Intervention (Hidden)
Theoretical Motivation:
Suppose people want to be nice to people who are nice to them and prefer to be nasty to those who are nasty to them. In a two-player sequential game, player 2’s initial beliefs about player 1’s action doesn’t matter when actions are elicited by the direct response method (assuming that her social-preferences are of fairly simple nature) as she will perfectly observe what player 1 does. Depending on player 1’s action, player 2 may reward or punish player 1, or simply take some selfish action. For a rational player 2, initial beliefs are also irrelevant when choices are elicited by the strategy method as she can simply make choices conditional on player 1’s hypothetical actions and her respective preferences.
We, however, conjecture that initial beliefs affect player 2’s actions, and that this effect differs across the two elicitation methods. There exist different underlying psychological mechanisms result in such possibilities.
One such possibility is that players may lack the ability to think conditionally. As a result, a player’s preferences over nice, nasty and selfish actions at a given node can be influenced by her preferences over these actions at alternative nodes. One way to model such lack of conditional thinking is via a belief-based model in which the second mover’s social concern is a combination of her true social-preferences at a given node and her preferences in response to the action she expects player 1 to do. For example, when player 2 initially expects player 1 to take a selfish action, she is more likely to respond with a selfish - or even nasty action - in response to all of player 1’s hypothetical actions – even if some of those actions are undoubtedly nice. The second mover doesn’t fully update how she views player 1, either in terms of player 1’s social-type or with regards to the nice or nastiness of his choice. In this model, beliefs do not directly affect a person’s social preferences, for instance through norms, but through altering the person’s thought processes. The motivation behind the lack-of-conditional-thinking theory is the casual observation that under the strategy method, we see fewer cases where a second mover rewards a first mover for his niceness.
Another possible psychological mechanism is that players prefer to signal their social types at the decision node that they think is rather unlikely. Assume a selfish player 2 who always takes the monetary payoff maximizing choice under the direct response method. When her choices are not payoff relevant, she would like to signal – either to herself or to outsiders – that she is nice to nice people and nasty to nasty people. For the strategy method, this has the implication that player 2 will respond to actions she thinks rather likely with her normal selfish responds but chooses a nice or nasty action in response to actions she views as rather unlikely.
We now proceed to outline the basic setup of our experiment and sketch out predictions of theories in which initial beliefs affect behavior in experiments that use the direct response method differently to those that use the strategy method.
Experiment:
To test the hypothesis that initial beliefs matter, we manipulate player 2’s beliefs about player 1’s behavior in a sequential prisoner’s dilemma (sPD) and a mini-ultimatum (UG) game. We employ a 2 by 2 design, varying beliefs and the elicitation method (strategy vs. direct response method) for both games.
Belief manipulation occurs through providing both subjects information about aggregate player 1 behavior from previous existing experiments.
In particular, we selected experiments that either featured a large fraction of selfish-behavior (a majority of defections in the sPD and unequal offers in the UG) or a large fraction of non-selfish-behavior (a majority of cooperations in the sPD and equal offers in the UG). The payoff structure in the cited experiments were either identical or very similar to the payoffs in our sPD and UG. We will refer to these treatments as selfish-belief treatment and non-selfish-belief treatment.
Null Hypothesis: Different expectations of player 1’s behavior can directly affect player 2’s (as well as player 1’s) behavior. By manipulating beliefs for both the direct response and the strategy method, we are able to check whether player 2’s preferences are directly affected by different beliefs about player 1, for example because social preferences are not only driven by preferences over outcomes but also by (1) whether the other player adheres to social norms, (2) by positive or negative surprises about the other player’s behavior, (3) by experimenter demands, etc. The null hypothesis is that the effect of beliefs is constant across the two elicitation methods.
When second movers suffer from a lack of conditional thinking, we derive the following predictions (holding constant the direct influence of beliefs on preferences)
sPD: for the strategy method, the second mover cooperates less in response to cooperation when she has more selfish-beliefs.
UG: for the strategy method, the second mover rejects an unequal offer less often for more non-selfish beliefs.
Note: such theory also predicts higher cooperation in response to defection for more non-selfish beliefs in the sPD and higher rejections of equal splits for more selfish-beliefs.
It is important to highlight, however, that the intensity for non-selfish actions is likely quite different for different nodes of the games. As such, we expect that these more extreme changes to behavior to occur relatively infrequent.
When second mover follows the alternative belief-based model of signaling their social type, the predictions are exactly the opposite of the previous model:
sPD: for the strategy method, the second mover cooperate more in response to cooperation when she has more selfish-beliefs
UG: for the strategy method, the second mover rejects an unequal offer more often for more non-selfish beliefs.