From ultimatum to Nash bargaining: Theory and experimental evidence

We consider a sequential two-party bargaining game with uncertain information transmission. When the first mover states her demand she does only know the probability with which the second mover will be informed about it. The informed second mover can either accept or reject the offer and payoffs are determined as in the ultimatum game. Otherwise the uninformed second mover states his own demand and payoffs are determined as in the Nash demand game. In the experiment we vary the commonly known probability of information transmission. Our main finding is that first movers’ and uninformed second movers’ demands adjust to this probability as qualitatively predicted, that is, first movers’ (uninformed second movers’) demands are lower (higher) the lower the probability of information transmission. JEL Classification C72 · C78 · C92     

Subgame perfection in ultimatum bargaining trees

In typical experiments on ultimatum bargaining, the game is described verbally and the majority of subjects deviate from subgame-perfect behavior. Proposers typically offer significantly more than the minimum possible and Responders reject “unfair” offers. In this work, we show that when the ultimatum bargaining game is presented as an abstract game tree, the vast majority of behavior is consistent with individualistic preferences and subgame-perfection. This finding raises doubts about theories that ignore the potential influence of social context and experiments that do not control for social context.     

Quantal-response equilibrium models of the ultimatum bargaining game

This paper investigates the implications of quantal response equilibrium (QRE) models [McKelvey and Palfrey, 1995, Games Econ. Behav. 10, 6–38; 1998, Exper. Econ. 1, 9–41] in the ultimatum bargaining game. It is shown that, in a normal-form QRE (NQRE), each bargainer's decision depends critically on the anticipated behavior of the other, and there is a NQRE in which the proposer makes any offer between zero and equal split as a strict best response. The application of NQRE to the experimental data [Slonim and Roth, 1998, Econometrica 66, 569–596] suggests that the history dependence observed in the experiment is a result of the strategic interactions between bargainers.     

Information acquisition in the ultimatum game: An experimental study

We experimentally investigate if free information disadvantages a player relative to when information is unavailable. We study an Ultimatum game where the Proposer, before making an offer, can obtain free information about the Responder's minimum acceptable offer. Theoretically, the Proposer should obtain the information and play a best reply to the Responder's minimum acceptable offer. Thus the Responder should get the largest share of the surplus. We find that an increasing number of Proposers become informed over time. Moreover, the proportion of Proposers who use the information to maximize money earnings increases over time. The majority of information-acquiring Proposers, however, refuse to offer more than one-half and play a best reply only to Responders who accept offers of one-half or less. This, together with a substantial proportion of Proposers who choose to remain uninformed, means that the availability of free information backfires for Proposers only by a little. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, D63, D80     

Positive- versus zero-sum majoritarian ultimatum games: An experimental study

Politics can involve a movement from a position off the Pareto frontier to a point on it (a positive-sum game as exemplified in the classic [Buchanan, J.M., Tullock, G., 1962. The Calculus of Consent. University of Michigan Press, Ann Arbor] work), or a movement along the Pareto frontier (a zero-sum game as exemplified in the classic [Riker, W., 1962. The theory of political coalitions. Yale University Press, New Haven] work). In this paper we shed light on their differentiation experimentally by making a comparison between a positive-sum and a zero-sum majoritarian ultimatum game. Our main findings include (i) the fraction of subjects who adopted minimum winning rather than oversized coalitions increases significantly as the game form varies from positive-sum to zero-sum, (ii) oversized coalitions are attributable to non-strategic considerations, and (iii) subjects who choose to adopt the minimum winning coalition have a tendency to seek cheaper responders as their partners in the zero-sum game, but there is no evidence of such a tendency in the positive-sum game. Overall, the weight of the evidence revealed by our experimental data indicates that relative scarcity (embodied in the zero-sum game) promotes behavior more in line with the predictions of economics.     

Advice and behavior in intergenerational ultimatum games: An experimental approach

In the real world, when people play a game, they often receive advice from those that have played it before them. Such advice can facilitate the creation of a convention of behavior. This paper studies the impact of advice on the behavior subjects who engage in a non-overlapping generational Ultimatum game where after a subject plays he is replaced by another subject to whom he can offer advice.Our results document the fact that allowing advice fosters the creation of a convention of behavior in Ultimatum games. In addition, by reading the advice offered we conclude that arguments of fairness are rarely used to justify the offers of Senders but are relied upon to justify rejections by Receivers.     

Cognitive ability and human behavior in experimental ultimatum games

Recent researches have shed light on the effect of cognitive ability on economic decision-making. By measuring cognitive ability applying Raven's progressive matrix test, we obtain two significant results that this effect affects decision-making in two types of experimental ultimatum games. First, the higher the cognitive ability, the larger the amount a sender offers when the offer is smaller than or equal to the half split. Second, the higher the responders’ cognitive ability, the smaller the offer they accept, when they accept it or not with the strategy method. This study not only finds new factors that affect decision-making in experimental ultimatum games, but also provides more evidences that cognitive ability influences economic decision-making.     

An analysis of bargaining power for milk cooperatives and milk processors in Florida

The Florida dairy market has a few fluid milk processors and many dairy farmers. The dairy farmers are represented in negotiation with the processors by a cooperative. This research builds a theoretical model of bargaining between the processors and a cooperative. The model is applied to the Florida dairy market to examine price negotiations between Florida milk processors and a dairy cooperative. An expectation maximization (EM) algorithm along with maximum likelihood estimation is used to estimate the econometric disequilibrium model with time series data for the period of October 1998 to May 2009. The results show that the class I price set by the Federal Milk Marketing Order is the major factor influencing the cooperative’s supply reservation price. Negotiated quantity and production seasonality affect the processors’ demand reservation price. The processors appear to be more patient and have higher average bargaining power (0.8804) than the cooperative (0.1196). The highest (lowest) bargaining power for the cooperative (processors) occurred in 2008 and the lowest (highest) bargaining power for the cooperative (processors) occurred in 2001.     

An experimental analysis of moral self-regulation

This article examines the validity of the moral self-regulation hypothesis in a laboratory setting. The experiment is comprised of a public good game preceded or followed by a matrix task. The data show that the recall of an immoral action (cheating in the matrix task) motivates the individual to do morally right thing (contributing to group account) and the recall of a moral action (contributing to group account) motivates the individual to act out self-interest (cheating in the matrix task). Both moral licensing and moral cleansing hypotheses are confirmed by the results of the experiment. Additionally, the findings indicate that the subjects who had been given a chance to cheat ‘at first’ allocated more funds to the group account; and the subjects who had been given a chance to voluntarily contribute ‘at first’ cheated more in the matrix task.     

Indicative bidding: An experimental analysis

Indicative bidding is a practice commonly used in sales of complex and very expensive assets. Theoretical analysis shows that efficient entry is not guaranteed under indicative bidding, since there is no equilibrium in which more qualified bidders are more likely to be selected for the final sale. Furthermore, there exist alternative bid procedures that, in theory at least, guarantee 100% efficiency and higher revenue for the seller. We employ experiments to compare actual performance between indicative bidding and one of these alternative procedures. The data shows that indicative bidding performs as well as the alternative procedure in terms of entry efficiency, while having other characteristics that favor it over the alternative procedure. Our results provide an explanation for the widespread use of indicative bidding despite the potential problem identified in the equilibrium analysis.     

An experimental analysis of the bandit problem

Summary.  We investigate, in an experimental setting, the behavior of single decision makers who at discrete time intervals over an “infinite” horizon may choose one action from a set of possible actions where this set is constant over time, i.e. a bandit problem. Two bandit environments are examined, one in which the predicted behavior should always be myopic (the two-armed bandit) and the other in which the predicted behavior should never be myopic (the one-armed bandit). We also investigate the comparative static predictions as the underlying parameters of the bandit environments are changed. The aggregate results show that the behavior in the two bandit environments are quantitatively different and in the direction of the theoretical predictions. Received: October, 27, 1994; revised version February 27, 1996     

The determinants of multilateral bargaining: a comprehensive analysis of Baron and Ferejohn majoritarian bargaining experiments

Experimental Economics - We analyze the data sets of all majoritarian Baron and Ferejohn (Am Political Sci Rev 83(4):1181–1206, 1989) experiments through 2018. By exploiting the variation of...     

An admissible set occurring in various bargaining situations

Given a set of alternatives S and a binary relation M on S the admissible set of the pair (S, M) is defined to be the set of maximal elements with respect to the transitive closure of M. It is shown that existing solutions in game theory and mathematical economics are special cases of this concept (they are admissible sets of a natural S and M). These include the core of an n-person cooperative game, Nash equilibria of a noncooperative game, and the max-min solution of a two-person zero sum game. The competitive equilibrium prices of a finite exchange economy are always contained in its admissible set. Special general properties of the admissible set are discussed. These include existence, stability, and a stochastic dynamic process which leads to outcomes in the admissible set with high probability.     

An advantage of the bargaining set over the core

An example of a market game is described for which the bargaining set seems to be intuitively more acceptable than the (nonempty) core. It also yields more insight into the nature of the competition that may exist among the traders.     

Corruption and culture: An experimental analysis

Why do some people choose corruption over honesty and others not? Do the social norms and values prevailing in the societies in which they grew up affect their decisions? In 2005, we conducted a bribery experiment and found that, among undergraduates, we could predict who would act corruptly with reference to the level of corruption in their home country. Among graduate students we could not. In 2007, we replicated our result and also found that time spent in the UK was associated with a decline in the propensity to bribe, although this does not explain our inability to predict graduate behaviour. We conclude that, while corruption may, in part, be a cultural phenomenon, individuals should not be prejudged with reference to their country of origin.     

Inter-gender interaction and communication in ultimatum games

In this article, we focus on bargaining within male–female pairs, the most pervasive partnership in humankind. We analyse data from an ultimatum game played by Greek participants. Parallel to this, we introduce a one-way communication protocol according to which the responders can send short messages to the receivers, after making their decisions. The analysis shows that gender and message effects exist and males are more effective bargainers.     

Walrasian bargaining

Given any two-person economy, consider an alternating-offer bargaining game with complete information where the proposers offer prices, and the responders either choose the amount of trade at the offered prices or reject the offer. We provide conditions under which the outcomes of all subgame-perfect equilibria converge to the Walrasian equilibrium (the price and the allocation) as the discount rates approach 1. Therefore, price-taking behavior can be achieved with only two agents.     

Cheap talk with multiple audiences: An experimental analysis

We examine strategic information transmission in a controlled laboratory experiment of a cheap talk game with one sender and multiple receivers. We study the change in equilibrium behavior from the addition of another audience as well as from varying the degree of conflict between the senderʼs and receiversʼ preferences. We find that, as in cheap talk games with just one receiver, information transmission is higher in games with a separating equilibrium, than in games with only a babbling equilibrium. More interestingly, we find clear evidence that the addition of another audience alters the communication between the sender and the receiver in a way consistent with the theoretical predictions. There is evidence of the presence of agents that are systematically truthful as senders and trusting as receivers: deviations from the theoretical predictions, however, tend to disappear with experience, and learning is faster precisely in the games where deviations are more pronounced.     

Implementing quotas in university admissions: An experimental analysis

This paper studies the implementation of quotas in matching markets. In a controlled laboratory environment, we compare the performance of two university admissions procedures that both initially reserve a significant fraction of seats at each university for a special subgroup of students. The first mechanism mimics the sequential procedure currently used by the central clearinghouse for university admissions in Germany. This procedure starts by allocating reserved seats among eligible students and then allocates all remaining seats among those who were not already assigned one of the reserved seats in the first part of the procedure. The second mechanism is based on a modified student-proposing deferred acceptance algorithm in which all seats are allocated simultaneously. In theory, the two mechanisms should lead to similar outcomes. Our experimental results, however, suggest that, relative to the sequential procedure, the simultaneous mechanism significantly improves the match outcomes for the beneficiaries of reserved seats.