Utility and sub game perfection
Ultimatum Game is an appropriate paradigm that investigates the discord between social motives like fairness and self-interest. UG bases on the assumption that bargainers maximize their outcome. The acceptance of the smallest offer can yield high outcomes and the alternative of refusing means no outcome at all. The social utility model implies that the utility of the outcome depends on both payoffs. The study aims to identify factors that can affect the relative importance in making UG.
A strong reciprocity model in the evolution of human cooperation gains acceptance because of support and experimental findings. An observation that unfair offers in the Ultimatum game frequently rejected provides an important piece of experimental evidence for strong reciprocity. The study challenges the idea that rejection response in the UG to provide evidence that assumes strong reciprocity. Positive reciprocity observed in the UG has a preference of fairness. The study conducts series of experiments that will predict inseparable relationship between positive and negative reciprocity. Some of the experiments conducted include trust game, prisoner’s dilemma, ultimatum game, and dictator game. The study finds no correlation between participants rejecting unfair offers in the ultimatum games and tendencies to exhibit pro-social behaviors in other games.
The findings of economic game experiments concerning rejection of unfair offers in the UG is a major impetus in the development of strong reciprocity theory of cooperation. The authors define UG as an economic game played by two individuals a proposer and responder. The experimenter gives the proposer an amount of money so that he can divide that amount between himself and the responder. The responder has on option of either accepting or rejecting the offer (Handgraaf et al. 165). If the responder accepts the offer, both proposer and responder benefit from the money. If the responder rejects the offer, both proposer and responder receive nothing. The two individuals that participate in UG are strangers. A proposer should be rational and self-regarding to give as minimal as possible to the responder. In the same light, a responder should be rational and self-regarding to accept nonzero offers.
In most UG experiments, most proposers use an equal split of the money while half of respondents reject unfair offers where they receive less than 30 percent of the funds. The author in this study argues that the rejection of unfair offer in the UG experiment is an illustration of strong reciprocity. Behavioral tendencies depict reciprocal fairness and inequality aversion. A fair individual is motivated to respond in kind. An equity-averse individual is motivated to avoid inequity and implement equitable outcomes. Regardless of the motivation that gives strong reciprocity any strong reciprocator that rejects an unfair offer should act in a positive reciprocal manner. The author argues that UG is a psychological response that challenges the integrity of the responder (Handgraaf et al. 165). Some researchers argue that those persons that reject unfair offers have high testosterone levels than individuals that accept the offers.In the impunity game, a responder given an unfair offer can achieve equality or punish the unfair proposer. Rejecting unfair offer in the impunity game can cause unfair distribution to the responder.
In the UG, a proposer makes an offer to a responder on how to divide the amount of money. The responder has the option to either accept or reject the proposed division. In the view of rejection, both will not get anything. The proposal will implement once there is acceptance in the outcome. A rejection will lead to no money for the standard economic theory to predict that the proposer will offer the responder a small amount of money and the responder accepts it. Underlying the prediction assumes that both parties care only for the money will get.
Contrary to the predictions, a proposer can offer more to the responders often reject small offers. Different authors that experiment with UG indicates that offers amount to 20 percent or less of the total amount reject more than half the time (Mussel et al. 52). The discrepancy between the empirical data and the prediction from economic theory gives different reasons for responders’ rejections when games are played in large stakes.
In a partner-specified condition, the experimenters ask the participants to split the colored ID code card together with a folded crest placed in a large bag. In the partner-unspecified conditions, the experimenters request the participants to keep the colored ID code until the end of the experiment
Declerck (341) assesses proposed expectations concerning respondents’ behavior through a post-experimental questionnaire. The proposer expectations are in four different classifications that include rational, threshold, altruistic, and others. The author does not find a significant difference between the expectations of partner-specified and partner-unspecified condition (Mussel et al. 52). The timing of matching affects responders equality expectations since it is compatible with interdependence strengthens in a fairness norm. Contrary to the actual behavior of proposers as the responders, expect equal offers in the partner-specified condition. The responders’ expectations of equal offers do not translate to actual rejection behavior since they accept unequal offers in a partner-specified condition. The finding contradicts the hypothesis that the state that the rejection rate will be higher in a partner-specific condition due to high-perceived sense of interdependence.
The manipulation of timing of partner matching will incidentally introduce other timing effects in the game with respect to the position of the moves. Players are yet to match themselves with a partner at the time of decision to assume a first mover position. The manipulation of subjects’ perception of decision-making will not result in a significant difference in accordance to the standard game theory. A series of experiments conclude that perceived sequential moves in one-time games activate competitive social interaction. A player in a first mover position employs strategic decision-making schemes. The unmatched responders in the experiment suppose that their future collaborates to give the illusion of control. The authors found that responders that filled in their decision forms before the proposers that are less willing to accept low offers in comparison to the decision forms after the proposers.
A post-experimental questionnaire data assesses validity of an alternative explanation. A responder in a partner-unspecified condition would result in rejection of low offers to establish a tough bargainer reputation that avoids vulnerability in the future interaction. The major outcome of the study is the manipulation of matching in the UG affects responders’ behaviors. Majority of proposers offer equal split while a proposed timing effects depict the strength of equality principle.
The main benefaction of the study is to provide more insight on the importance of framing effects in economic games while using the strategy method in the timing effects. The issue can have an effect in future UG research. In some of the studies, participants of the UG match with their partners before decision-making. This study calls the attention to future researchers to state whether matching times result in diverse perceptions of interpersonal relationships explicitly. That can lead to inconsistent across cultures and the same societies.
Utility and Sub-Game Perfection
Backward induction is a powerful solution that has an intuitive appeal. The sub-game perfect equilibrium applies only to perfect information games with finite horizon. The intuition extends beyond the games through sub-game perfection. The extensive-form game contains a small game embedded in a large game called sub game. The main item of backward induction is that when restricted to a sub-game of the game the computation remains at equilibrium. Sub game perfection generalizes the notion of general dynamic games. Nash equilibrium has sub-game perfect that has an initial node as all the information remain in the sub-game. The equilibrium computed through backward induction remains to be the equilibrium of the sub game. A matching penny game with perfect information has three sub-games. One player can choose Head; another player can choose Tail and the game itself. The computation of equilibrium through backward induction is Nash equilibrium at each sub game. One cannot apply backward induction in an imperfect equilibrium. One computes sub-game equilibrium as follows: fixing the equilibrium actions, taking the equilibrium payoffs and computing the Nash equilibrium in the remaining game.
Works Cited
Declerck, Carolyn H., Toko Kiyonari, and Christophe Boone. "Why Do Responders Reject Unequal Offers In The Ultimatum Game? An Experimental Study On The Role Of Perceiving Interdependence." Journal Of Economic Psychology 30.3 (2009): 335-343.
Handgraaf, Michel J. J., et al. "The Salience Of A Recipient’S Alternatives: Inter- And Intrapersonal Comparison In Ultimatum Games." Organizational Behavior & Human Decision Processes 90.1 (2003): 165.
Karagonlar, Gokhan, and David M. Kuhlman. "The Role Of Social Value Orientation In Response To An Unfair Offer In The Ultimatum Game." Organizational Behavior & Human Decision Processes 120.2 (2013): 228-239.
Mussel, Patrick, et al. "The Influence Of Affect Induction In The Ultimatum Game On Decision- Making And Feedback-Related Negativity." Neuropsychoeconomics Conference Proceedings (2011): 52.
Asilis, Carlos M. "A Note On The Equivalence Of Time Consistency And Subgame Perfection In Stochastics Games." European Economic Review 39.2 (1995): 245-251.
Greenberg, Joseph, Sudheer Gupta, and Xiao Luo. "Mutually Acceptable Courses Of Action." Economic Theory 40.1 (2009): 91-112.
