD2 does not support the evidence of negative reciprocity in this experiment what is consistent with the expectations of players 1.

Further Readings

• Cox, James C. and Cary Deck, ''On the Nature of Reciprocal Motives,'' University of Arizona discussion paper, 2002.
  
• Cox, James C. and Daniel Friedman, "A Tractable Model of Reciprocity and Fairness," University of Arizona discussion paper, September 2002.
  
• Falk, Armin, Ernst Fehr, and Urs Fischbacher, “On the Nature of Fair Behavior,” Economic Inquiry, forthcoming.
  
• Hoffman, Elizabeth, Kevin A. McCabe, Keith Shachat, and Vernon L. Smith, “Preferences, Property Rights, and Anonymity in Bargaining Games,” Games and Economic Behavior, VII(1994), pp. 346-80.