Rent-seeking with uncertain discriminatory power

We consider a two-player Tullock rent-seeking contest with uncertain discriminatory power in the contest success function. We examine the cases where both players are either informed or uninformed about the size of the discriminatory power, as well as the case where only one player has private information about it. We show that in all three cases the contest has a unique (Bayesian) Nash equilibrium. In each case we characterize key properties of the equilibrium.     

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.     

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.     

Quality distortions in vertical relations

This paper examines how delivery tariffs and private quality standards are determined in vertical relations that are subject to asymmetric information. We consider an infinitely repeated game where an upstream firm sells a product to a downstream firm. In each period, the firms negotiate a delivery contract comprising the quality of the good as well as a non-linear tariff. Assuming asymmetric information about the actual quality of the product and focusing on incentive compatible contracts, we show that from the firms’ perspective delivery contracts lead to more efficient contracts and thus higher overall profits the lower the firms’ outside options, i.e. the higher their mutual dependency. Buyer power driven by a reduced outside option of the upstream firm enhances the efficiency of vertical relations, while buyer power due to an improved outside option of the downstream firm implies less efficient outcomes.     

Variable temptations and black mark reputations

Reputations often guide sequential decisions to trust and to reward trust. We consider situations where each player is randomly matched with a partner in every period. One player – the truster – decides whether to trust. If trusted, the other player – the temptee – has a temptation to betray. The strength of temptation, private information to the temptee, varies across encounters. Betrayals are recorded as publicly known black marks. First, we identify equilibria when players only condition on the number of a temptee's black marks. Second, we show that conditioning on the number of interactions as well as on the number of black marks does not prolong trust. Third, we examine stochastic variations where black marks may be forgotten. Perhaps surprisingly, such variations do not improve outcomes. Fourth, when players condition on more general summary statistics of a temptee's past, we study equilibria where trust is suspended temporarily.     

Incomplete information in rent-seeking contests

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.     

Signaling in a Rent‐Seeking Contest with One‐Sided Asymmetric Information

We consider a two‐player rent‐seeking Tullock contest where one player has private information about his valuation of the prize, which can be high or low. This player can send a costly signal to his opponent, i.e., he can commit to reduce the prize either by some absolute amount of money or proportionally, conditional on winning it. We show that both kinds of signaling imply completely opposite results for separating equilibria, both in terms of conditions for existence and the type of player who sends the costly signal.     

EFFICIENT MECHANISMS FOR MERGERS AND ACQUISITIONS*

We characterize incentive‐efficient merger outcomes when payments can be made both in cash and stock. Each firm has private information about both its stand‐alone value and a component of the (possibly negative) potential synergies. We study two cases: when transfers can, and cannot, be made contingent on the value of any new firm. When they can, we show that redistributing shares of any nonmerging firm generates information rents and provides necessary and sufficient conditions for the implementability of efficient merger rules. When they cannot, private information undermines efficiency more when it concerns stand‐alone values than synergies. Here, acquisitions emerge as optimal mechanisms.     

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     

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.     

Limited Depth of Reasoning and Failure of Cascade Formation in the Laboratory

We examine the robustness of information cascades in laboratory experiments. Apart from the situation in which each player can obtain a signal for free (as in the experiment by Anderson and Holt (1997) , American Economic Review , 87 (5), 847–862), the case of costly signals is studied where players decide whether or not to obtain private information, at a small but positive cost. In the equilibrium of this game, only the first player buys a signal and makes a decision based on this information whereas all following players do not buy a signal and herd behind the first player. The experimental results show that too many signals are bought and the equilibrium prediction performs poorly. To explain these observations, the depth of the subjects' reasoning process is estimated, using a statistical error-rate model. Allowing for different error rates on different levels of reasoning, we find that the subjects' inferences become significantly more noisy on higher levels of the thought process, and that only short chains of reasoning are applied by the subjects.     

The folk theorem for repeated games with observation costs

The folk theorem literature has been relaxing the assumption on how much players know about each other's past action. Here we consider a general model where players can “buy” precise information. Every period, each player decides whether to pay a cost to accurately observe the actions chosen by other players in the previous period. When a player does not pay the cost, he obtains only imperfect private signals. Observational decisions are unobservable to others. Known strategies such as trigger strategies do not work since they fail to motivate players to pay for information. This paper shows that the folk theorem holds for any level of observation costs. Unlike existing folk theorems with private monitoring, ours imposes virtually no restriction on the nature of costless imperfect signals. The theorem does not use explicit or costless communication, thereby having implications on antitrust laws that rely on evidence of explicit communication. The main message is that accurate observation alone, however costly, enables efficient cooperation in general repeated games.     

Learning in society

In an individual experimentation problem a decision maker learns only from his own experience. It is well known that an optimal experimentation strategy for such problems sometimes results in the best alternative being dropped altogether, which is the so-called “Rothschild effect.” Many experimentation problems of interest, however, involve learning from both individual experience and the experience of others. This paper shows that learning in society can overcome the Rothschild effect. We consider an economy with a continuum of infinitely lived players in which each player faces a multi-armed bandit and in each period a player observes the action choice of another randomly chosen player. We show that social conformity always happens in the long run, and we use this fact to derive a condition on the distribution of prior beliefs that implies that the fraction of players who choose the best alternative always converges to one in the long run.     

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare.We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium.We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.     

Communication in repeated network games with imperfect monitoring

I consider repeated games with private monitoring played on a network. Each player has a set of neighbors with whom he interacts: a player's payoff depends on his own and his neighbors' actions only. Monitoring is private and imperfect: each player observes his stage payoff but not the actions of his neighbors. Players can communicate costlessly at each stage: communication can be public, private or a mixture of both. Payoffs are assumed to be sensitive to unilateral deviations. First, for any network, a folk theorem holds if some Joint Pairwise Identifiability condition regarding payoff functions is satisfied. Second, a necessary and sufficient condition on the network topology for a folk theorem to hold for all payoff functions is that no two players have the same set of neighbors not counting each other.     

Horizontal Mergers Under Asymmetric Information About Synergies

This paper analyses a situation in which there are three quantity‐setting firms, two of which are considering whether or not to merge. When these two firms have private information about the potential cost‐saving synergies of the merger, they may have an incentive to overstate them. This is because if they succeed in making the non‐merging rival firm believe that the synergies are high, the rival firm reduces output and the merger becomes more profitable. Under some conditions, anticipating that the rival will form such a belief, low‐synergy firms that would never merge under complete information will mimic high‐synergy firms by merging. Such pooling behaviour by the merging firms can have a negative impact on social welfare.     

Implementation without incentive compatibility: Two stories with partially informed planners

We consider two stories, Typhoon by Conrad and Traveler's Dilemma by Basu, 1994, Basu, 2007, as implementation problems under incomplete information without incentive compatibility, but where the planner has some private information regarding the state. If social choice functions do not satisfy incentive compatibility, full implementation is unattainable via existing approaches. For each story, we construct a direct mechanism that relies on the planner's private information. We provide a sufficient condition on players' beliefs regarding the state under which every player has a unique rationalizable action, namely, telling the truth. Thus, in these stories, the planner's information can bypass the lack of incentive compatibility.     

外部选择权增加一定会刺激专用性投资吗*——基于云南烟草合同的微观证据

学术界对于外部选择权和专用性投资的关系一直存有争论。产权理论（主要是GHM模型）认为当事人外部选择权增加会提高谈判力,从而提高参与人的专用性投资激励,这是产权成为最重要激励工具的基本逻辑。然而,另一些学者则认为,当参与人外部选择权是紧的时候,外部选择权增加反而会降低参与人的投资激励。这意味着,产权不一定能够提高激励。本文在梳理已有文献争论的基础上,构建理论模型重新定义了外部选择权的范围,并在非合作博弈的框架下,得到与后一部分学者一致的结论：外部选择权的增加反而会降低参与人专用性投资的激励。同时,笔者使用云南烟草合同的微观数据,实证分析了外部选择权和专用性投资之间的关系,发现两者呈负相关关系,这进一步支持了该结论。本文的发现与主流的产权理论有所不同,具有一定的理论贡献和现实意义。     

Horizontal Mergers and Merger Waves in a Location Model

We consider sequential mergers in a spatial model with Cournot competition. This model is suitable for explaining the behaviour of some industries where several brands of the same product are delivered by plants. The automobile and oil product industries are examples. To discuss sequential mergers, we use the method of Nilssen and Sørgard (1998). We show that if the transportation cost per length is large relative to market size, a merger wave occurs. In addition, it might improve social surplus. On the other hand, if the transportation cost per length is relatively small, a merger wave does not occur even though firms would be better off with sequential mergers.
We also compare our model to that of Levy and Reitzes (1992) who consider horizontal mergers with spatial price competition. We show that in a merger of neighbouring firms the merged firm's profit decreases. This result is opposite to that of Levy and Reitzes (1992).
Finally, we consider how a regulator affects sequential mergers. When each merger occurs, the regulator assesses each merger. In this case, there is a possibility that the existence of the regulator deters welfare-improving sequential mergers.     

Dismissals and quits in repeated games

This paper studies repeated games, where player 1 can decide to let the opponent continue or replace her by a new player. We also allow for the possibility of player 2 quitting the game. When only layoffs can occur, a folk theorem for finite horizons obtains due to the threat that termination of the relationship imposes on player 2. However, quits limit this result to those cases in which the outside option for player 2 is small (lower than some Nash equilibrium payoff of the stage game).