Unstructured Bargaining Research Articles

Contracting under asymmetric information and externalities: an experimental study

We investigate contract negotiations in the presence of externalities and asymmetric information in a controlled laboratory experiment. In our setup, it is commonly known that it is always ex post efficient for player A to implement a project that has a positive external effect on player B. However, player A has private information about whether or not it is in player A’s self-interest to implement the project even when no agreement with player B is reached. Theoretically, an ex post efficient agreement can always be reached if the externality is large, whereas this is not the case if the externality is small. We vary the size of the externality and the bargaining process. The experimental results are broadly in line with the theoretical predictions. However, even when the externality is large, the players fail to achieve ex post efficiency in a substantial fraction of the observations. This finding holds in ultimatum-game bargaining as well as in unstructured bargaining with free-form communication.

Initially contestable property rights and Coase: Evidence from the lab

This article investigates how the existence of initially contestable property rights affects the efficiency of the Coase theorem. We design a two-stage experiment that incorporates a stage where property rights are initially allocated to participants followed by a stage that allows bargaining between participants. In stage one, participants endogenously choose rent-seeking effort (and thus the probability) to initially obtain property rights before entering an unstructured bargaining game. We find the presence of costly rent seeking to obtain the property rights makes it significantly less likely that the efficient outcome is reached. We introduce bargaining costs and find that allowing for symmetric bargaining costs has no impact on the likelihood of the efficient outcome being reached, whereas asymmetric bargaining costs – costs that differ if the player wins or loses the initial property rights – substantially reduces the likelihood of reaching an efficient outcome. Our analysis is applicable to contexts with initially contestable and tradable nature resource rights.

Private Information and Dynamic Bargaining in Supply Chains: An Experimental Study

Problem definition: We conduct a controlled human-subjects experiment in a two-tier supply chain where a supplier’s per-unit production cost may be private information while bargaining with a buyer. Academic/practical relevance: Academically, supply chain studies often assume full-information or highly structured bargaining. We consider private information with dynamic, unstructured bargaining. In practice, a buyer may not know its supplier’s cost exactly and interact with its supplier in a back-and-forth bargaining environment. Thus, understanding how a supplier’s private cost information affects both supply chain outcomes and bargaining is new to the literature and relevant to practice. Methodology: We employ insights from mechanism design to generate restrictions on the space of agreements and solve for a specific bargaining solution under private information to generate precise predictions. These predictions are then tested through a human-subjects experiment. Results: In our experiment, theory predicts that all supplier types should earn at least 50% of total profits when their cost information is private. However, we find that high-cost suppliers earn a disproportionately low share of total profits under private information, 20.16%. We show that this is because buyers, under private information, act as if they are bargaining with the lowest-cost supplier and suppliers do not appear to blame buyers for behaving this way. Based on these findings, we conduct an additional experiment where suppliers have the ability to communicate their private costs to buyers and observe that verifiable disclosure significantly increases profits for high-cost suppliers. Managerial implications: High-cost suppliers actually suffer from having their costs as private information, which runs counter to theory. However, if high-cost suppliers can credibly disclose their costs to buyers, they can significantly increase profits. Lastly, although private information does not lead to more disagreements, negotiations do take longer, which can be costly to firms.

On the empirical validity of axioms in unstructured bargaining

We report experimental results and test axiomatic models of unstructured bargaining by checking the empirical relevance of the underlying axioms. Our data support strong efficiency, symmetry, independence of irrelevant alternatives and monotonicity, and reject scale invariance. Individual rationality and midpoint domination are violated by a significant fraction of agreements that implement equal division in highly unequal circumstances. Two well-known bargaining solutions that satisfy the confirmed properties explain the observed agreements reasonably well. The most frequent agreements in our sample are the ones suggested by the equal-division solution. In terms of the average Euclidean distance, the theoretical solution that best explains the data is the deal-me-out solution (Sutton, 1986; Binmore et al., 1989, 1991). Popular solutions that satisfy scale invariance, individual rationality, and midpoint domination, as the well-known Nash or Kalai-Smorodinsky bargaining solutions, perform poorly in the laboratory.

Money or morality: fairness ideals in unstructured bargaining

We augment the Nash bargaining solution by fairness ideals in order to predict the outcomes of unstructured bargaining after the individual production of a joint surplus. If production depends on individual effort, talent, and luck, fairness ideals might be based on the accountability principle. In a lab experiment with real production and unstructured bargaining, we investigate subjects’ fairness ideals, their bargaining behaviour, and the outcomes of the bargaining process. As impartial spectators, about 75% of the subjects hold meritocratic or libertarian fairness ideals. However, these ideals do not affect their bargaining behaviour which is strongly opportunistic. Therefore the fairness-augmented Nash solution with opportunistic fairness ideals predicts the bargaining outcome best.

Dynamic Unstructured Bargaining with Private Information: Theory, Experiment, and Outcome Prediction via Machine Learning

We study dynamic unstructured bargaining with deadlines and one-sided private information about the amount available to share (the “pie size”). Using mechanism design theory, we show that given the players’ incentives, the equilibrium incidence of bargaining failures (“strikes”) should increase with the pie size, and we derive a condition under which strikes are efficient. In our setting, no equilibrium satisfies both equality and efficiency in all pie sizes. We derive two equilibria that resolve the trade-off between equality and efficiency by favoring either equality or efficiency. Using a novel experimental paradigm, we confirm that strike incidence is decreasing in the pie size. Subjects reach equal splits in small pie games (in which strikes are efficient), while most payoffs are close to either the efficient or the equal equilibrium prediction, when the pie is large. We employ a machine learning approach to show that bargaining process features recorded early in the game improve out-of-sample prediction of disagreements at the deadline. The process feature predictions are as accurate as predictions from pie sizes only, and adding process and pie data together improves predictions even more.Data are available at https://doi.org/10.1287/mnsc.2017.2965 .This paper was accepted by Uri Gneezy, behavioral economics.

How Are Individual Time Preferences Aggregated in Groups? A Laboratory Experiment on Intertemporal Group Decision-Making

The study of intertemporal decision-making is an interdisciplinary scientific topic of economics, psychology, and neuroscience. Most of these studies focus on individual intertemporal decisions, but little is known about the relationship between groups and individual time preferences. As a result, we aim to assess the role of group intertemporal decision-making. We experimentally investigate how to aggregate individual time preferences by clarifying who has the most influence on group decisions among heterogeneous group members. We formulate two hypotheses. The first is the multilateral bargaining hypothesis, which is based on the multilateral bargaining model. If people employ this model to reach agreement, the most patient member in a group has the greatest impact on group choices. The second is the median voter hypothesis, which is based on the median voter model. When people employ this model to reach agreement, the median patient member in a group has the greatest impact on group choices. Here, we find that the median patient member in a group has a significant impact on group decisions in an unstructured bargaining situation. This finding suggests that people use the majority voting rule during group intertemporal decision-making. Thus, our findings support the median voter hypothesis. Furthermore, the results of a chat analysis show that this result is partially due to people’s conformity with the majority opinion.

How fully do people exploit their bargaining position? The effects of bargaining institution and the 50–50 norm

A recurring puzzle in bargaining experiments is that individuals under-exploit their bargaining position, compared to theoretical predictions. We conduct an experiment using two institutions: Nash demand game (NDG) and unstructured bargaining game (UBG). Unlike most previous experiments, disagreement payoffs are earned rather than assigned, and about one-fourth of the time, one bargainer's disagreement payoff is more than half the cake size (“dominant bargaining power”), so that equal splits are not individually rational.Subjects under-respond to their bargaining position most severely in the NDG without dominant bargaining power. Responsiveness increases in the UBG, but is still lower than predicted; the same is true for the NDG with dominant bargaining power. Only in the UBG with dominant bargaining power – the combination of a bargaining institution with low strategic uncertainty and elimination of the 50–50 “security blanket” – do subjects approximately fully exploit their bargaining position.

Efficiency in Auctions with (Failed) Resale

We analyze how the possibility of resale affects efficiency in multi-object uniform-price auctions with asymmetric bidders using a combination of theory and experiments. The resale market is modeled as an unstructured bargaining game between auction bidders. Our experimental design consists of four treatments that vary the (exogenous) probability that bidders participate in a resale market after the auction. In all treatments, the possibility of resale increases efficiency after the auction, but it also induces demand reduction by high-value bidders during the auction, which reduces auction efficiency. In contrast to what is usually argued, resale does not necessarily increase final efficiency. When there is a low probability of a resale market, final efficiency is actually lower than in an auction without resale.

Unstructured Bargaining Over an Endogenously Produced Surplus and Fairness Ideals An Experiment

Fairness considerations are important determinants of behavior in unstructured bargaining situations with equal bargaining power. If the surplus over which the bargaining takes place was created by separate, individual efforts, several entitlement related fairness ideals might be relevant. In our experiment we first elicit subjects’ fairness ideals using a questionnaire. In the following production phase each player generates output by luck, individual effort and talent. We analyze whether the elicited fairness ideals guide subjects’ behavior in the subsequent bargaining in which the joint output is distributed among two individuals. We find that bargaining claims deviate significantly from the elicited fairness ideals and are strongly related to performance if one individual had produced more than the partner. These findings contrast the previous literature on fairness ideals and enrich the findings on self-serving fairness.

Predicting Behavior in Unstructured Bargaining with a Probability Distribution

In experimental tests of human behavior in unstructured bargaining games, typically many joint utility outcomes are found to occur, not just one. This suggests we predict the outcome of such a game as a probability distribution. This is in contrast to what is conventionally done (e.g, in the Nash bargaining solution), which is predict a single outcome. We show how to translate Nash's bargaining axioms to provide a distribution over outcomes rather than a single outcome. We then prove that a subset of those axioms forces the distribution over utility outcomes to be a power-law distribution. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However, in general these modes of the joint utility distribution are not the experimentalist's Bayes-optimal predictions for the joint utility. Nor are the bargains corresponding to the modes of those joint utility distributions the modes of the distribution over bargains in general, since more than one bargain may result in the same joint utility. After introducing distributional bargaining solution concepts, we show how an external regulator can use them to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System. We emphasize that while our results are formulated for unstructured bargaining, they can also be used to make predictions for noncooperative games where the modeler knows the utility functions of the players over possible outcomes of the game, but does not know the move spaces the players use to determine those outcomes.

How sensitive are bargaining outcomes to changes in disagreement payoffs?

We use a human-subjects experiment to investigate how bargaining outcomes are affected by changes in bargainers’ disagreement payoffs. Subjects bargain against changing opponents, with randomly drawn asymmetric disagreement outcomes that vary over plays of the game, and with complete information about disagreement payoffs and the cake size. We find that subjects only respond about half as much as theoretically predicted to changes in their own disagreement payoff and to changes in their opponent’s disagreement payoff. This effect is observed in a standard Nash demand game and a related unstructured bargaining game, in both early and late rounds, and is robust to moderate changes in stake sizes. We show theoretically that standard models of expected utility maximisation are unable to account for this under-responsiveness, even when generalised to allow for risk aversion. We also show that quantal-response equilibrium has, at best, mixed success in characterising our results. However, a simple model of other-regarding preferences can explain our main results.

A Theory of Unstructured Bargaining Using Distribution-Valued Solution Concepts

In experimental tests of human behavior in unstructured bargaining games, typically many joint utility outcomes are found to occur, not just one. This suggests we predict the outcome of such a game as a probability distribution. This is in contrast to what is conventionally done (e.g, in the Nash bargaining solution), which is predict a single outcome. We show how to translate Nash’s bargaining axioms to provide a distribution over outcomes rather than a single outcome. We then prove that a subset of those axioms forces the distribution over utility outcomes to be a power-law distribution. Unlike Nash’s original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However, in general these modes of the joint utility distribution are not the experimentalist’s Bayes-optimal predictions for the joint utility. Nor are the bargains corresponding to the modes of those joint utility distributions the modes of the distribution over bargains in general, since more than one bargain may result in the same joint utility. After introducing distributional bargaining solution concepts, we show how an external regulator can use them to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System. We emphasize that while our results are formulated for unstructured bargaining, they can also be used to make predictions for noncooperative games where the modeler knows the utility functions of the players over possible outcomes of the game, but does not know the move spaces the players use to determine those outcomes.

Does it Take Three to Make Two Happy? An Experimental Study on Bargaining with Mediation

Mediation is a conflict resolution method in which a third neutral party provides assistance to the conflict parties. The process of mediation, as well as any solution to the conflict arising from it, is implemented only by the consent of all conflict parties. It is the role of a mediator to stimulate communication that leads to mutual understanding of the feasible conflict outcomes, i.e., to complete information on solution consequences among the parties of the conflict. This information is used by the parties of the conflict to evaluate their own, as well as the others consequences of a proposed solution to the conflict. However, it is not clear whether the information itself, or the way it was obtained (by voluntary participation in a process in which it was collected), leads to a conflict resolution. This paper concentrates on the bargaining behavior in a conflict, abstracting from the mediators methods and techniques. We design an experiment where two-person conflicts are resolved in an unstructured bargaining and study whether the way of obtaining information on the relative payoffs influences the conflict resolution process. We also study the demand for such information by individuals with various types of social preferences. This allows us to address the role of self-selection in the mediation process.

A Suggested Interpretation of Some Experimental Results on Preplay Communication

M. Rabin (1994, J. Econ. Theory63, 370–391) proposes a model of behavior in two-person complete-information games with preplay communication, using non-equilibrium notions in the spirit of rationalizability to derive lower bounds on players' expected payoffs when players have unlimited communication opportunities. This paper adapts Rabin's model so that it can be used to analyze the results of the experiments of R. Cooper et al. (1989, Rand J. Econ.20, 568–587) on structured preplay communication in the Battle of the Sexes and the results of the unstructured bargaining experiments of Roth, Malouf, and Murnighan. Adding empirically motivated restrictions that allow the model to predict the payoff effects of changes in bounded communication possibilities like those in the experiments, it is shown that the data from both experiments are generally consistent with Rabin's model, and with the predictions of the extended model. Journal of Economic Literature Classification Numbers: C70, C72, C78, C91.