Ultimatum Bargaining Game Research Articles

Initial Ownership in Bargaining: Introducing the Giving, Splitting, and Taking Ultimatum Bargaining Game

In three experiments, the authors studied the role of initial ownership of property in bargaining behavior. For this purpose, they created three new variations of the Ultimatum Bargaining Game (UBG): giving, splitting, and taking UBGs. On the basis of insights of loss aversion and the do-no-harm principle, the authors predicted and found that allocations to the recipient were highest in the taking UBG and lowest in the giving UBG. Additional measures to study the underlying mechanism of this effect indicate that the game type effect was mediated by perceptions of entitlement, which allocators did not want to infringe on. Moreover, the effect was not affected by strategic options as provided by deception or power.

The Importance of Foregone Options: Generalizing Social Comparisons in Sequential-Move Games

Recent experimental evidence supports the influence of a player's unchosen alternatives on other agent's actions. This paper examines a tractable theoretical model of reference-dependent preferences in which individuals compare other players' chosen action with respect to their unchosen alternatives. We analyze the equilibrium prediction in complete information sequential-move games, and compare it with that of standard games where players are not concerned about unchosen alternatives. We show that, without relying on interpersonal payoff comparisons (i.e., with strictly individualistic preferences), our model predicts higher cooperation among the players than standard game-theoretic models. In addition, our framework embodies different models from the literature on social status acquisition and intentions-based reciprocity as special cases. Finally, we confirm our results in three economic applications: the ultimatum bargaining game, the labor market gift exchange game, and the sequential public good game.

Too Good to Be True - Suspicion-Based Rejections of Ultimatum Offers

Prior research on negotiation and especially ultimatum bargaining has shown that fear of rejection may induce bargainers make high offers. In the current study we show that there is a limit to the beneficial effects of making high offers and that becoming to generous may backfire. participants were recipients in a variant of the Ultimatum Bargaining Game (UBG) in which only the allocator knew the amount of money that had to be distributed. The allocator then informed the participant that the pot contained 12 euros and offered the recipient either 5 euros (self-serving offer), 6 euros (equal offer), or 7 euros (altruistic offer). Results showed that altruistic offers roused more suspicion about the ommunicated pot size than self-serving and equal offers. Moreover, participants rejected self-serving and altruistic offers more often than equal offers. Subsequent analyses showed that these effects were explained by raised suspicion. Taken together, these results show that recipients in an UBG reject offers when they feel exploited and support our reasoning that bargainers may become suspicious that they are exploited when an altruistic offer appears too good to be true.

The Role of Fairness and Self-Interest in Positive and Negative Valence Ultimatum Bargaining

In this article we investigate the behavior and motives of people in a positive and negative valence Ultimatum Bargaining Game (UBG). In this last game the allocator and recipient both have the same initial endowment and bargain about how to divide a certain loss. In Experiment 1 we show by means of a word completion task, that the justice concept was more salient in the negative valence UBG than in the positive valence UBG. In Experiment 2 we studied the behavior and motives of allocators. We show that allocators in the negative valence UBG allocated more to the recipient than allocators in the positive valence UBG. Additionally, the influence of self-interest and fairness fully mediated this effect. Taken together, we show that ultimatum bargaining situation about losses is not the same as bargaining about gains. We explain our results in terms of the 'Do-no-harm'-principle (Baron, 1996).

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.

Examining the impact of relative standing using an ultimatum bargaining game experiment

This paper presents the results of an experiment designed to examine the extent to which a decision-maker's relative standing affects bargaining behaviour. In each session, 14 participants played a series of one-shot ultimatum bargaining games. In one treatment, the participants were made aware of only their own cumulative outcome rank as they started each new game, while in a second treatment both their own rank and the rank of their bargaining partner was known. The results indicate relative standing does affect bargaining behaviour, particularly when the decision-maker knows both his own rank and the rank of the bargaining partner. A primary finding is that the provision of relative standing information can enhance well-being because it promotes the formation of mutually beneficial bargaining agreements.

Dependency and Deception in Ultimatum Bargaining

In two experiments we studied the relation between dependency and deception in the ultimatum bargaining game. Participants could deceive the other player about the value of the chips they bargained over. Dependency was manipulated by manipulating the consequences of rejecting a proposal for both parties. In one condition the share of the allocator was decreased by 90% when the proposal was rejected, while the share of the recipient was only decreased by 10%. In the other condition these values were reversed. In our first experiment all participants were assigned the role of recipient. Results showed that recipients deceived more often when they were high dependent. This finding was replicated in our second experiment in which participants were either recipient or allocator. Allocators did not deceive more often when they were high dependent, but offered more chips to the recipient instead. The results are discussed in terms of the instrumentality of deception.

AN EXPERIMENT WITH ULTIMATUM BARGAINING IN A CHANGING ENVIRONMENT*

We present experimental results on the ultimatum bargaining game which support an evolutionary explanation of subjects' behaviour in the game. In these experiments subjects interacted with each other and also with virtual players, i.e. computer programs with prospecified strategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behaviour closer to the subgame-perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behaviour of real subjects depending on the type of "mutants" (virtual players) that were present in their environment. © Japanese Economic Association 2005.

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.

Punishment as a public good. When should monopolists care about a consumer boycott?

The usual analysis of monopolistic markets focuses merely on the seller's behavior. In this paper, we interpret the relationship between seller and buyers as a multiple Ultimatum Bargaining Game. We show that a profit maximizing monopolist may not sell at Cournot Price. When buyers are committed to reject price offers leading to an unfair split of the surplus, a monopolist will have to reduce the sales price substantially. However, as the number of consumers increases the common propensity to punish a monopolist for charging Cournot Prices is similar to the private provision of a public good. Therefore, in the case of many consumers, price taking behavior might emerge unless there are strong enough solidarity motives among the consumers.

Satisficing and fairness in ultimatum bargaining game experiments

We re-examine the subjects’ behavior in the ultimatum bargaining experiments studied by Roth et al. (1991, American Economic Review). In our model, un-modeled factors including rationality determine players’ initial aspirations, and a modified version of the case-based learning process governs subsequent adaptations. The calibration results of this paper show that ‘satisficing’ can explain the actual subjects’ behavior surprisingly well. More precisely, it is shown that 77.7% to 96.7% of the observed behavior is consistent with our model prediction. We also argue that the closer the initial aspiration levels are to the perfect equilibrium payoff, the lower the mean or modal offer tends to be in the actual experiments.

Maximizing versus satisficing: Happiness is a matter of choice.

Can people feel worse off as the options they face increase? The present studies suggest that some people--maximizers--can. Study 1 reported a Maximization Scale, which measures individual differences in desire to maximize. Seven samples revealed negative correlations between maximization and happiness, optimism, self-esteem, and life satisfaction, and positive correlations between maximization and depression, perfectionism, and regret. Study 2 found maximizers less satisfied than nonmaximizers (satisficers) with consumer decisions, and more likely to engage in social comparison. Study 3 found maximizers more adversely affected by upward social comparison. Study 4 found maximizers more sensitive to regret and less satisfied in an ultimatum bargaining game. The interaction between maximizing and choice is discussed in terms of regret, adaptation, and self-blame.

Fairness and Rejection in the Ultimatum Bargaining Game

The ultimatum game is a standard instrument for laboratory experimentalists. It has been replicated in a large number of environments and points to special considerations for fairness. Although it has been popular in the experimental community, researchers have not harnessed all the statistical power they should to evaluate the dynamics at work in this type of a bargaining game. This research uses two planned treatments, the first involving a signaling condition concerning a subject's “type”, and the second a price effect built into the structure of the game. We find that there are no significant main effects as a result of the signaling condition of a subject's type, but that there are strong effects as a result of the different payoff parameters. Using a variety of multivariate models we find important, nonobvious interactions with the gender of the subjects. The lesson that we take away from this research is that experimentalists can learn more from data collected in the tightly controlled laboratory environment by using statistical techniques that complement their research designs.

Rationality and Emotions in Ultimatum Bargaining

The Ultimatum Bargaining paradigm is often thought of as a demonstration of extreme disagreement between experimental evidence and 'game theoretical predictions' and the basic assumption of rationality from which they are derived. Using the data of four experiments on Ultimatum Bargaining which I am involved in, I argue that, quite differently from this general impression, rationality in the sense of self-interested motives, is very much present in the observed behavior of both proposers and responders in the Ultimatum Bargaining game. Part of the argument calls for a broader interpretation of the notion of rationality than just imme- diate money maximization and the backward induction argument.

Framing the Game: Examining Frame Choice in Bargaining

This article introduces the study of frame choice in negotiation. Here, the selection of a procedural frame is treated as a dependent variable—a choice that bargainers make in addition to determining their offers. The empirical focus of the article is on whether, when given a choice between two alternative versions of the ultimatum bargaining game, negotiators choose the description that maximizes their expected payoffs. For example, in one frame-choice task, negotiators assigned to the Player 1 role were asked to select between framing the game as “Player 1 proposes a division and Player 2 accepts or rejects it” or “Player 1 makes a claim from a common pool and Player 2 makes a counterclaim.” Past research has shown that the second frame leads to higher expected payoffs for Player 1 than does the first. Across four studies and three established framing effects, it is found that participants consistently fail to select the procedural frames that optimize monetary outcomes. Subsequent analyses suggest that this tendency is due to two factors: (a) nonmonetary motivations, such as fairness and respect, that influence frame-choice preferences and (b) cognitive limitations that inhibit the ability to accurately predict the effect of alternative procedural frames on opponents' responses

Learning in High Stakes Ultimatum Games: An Experiment in the Slovak Republic

This paper reports an experiment involving an ultimatum bargaining game, played in the Slovak Republic. Financial stakes were varied by a factor of 25, and behavior was observed both when players were inexperienced and as they gained experience. Consistent with prior results, changes in stakes had only a small effect on play for inexperienced players. But the present experimental design allows us to observe that rejections were less frequent the higher the stakes, and proposals in the high stakes conditions declined slowly as subjects gained experience. This Slovak experiment is the first to detect a lower frequency of rejection when stakes are higher and this can be explained by the added power due to multiple observations per subject in the experimental design. A model of learning suggests that the lower rejection frequency is the reason that the proposers in the higher stakes conditions of the ultimatum game learn to make lower offers.

The effects of relationships and justification in an interdependent allocation task

Two factors, the type of relationship between the involved parties and the justification of the decision maker for being in his or her position, are predicted to influence resource allocation decisions. These predictions are based on a synthesis of several forces, including self-interest, a politeness norm, and a norm of reciprocity, that we argue underlie the selection of allocation norms that guide interdependent resource allocation decisions. An ultimatum bargaining game, in which player 1 divides a resource ($10) and player 2 decides to either reject or accept this division, is employed in a laboratory study to test the hypotheses. For subjects in the player 1 position, subjects with friends as player 2 or those assigned to their position randomly allocated lower amounts of money to themselves than did subjects with strangers as player 2 or those who earned their position. Friends in the player 2 position demanded significantly less to reach an agreement than strangers. These and other results are discussed in terms of the various allocation norms, particularly equity and equality, that appeared to influence subjects' decisions.

Ultimatum bargaining behavior: A survey and comparison of experimental results

In an ultimatum bargaining game players 1 and 2 can distribute a positive amount of money in the following way: first, player 1 determines his demand which player 2 can then either accept or induce conflict, i.e. player 2 faces the ultimatum either to accept player 1's proposal or to have no agreement at all. Experimentally observed ultimatum bargaining decisions with amounts ranging from 0.50 to 100 German marks are statistically analysed. The demands of player 1 are compared with the acceptance behavior of player 2 with the help of consistency tests in which a subject has to decide in the position of both players. Finally, we consider ultimatum bargaining games with more than just one round where, except for the final round, nonacceptance does not cause conflict but another round of ultimatum bargaining for a smaller cake.

Entitlements, Rights, and Fairness: An Experimental Examination of Subjects' Concepts of Distributive Justice

THE research reported in this paper arose from a previous experimental study conducted by the authors.' That study involved bargains struck between two subjects who had opposing payoff functions and full information of one another's payoffs. By a flip of a coin one participant could choose a noncooperative outcome, unilaterally: the winner of the coin toss could simply choose an outcome which gave him $12 and left the other subject nothing, whether or not the loser agreed. However, if the two subjects cooperated, they could obtain from the experimenter $14, which could be split between the subjects in any mutually agreed-on manner. Cooperative game theory predicts that the subjects will cooperate and divide the rewards $13 to $1 (the Nash bargaining solution: an even division of the $2 gain from trade). Under no circumstances should the winner of the coin flip settle for less than $12, according to game