Asymmetric Information in Simple Bargaining Games: An Experimental Study

Bilateral bargaining situations are often characterized by informational asymmetries concerning the size of what is at stake: in some cases, the proposer is better informed, in others, it is the responder. We analyze the effects of both types of asymmetric information on proposer behavior in two different situations which allow for a variation of responder veto power: the ultimatum and the dictator game. We find that the extent to which proposers demand less in the ultimatum as compared to the dictator game is (marginally) smaller when the proposer is in the superior information position. Further we find informed proposers to exploit their informational advantage by offering an amount that does not reveal the true size of the pie, with proposers in the ultimatum game exhibiting this behavioral pattern to a larger extent than those in the dictator game. Uninformed proposers risk imposed rejection when they ask for more than potentially is at stake, and ask for a risk premium in dictator games. We concentrate on proposers, but also explore responder behavior: We find uninformed responders to enable proposers’ hiding behavior, and we find proposer intentionality not to play an important role for informed responders when they decide whether to accept or reject an offer by an (uninformed) proposer.     

外部选择与关系专用性投资激励——基于GHM模型的研究

现实中的契约总是不完全的,当自然状态被参与人观察到之后,为了保证交易有效率,通常会对事前契约进行再谈判.首先,论文研究了事后再谈判时参与人的外部选择对事后合作租金的分配影响及事前关系专用性投资激励问题;其次,根据外部选择是否具有约束力,将外部选择区分为威胁点和现状点.研究结果显示:当外部选择为现状点时,不完全契约会导致事前关系专用性投资不足;而如果事后外部选择为威胁点时,投资方会作出有效率投资或投资过度     

Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis

This paper reports the findings of a meta-analysis of 37 papers with 75 results from ultimatum game experiments. We find that on average the proposer offers 40% of the pie to the responder. This share is smaller for larger pie sizes and larger when a strategy method is used or when subjects are inexperienced. On average 16% of the offers is rejected. The rejection rate is lower for larger pie sizes and for larger shares offered. Responders are less willing to accept an offer when the strategy method is employed. As the results come from different countries, meta-analysis provides an alternative way to investigate whether bargaining behavior in ultimatum games differs across countries. We find differences in behavior of responders (and not of proposers) across geographical regions. With one exception, these differences cannot be attributed to various cultural traits on which for instance the cultural classifications of Hofstede (1991) and Inglehart (2000) are based.     

Fairness, errors and the power of competition

In this paper, we investigate the effects of competition on bargained outcomes. We show that the neglect of either fairness concerns or decision errors will prevent a satisfactory understanding of how competition affects bargaining. We conducted experiments which demonstrate that introducing a small amount of competition to a bilateral ultimatum game – by adding just one competitor – induces large behavioral changes among responders and proposers, causing large changes in accepted offers. Models that assume that all people are self-interested and fully rational do not adequately explain these changes. We show that a model which combines heterogeneous fairness concerns with decision errors correctly predicts the comparative static effects of changes in competition. Moreover, the combined model is remarkably good at predicting the entire distribution of offers in many different competitive situations.     

BETTER LATER THAN NEVER? AN EXPERIMENT ON BARGAINING UNDER ADVERSE SELECTION

A central result in the literature on bargaining with asymmetric information is that the uninformed party (buyer) can screen the informed party (seller) over time. Screening eliminates trade failures that are otherwise common in the presence of adverse selection, but the downside of the bargaining institution is the cost associated with repeated offers and time frictions. This article reports an experimental test of these predictions. We find that rates of trade are substantially higher in the bargaining institution than in control treatments in which we remove the possibility to make repeated offers (take‐it‐or‐leave‐it offer) or the time frictions. However, we also observe a persistent overdelay before agreements are reached, that is, bargaining takes longer than theoretically predicted. This lowers efficiency below its predicted level and below the level observed in the take‐it‐or‐leave‐it offer institution. We identify possible channels for overdelay in the form of fairness preferences and loss aversion, concluding that there are important behavioral deviations from the standard model that are detrimental to the efficiency of bargaining under incomplete information.     

Randomly available outside options in bargaining

We consider an extension of the standard Rubinstein model where both players are randomly allowed to leave the negotiation after a rejection, in which case they obtain a payoff of known value. We show that, when the value of the outside opportunities is of intermediate size, there exist a continuum of subgame-perfect equilibrium outcomes, including some with delayed agreements. Considering outside opportunities of significant value, we prove that efficient delays arise caused by the bargainers' aspirations, in waiting for their outside, option rather than by threats. Moreover, if taking the outside option decreases the probability that the opponent receives an outside option in the future, then it is possible that exactly two equilibrium payoffs coexist. In this latter case, inefficiencies may be created by agreeing too early.     

On the Non-Existence of Redundant Options

In a seminal paper, Ross (Q J Econ 90:75–89, 1976) shows that if security markets are resolving, then there exist (non-redundant) options that generate complete security markets. Complementing his work, Aliprantis and Tourky (2002) show that if security markets are strongly resolving and the number of primitive securities is less than half the number of states, then every option is non-redundant. Our paper extends Aliprantis and Tourky’s result to the case when their condition on the number of primitive securities is not imposed. Specifically, we show that if there exists no binary payoff vector in the asset span, then for each portfolio there exists a set of exercise prices of full measure such that any option on the portfolio with an exercise price in this set is non-redundant. Since the condition that there exists no binary payoff vector in the asset span holds generically, redundant options are thus rare. I am grateful to an anonymous referee for very helpful comments. Research support from the School of Business at The George Washington University is gratefully acknowledged     

The dynamics of responder behavior in ultimatum games: a meta-study

Using data aggregated from seven papers that study repeated play in standard ultimatum games with either stranger or absolute stranger matching, we show that the behavior of responders changes with experience. High offers are more likely to be accepted with experience and low offers are more likely to be rejected. At the individual level, there is a negative relationship between the likelihood that a given offer is accepted and the size of the preceding offer. We compare the results with predictions generated by static models of distributional preferences, implicitly dynamic models of preferences with reciprocity, and explicitly dynamic models of adaptive learning. The data is most consistent with models of preferences with reciprocity.     

Information Revelation and Market Incompleteness

This paper introduces a theory of market incompleteness based on the information transmission role of prices and its adverse impact on the provision of insurance in financial markets. We analyse a simple security design model in which the number and payoff of securities are endogenous. Agents have rational expectations and differ in information, endowments, and attitudes toward risk. When markets are incomplete, equilibrium prices are typically partially revealing, while full relevation is attained with complete markets. The optimality of complete or incomplete markets depends on whether the adverse selection effect (the unwillingness of agents to trade risks when they are informationally disadvantaged) is stronger or weaker than the Hirshleifer effect (the impossibility of trading risks that have already been resolved), as new securities are issued and prices reveal more information. When the Hirshleifer effect dominates, an incomplete set of securities is preferred by all agents, and generates a higher volume of trade.     

Prosecutorial Resources, Plea Bargaining, and the Decision to Go to Trial

This article examines the strategic interaction between a defendantand a prosecutor during the plea bargaining process. A four-stagegame of incomplete information is developed where the defendant'sguilt or innocence is private information but the amount ofresources available to the prosecutor is common knowledge. Thebasic result of the article is that equilibrium is semiseparating;the plea offer is accepted by a proportion of the guilty defendantsand is rejected by all of the innocent defendants and the remainingguilty defendants. In this model an increase in the resourcesavailable to the prosecutor increases the proportion of guiltydefendants who accept plea offers. Although the prosecutor isunable to generate complete separation of the guilty and innocentdefendants through the plea bargaining process, prosecutorialresources are beneficial from a societal standpoint.     

A risk index to model uncertain portfolio investment with options

This paper models the portfolio investment performance with options by using a risk index, which is defined as the average loss below the risk-free interest rate. Using a risk-free interest rate as the uniform reference rate for all portfolios, the risk index offers an easier-to-compare loss value than the value-at-risk return, where portfolio specific references are used to calculate the average losses. Besides, uncertainty theory is used in the paper to derive the portfolio decision when stock prices are subject to experts' estimations. By analytical computation and empirical analysis, we find that portfolios considering options generate better return than the ones without options. The empirical analysis reveals that the options can effectively hedge the risk, and the call option with a higher exercise price offers higher return per unit of option premium. Furthermore, our proposed model produces higher expected return in most cases than the model where the risk is measured by the chance of the total return failing to reach the threshold level of return.     

The role of optimal threats in auction design

This paper studies revenue-maximizing auctions when buyers' outside options depend on their private information and are endogenously chosen by the seller. We show that the revenue-maximizing assignment of the object can depend crucially on the outside options that the seller can choose as threats. Depending on the shape of outside options, sometimes an optimal mechanism allocates the object in an ex-post efficient way, and, other times, buyers obtain the object more often than is efficient.     

Coordination,timing and common knowledge

There is tight link between coordination and common knowledge. The role of higher order beliefs in static incomplete information games has been widely studied. In particular, information frictions break down common knowledge. A large body of literature in economics examine dynamic coordination problems when there are timing frictions, in the sense that players do not all move at once. Timing frictions in dynamic coordination games play a role that is closely analogous to information frictions in static coordination games.This paper makes explicit the role of higher order beliefs about timing in dynamic coordination games with timing frictions. An event is said to be effectively known if a player knew the event when he last had an option to change his behavior. The lack of effective common knowledge of the time drives results of dynamic coordination games.     

An investment game with third-party intervention

This paper explores the effect of the possibility of third-party intervention on behavior in a variant of the Berg et al. [Berg, J., Dickhaut, J., McCabe, K., 1995. Trust, reciprocity and social history. Games and Economic Behavior 10, 122–142] “Investment Game”. A third-party's material payoff is not affected by the decisions made by the other participants, but this person may choose to punish a responder who has been overly selfish. The concern over this possibility may serve to discipline potentially selfish responders. We also explore a treatment in which the third party may also choose to reward a sender who has received a low net payoff as a result of the responder's action. We find a strong and significant effect of third-party punishment in both punishment regimes, as the amount sent by the first mover is more than 60% higher when there is the possibility of third-party punishment. We also find that responders return a higher proportion of the amount sent to them when there is the possibility of punishment, with this proportion slightly higher when reward is not feasible. Finally, third parties punish less when reward is feasible, but nevertheless spend more on the combination of reward and punishment when these are both permitted than on punishment when this is the only choice for redressing material outcomes.     

Screening in a Matching Market

Contract design under incomplete information is often analysed in a bilaterally monopolistic setting. If the informed party's reservation value does not depend on its private information (its type), it is a standard result that the uninformed side offers "low" types distorted contracts to reduce the information rent left to "high7rdquo; types.
We challenge this result by embedding contract design in a matching market environment. We consider a market where players meet pairwise and where, in each match, either side may be chosen to make a take-it-or-leave-it offer. As frictions become sufficiently low, we find that the set of equilibria is independent of whether there is complete or incomplete information. In particular, all contracts are free of distortions.     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

Laboratory Testbeds and Non-Market Valuation: The Case of Bidding Behavior in a Second-Price Auction with an Outside Option

Researchers now use the lab to examine the behavioral underpinnings of valuation before the field application which some argue has less experimental control. But lab valuation work raises its own set of concerns when it uses private goods to explore non-market valuation behavior because private goods have substitutes often unaccounted for in the lab. Therefore, the lab as a tool to testbed field valuation work may be limited. Herein we design an induced valuation experiment to explore bidding behavior in a second-price auction with an outside option that is a perfect substitute for the auction commodity. Theory predicts that rational bidders will consider the prices of outside options when formulating bidding strategies, and will reduce their bids whenever their resale value exceeds the price of the outside option. Our results suggest that bidders account for outside options when formulating bids with behavior following comparative static predictions. In addition, we provide evidence concerning hypothetical versus actual behavior with induced values – the data suggesting a hypothetical bias in the level of bids but not in bid shaving.     

Bidding for Firms with Unknown Characteristics

When a region successfully attracts a firm by offering subsidies, the firm often commits itself to performance targets in terms of employment. In this paper, we interpret these firm‐specific targets as a consequence of incomplete information. We analyze a model of two regions that compete for a firm, assuming that the firm's productivity is ex ante unknown. We show that performance targets often induce overemployment in high‐productivity firms, and that tax credits are often superior to lump‐sum payments. Moreover, when regions differ in wage rates, the low‐wage region wins the bid and has a higher surplus than under complete information. Finally, we show that, under incomplete information, bidding might not lead to efficient firm location.     

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.     

‘To sell or not to sell’: Licensing versus selling by an outside innovator

We study various modes of technology transfer of an outside innovator in a spatial framework when the potential licensees are asymmetric. In addition to different licensing options, we also look into the option of selling the property rights of innovation and find the optimal mode of technology transfer. For licensing we find the optimal policy is to offer pure royalty contracts to both licensee firms when cost differentials between the firms are relatively small compared to the transportation cost, otherwise offer a fixed fee licensing contract to the efficient firm only. Interestingly, we show the innovator is always better-off selling the innovation to any one of the firms who further licenses it to the rival firm. The result holds irrespective of the size of the innovation (drastic or non-drastic) and the degree of cost asymmetry between the licensees. Social welfare is greater under selling than licensing.