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This paper presents an empirical model of sponsored search auctions in which advertisers are ranked by bid and ad quality. We introduce a new nonparametric estimator for the advertiser's ad value and its distribution under the 'incomplete information' assumption. The ad value is characterized by a tractable analytical solution given observed auction parameters. Using Yahoo! search auction data, we estimate value distributions and study the bidding behavior across product categories. We find that advertisers shade their bids more when facing less competition. We also conduct counterfactual analysis to evaluate the impact of score squashing (ad quality raised to power θ < 1) on the auctioneer's revenue. Our results show that product-specific score squashing can enhance auctioneer revenue at the expense of advertiser profit and consumer welfare.

Usury is a frequent occurrence in consumer credit markets and particularly affects low-income households. Although the term usury conjures images of a greedy individual consciously acting to exploit the weak bargaining position of another by deceitful and even fraudulent means, we consider it as a systemic issue: as a problem of social discrimination, where belonging to a group which is statistically discriminated against leads to entrapment in a chain of usurious credit and financial contracts. This paper reviews the economic rationale for usury legislation and evaluates the European Consumer Credit Directive 2008/48/EC in this context. It identifies systemic usury as the product of market failure: the most powerful explanations for which are monopoly power, where the consumer is locked in a bilateral credit relationship; discrimination through risk-based pricing, and negative externalities. Contrary to the main focus of the European Consumer Credit Directive, improved disclosure of contract terms and other relevant information to consumers at the point of contracting cannot address systemic usury in credit markets. Even fully informed consumers can be discriminated against and become trapped in a situation of bilateral monopoly. As a consequence, the Directive is found to be ineffective: it implicitly acknowledges usurious practices and products as legal and undermines the national fight against usury. The Directive must be reformed. Wucher ist ein häufiges Phänomen auf den Verbraucherkreditmärkten und betrifft insbesondere Haushalte mit niedrigem Einkommen. Obwohl der Begriff Wucher Bilder eines gierigen Individuums beschwört, das bewusst handelt, um die schwache Verhandlungsposition eines anderen mit irreführenden und sogar betrügerischen Mitteln auszunutzen, betrachten wir ihn als systemisches Problem: als ein Problem der sozialen Diskriminierung, bei dem die Zugehörigkeit zu einer statistisch diskriminierten Gruppe zu einer Einklemmung in eine Kette von wucherischen Kredit- und Finanzverträgen führt. Dieses Papier untersucht die ökonomischen Argumente für die Wuchergesetzgebung und bewertet in diesem Zusammenhang die Europäische Verbraucherkreditrichtlinie 2008/48/EG. Es identifiziert systemischen Wucher als das Ergebnis von Marktversagen: Die überzeugendsten Erklärungen dafür sind Monopolmacht, bei der der Verbraucher in einer bilateralen Kreditbeziehung gefangen ist, Diskriminierung durch risikoorientierte Preisgestaltung und negative Externalitäten. Im Gegensatz zum Hauptaugenmerk der Europäischen Verbraucherkreditrichtlinie kann eine verbesserte Offenlegung von Vertragsbedingungen und anderen relevanten Informationen für die Verbraucher zum Zeitpunkt der Vertragsunterzeichnung nicht auf systemischen Wucher auf den Kreditmärkten abzielen. Selbst voll informierte Verbraucher können diskriminiert werden und in einer Situation des bilateralen Monopols gefangen sein. Infolgedessen erweist sich die Richtlinie als unwirksam: Sie erkennt implizit wucherische Praktiken und Produkte als legal an und untergräbt die nationale Bekämpfung von Wucher. Die Richtlinie muss reformiert werden.

Anchoring is a robust behavioral phenomenon modeled predominantly as a bias in individual judgment. We propose a game-theoretic model that considers players��� beliefs about others��� behavior as a mediator for the effect of the anchor on a player���s choice. The results establish that anchoring in strategic interactions reported in the literature can be rationalized by anchored beliefs about the opponents��� intentions. Notwithstanding, we also demonstrate that a player might adjust away from rather than toward the anchor in games where choices are strategic substitutes.

We consider ultimatum bargaining over the provision of a public good. Offer-maker and responder can delegate their decisions to agents, whose actual decision rules are opaque. We show that the responder will benefit from strategic opacity, even with bilateral delegation. The incomplete information created by strategic opacity choices does not lead to inefficient negotiation failure in equilibrium. Inefficiencies arise from an inefficient provision level. While an agreement will always be reached, the public good provision will, however, fall short of the socially desirable level. Compared to unilateral delegation, bilateral delegation is never worse from a welfare perspective.

We analyze strategic leaks due to spying out a rival’s bid in a first-price auction. Such leaks induce sequential bidding, complicated by the fact that the spy may be a counterspy who serves the interests of the spied at bidder and reports strategically distorted information. This ambiguity about the type of spy gives rise to a non-standard signaling problem where both sender and receiver of messages have private information and the sender has a chance to make an unobserved move. Whereas spying without counterspy exclusively benefits the spying bidder, the potential presence of a counterspy yields a collusive outcome, even if the likelihood that the spy is a counterspy is arbitrarily small. That collusive impact shows up in all equilibria and is strongest in the unique pooling equilibrium which is also the payoff dominant equilibrium.

This paper studies incentives for the interim voluntary disclosure of verifiable information in probabilistic all-pay contests. Considered are unfair contests, i.e., contests in which, subject to activity conditions, one player (the favorite) is interim always more likely to win than the other player (the underdog). A condition is identified that ensures that a given contest is unfair regardless of disclosure decisions. Under this condition, full revelation is the unique perfect Bayesian equilibrium outcome of the contest with pre-play communication. This is so because the weakest type of the underdog will try to moderate the favorite, while the strongest type of the favorite will try to discourage the underdog - so that the contest unravels. We also show that self-disclosure may, with positive probability, provoke unintended reactions, i.e., "dominant" or "defiant" behavior. Moreover, while individually rational for the marginal type, the unraveling may be strictly Pareto inferior from an ex-ante perspective. Our main conclusion is just the opposite of the corresponding finding for the deterministic all-pay auction. The proofs employ lattice-theoretic methods and an improved version of Jensen's inequality.

In a two-sided asymmetric information market, the role of the accuracy of consumers&rsquo, imperfect and private information on the level of fraud, incidence of fraud and trade under price rigidity is examined. Consumers receive a costless but noisy private signal of quality. The product offered in the market can be of two exogenously given qualities and it is common knowledge that the consumer is not willing to pay a high price for a low quality product. A low quality seller chooses to be either honest (by charging the lower market price) or dishonest (by charging the higher price). We show that equilibria involving fraud exist for all parameter values. Furthermore, for some parameter values, we find that -in equilibrium- a higher precision of consumers&rsquo, private information leads to higher levels of fraud and incidence of fraud, reducing consumers&rsquo, welfare. We provide conditions for the public revelation of consumers&rsquo, private information to be a Pareto improvement.

We study repeated games in which players learn the unknown state of the world by observing a sequence of noisy private signals. We find that for generic signal distributions, the folk theorem obtains using ex post equilibria. In our equilibria, players commonly learn the state, that is, the state becomes asymptotic common knowledge.

We study the role of information about the multiplier in a finitely repeated investment game. A high multiplier increases the reputational incentives of a trustee, leading to more repayments. Our perfect Bayesian equilibrium analysis shows that if the trustee is privately informed about the multiplier, both the expected frequency of investments and repayments as well as the expected payoffs of both players are higher compared to a situation where the multiplier is public knowledge. We test this result in a laboratory experiment. The data cannot confirm the predicted welfare dominance of private information about the multiplier. We discuss potential reasons for the deviation between theory and experimental data.

This paper models the US-China trade conflict initiated in 2018 and attempts to analyze the (optimal) strategic choices of the United States and China. In contrast to the existing literature on the topic, we employ the expected utility theory and examine the conflict mathematically. In both perfect information and incomplete information games, we show that expected net gains diminish as the utility of winning increases because of the costs incurred during the struggle. We find that the best response function exists for China but not for the US during the conflict. The results of our models indicate that the less the US pressures China to change its existing trade practices, the higher the US expected net gains. China’s best choice is to maintain the status quo, and any further aggression in its policy and behavior, such as artificially adjust exchange rates and slash imports from the US, will aggravate the situation. The theoretical framework designed in this paper can be also used to examine the bilateral technological frictions. This economics paper models the U.S.-China trade war and explains the strategic decision-making of both sides. Math-driven findings include (1) For the bilateral trade frictions which involve not only the balance of payments but also tech rivalry, the probability for the U.S. win is higher than China's. (2) In both perfect information and incomplete information games, the U.S. cannot find a strategy to achieve the optimal result (i.e. maximum expected net benefits). (3) In both above-mentioned games, China has the best response function to achieve its maximum expected net gains if it can maintain the status quo. (4) During the ongoing trade war, the more the U.S. pressures China through protectionist tariffs or other punitive measures, the less the U.S. expected net benefits. On the Chinese side, any aggression in its policies or practices, such as slash imports from the U.S. and artificially depreciate the renminbi, will reduce China's expected net utilities and the situation will be aggravated. (5) The theoretical framework and mathematical models designed in the article contribute to the existing scholarly literature on the U.S.-China trade war and the expected utility theory and can be applied to analyzing technological competition/financial flare-ups between the two economic powers.

Standard program evaluations implicitly assume that individuals are perfectly informed about the considered policy change and the related institutional rules. This seems not very plausible in many contexts, as diverse examples show. However, evidence on how incomplete information affects the size of measured treatment effects is broadly missing. We exploit a unique set of natural experiments to assess the importance of incomplete information in shaping policy effects. We compare different large-scale quasi-experiments on changing potential benefit duration (PBD) in unemployment insurance (UI). Thereby, we confront the benchmark case, in which individuals are fully informed about their different PBD levels, with cases in which job seekers experience a change of their benefit eligibility without being initially informed. However, in any of the considered cases they face exactly the same size of treatment: an increase or decrease of the PBD by 200 days. We identify the treatment effects around the threshold of age 25 where PBD rules change in the considered Swiss UI system. We find substantial differences in the treatment effects across cases with different information conditions on benefit levels. The differences can be rationalized by a model in which individuals invest different amounts of effort to acquire the necessary information. Quantifications of the impact of incomplete information on the PBD effects demonstrate the policy relevance of this usually ignored issue.

This paper studies a stability notion and matching processes in the job market with incomplete information on the workers' side. Each worker is associated with a type, and each firm cares about the type of her employee under a match. Moreover, firms' information structure is described by partitions over possible worker type profiles. With this firm‐specific information, we propose a stability notion which, in addition to requiring individual rationality and no blocking pairs, captures the idea that the absence of rematching conveys no further information. When an allocation is not stable under the status quo information structure, a new pair of an allocation and an information structure will be derived. We show that starting from an arbitrary allocation and an arbitrary information structure, the process of allowing randomly chosen blocking pairs to rematch, accompanied by information updating, will converge with probability one to an allocation that is stable under the updated information structure. Our results are robust with respect to various alternative learning patterns.

We theoretically and experimentally study a college admissions problem in which colleges accept students by ranking students' efforts in entrance exams. Students hold private information regarding their ability level that affects the cost of their efforts. We assume that student preferences are homogeneous over colleges. By modeling college admissions as contests, we solve and compare the equilibria of "centralized college admissions" (CCA) in which students apply to all colleges, and "decentralized college admissions" (DCA) in which students can only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. The main qualitative predictions of the theory are supported by the experimental data, yet we find a number of behavioral differences between the mechanisms that render DCA less attractive than CCA compared to the equilibrium benchmark.

Information asymmetries in economic transactions are omnipresent and a regular source of fraudulent behavior. In a theoretical and an experimental analysis of a sender-receiver game we investigate whether sanctions for lying induce more truth-telling. The novel aspect in our model is that senders may not only choose between truth-telling and (explicit) lying, but may also engage in evasive lying by credibly pretending not to know. While we find that sanctions promote truth-telling when senders cannot engage in evasive lying, this is no longer true when evasive lying is possible. Then, explicit lying is largely substituted by evasive lying, which completely eliminates the otherwise positive effect of sanctions on the rate of truth-telling. As outlined in our model, the necessary prerequisite for such an ‘erosion’ effect is that evasive lying is perceived as sufficiently less psychologically costly than direct lying. Evidence from our experimental data and a survey conducted with additional participants indicate that the shift towards evasion can indeed be attributed to lower psychological costs. Overall, our results clearly demonstrate the limitations of sanctioning lying to counteract the exploitation of informational asymmetries and may explain the empirical evidence from the finance industry that sanctions for financial misconduct eventually appear to be not very effective.

Usury is a frequent occurrence in consumer credit markets and particularly affects low-income households. Although the term usury conjures images of a greedy individual consciously acting to exploit the weak bargaining position of another by deceitful and even fraudulent means, we consider it as a systemic issue: as a problem of social discrimination, where belonging to a group which is statistically discriminated against leads to entrapment in a chain of usurious credit and financial contracts. This paper reviews the economic rationale for usury legislation and evaluates the European Consumer Credit Directive 2008/48/EC in this context. It identifies systemic usury as the product of market failure: the most powerful explanations for which are monopoly power, where the consumer is locked in a bilateral credit relationship; discrimination through risk-based pricing, and negative externalities. Contrary to the main focus of the European Consumer Credit Directive, improved disclosure of contract terms and other relevant information to consumers at the point of contracting cannot address systemic usury in credit markets. Even fully informed consumers can be discriminated against and become trapped in a situation of bilateral monopoly. As a consequence, the Directive is found to be ineffective: it implicitly acknowledges usurious practices and products as legal and undermines the national fight against usury. The Directive must be reformed. revised version Dezember 2019

Anchoring is one of the most studied and robust behavioral biases, but there is little knowledge about its persistence in strategic settings. This article studies the role of anchoring bias in private-value auctions. We test experimentally two different anchor types. The announcement of a random group identification number but also of an upper bid limit in the first-price sealed-bid auction result in higher bids. We show that such behavior can be explained as a rational response to biased beliefs. In Dutch auctions, the effect of a starting price, is negative. We demonstrate that the long-established ranking that the Dutch auction generates lower revenue than the first-price sealed-bid auction crucially depends on the size of the anchor.

Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989) Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICR λ , where λ is a sequence whose term λ n is the probability players attach to ( n − 1)th‐order belief in rationality. We find that Weinstein and Yildiz's discontinuity remains when λ n is above an appropriate threshold for all n, but fails when λ n converges to 0. That is, if players' confidence in mutual rationality persists at high orders, the discontinuity persists, but if confidence vanishes at high orders, the discontinuity vanishes.

We analyze spying out a rival’s price in a Bertrand market game with incomplete information. Spying transforms a simultaneous into a robust sequential moves game. We provide conditions for profitable espionage. The spied at firm may attempt to immunize against spying by delaying its pricing decision if its cost is low. This, however, adversely affects beliefs and becomes self-defeating. The spy may also be a counterspy or be fooled to report strategically distorted information. This gives rise to an intriguing signaling problem that admits only partially separating equilibria. Surprisingly, counter-espionage may aggravate the price leadership induced by spying. Altogether, our analysis offers an explanation and generalization of robust Stackelberg-Bertrand games.

This paper introduces incomplete information in the standard model of cultural transmission (Bisin and Verdier, 2001). We allow parents to ignore own group size and the efficiency of their cultural transmission technology, while receiving a feedback from their children. Using the selfconfirming equilibrium concept, parents may end up to sustain, and be confirmed about, wrong conjectures. We show that in equilibrium optimal socialization efforts display cultural complementarity with respect to own population share, while the standard substitution result holds with respect their own conjectured population shares. Considering the population dynamics, if conjectures about population shares are shaped by cultural leaders who want to maximize the presence of own traits in the next period, then conjectures are characterized by negative biases. Our main finding is that, depending on the magnitude of the bias, the dynamics can display stable or unstable polymorphic equilibria, or just a stable homomorphic equilibrium, potentially reverting standard predictions.

I use game-theoretical models to compare a sender's expected payoff under two methods of wielding influence under incomplete information: offering rewards or threatening punishments. Attempts to influence another's behaviour can have the perverse effect of actually encouraging the behaviour that one is trying to discourage by creating, albeit different, incentives to bluff. Under a reward regime, targets can bluff in order to extort larger inducements. Under a sanction regime, targets can bluff in order to deter coercion attempts. I find that while sanctions are a weakly dominant tool of influence under complete information, rewards can be preferable under incomplete information. The sender often could do better by committing to a certain course of action for the entire duration of interaction. Moreover, using rewards and sanctions in combination can mitigate their adverse effects on targets' bluffing incentives when deploying only one instrument of influence separately.

We examine the impact of airline codesharing on consumer choice behavior in non-stop international route markets. Using stated preference data, we document that consumer valuation of flights by alien foreign carriers is significantly higher if these flights are offered as codeshare products by consumers' own national carrier or, to a lesser extent, a neighboring national carrier. We empirically rule out quality improvements and frequent flier programs as underlying drivers and explore two alternative explanations: misconceptions about codesharing and codesharing as a quality signal. We find that misconceptions are widespread, but that they do not cause higher valuation of codeshare products. Consistent with signaling, however, codeshare products are valued higher by more risk-averse consumers and on less familiar routes.

In this study, I examine the alternating-offer bilateral bargaining model with private correlated values. The correlation of values is modeled via the global games information structure. I focus on the double limits of perfect Bayesian equilibria as offers become frequent and the correlation approaches perfect. I characterize the Pareto frontier of the double limits and show that it is efficient, but the surplus split generally differs from the Nash bargaining split. I then construct a double limit that approximates the Nash bargaining split in the ex post surplus, but with a delay. Further, I prove the folk theorem when the range of the buyer's values coincides with the range of the seller's costs: any feasible and individually rational ex ante payoff profile can be approximated by a double limit.

I investigate the decision problem of a player in a game of incomplete information who faces uncertainty about the other players' strategies. I propose a new decision criterion which works in two steps. First, I assume common knowledge of rationality and eliminate all strategies which are not rationalizable. Second, I apply the maximin expected utility criterion. Using this decision criterion, one can derive predictions about outcomes and recommendations for players facing strategic uncertainty. A bidder following this decision criterion in a first-price auction expects all other bidders to bid their highest rationalizable bid given their valuation. As a consequence, the bidder never expects to win against an equal or higher type and resorts to win against lower types with certainty.

In this article we analyse the impact of spousal preference expectations on mothers' willingness to invest in children's food/nutrition and health/medical expenses. We use a survey conducted in Karnataka, South India, where women with children were asked to state their investment preference in child food and health corresponding to three endowment levels. Alongside, we also attempted to derive their expectations about spousal relative investment choices. We find that if mothers are able to elicit expectations about spousal preference, their own preferences remain unaffected, whereas, if expectation elicitation is impossible, female investments in children reduce significantly. We argue that in the absence of information sharing, uncertainty is created which decreases cooperation by mothers by reducing their willingness to invest in children, especially in girls and increasing their precautionary savings. These results remain consistent across the all endowments. Our study is particularly of relevance for policies that aim to alleviate poverty and improve child human capital accumulation with cash transfer policies. It also suggests that in a noncooperative set up, where household members do not share their financial information, resources tend to be under-allocated in household public goods such as children.

Due to intensive competition among business corporations, the selection of supplier becomes more significant for business success. However, supplier selection problems are complex since a large number of criteria need to be considered and, frequently, some criteria cannot be assessed precisely. Moreover, fluctuations of supplier performances as well as unknown information always exist in real-world decisions. This study, therefore, aims to propose a method to facilitate practitioners to logically select a supplier, even when uncertainty and/or unavailability of the assessment information emerge. The TOPSIS method is chosen to be the basis for this development. The rank order centroid (ROC) method is chosen to determine the weights of criteria in order to lessen the degree of subjectivity required from the decision makers as well as uncertainty of the weights assignment. A case of egg supplier selection is given to demonstrate the implementation procedures of the proposed method. Keywords: TOPSIS, Supplier selection, Supplier evaluation, Rank order centroid, Uncertain information, Incomplete information

We provide a new theory of expectations-driven business cycles in which consumers' learning from prices dramatically alters the effects of aggregate shocks. Learning from prices causes changes in aggregate productivity to shift aggregate beliefs, generating positive price-quantity comovement. The feedback of beliefs into prices can be so strong that even arbitrarily small productivity shocks lead to substantial fluctuations. Augmented with a public signal, the model can generate a rich mix of supply- and demand-driven fluctuations even though productivity is the only source of aggregate randomness. Our results imply that many standard identification assumptions used to disentangle supply and demand shocks may not be valid in environments in which agents learn from prices.

Existing theoretical and experimental studies have established that unanimity is a poor decision rule for promoting information aggregation. Despite this, unanimity is frequently used in committees making decisions on behalf of society. This paper shows that when committee members are exposed to "idiosyncratic" payoffs that condition on their individual vote, unanimity can facilitate truthful communication and optimal information aggregation. Theoretically, we show that since agents" votes are not always pivotal, majority rule suffers from a free-rider problem. Unanimity mitigates free-riding since responsibility for the committee's decision is equally distributed across all agents. We test our predictions in a controlled laboratory experiment. As predicted, if unanimity is required, subjects are more truthful, respond more to others' messages, and are ultimately more likely to make the optimal decision. Idiosyncratic payoffs such as a moral bias thus present a rationale for the widespread use of unanimous voting.

We survey the results on representations of committees and constitutions by game forms that possess some kind of equilibrium strategies for each profile of preferences of the players. The survey is restricted to discrete models, that is, we deal with finitely many players and alternatives. No prior knowledge of social choice is assumed: As far as definitions are concerned, the paper is self-contained. Section 2 supplies the necessary general tools for the rest of the paper. Each definition is followed by a simple (but nontrivial) example. In Section 3 we give a complete account of representations of committees (proper and monotonic simple games), by exactly and strongly consistent social choice functions. We start with Peleg’s representations of weak games, and then provide a complete and detailed account of Holzman’s solution of the representation problem for simple games without veto players. In Section 4 we deal with representations of constitutions by game forms. Following Gärdenfors we model a constitution by a monotonic and superadditive effectivity function. We fully characterize the representations for three kinds of equilibrium: Nash equilibrium; acceptable equilibrium (Pareto optimal Nash equilibrium); and strong Nash equilibrium. We conclude in Section 5 with a report on two recent works on representations of constitutions under incomplete information.

This article provides a theoretical model analyzing wholesale pricing tariffs set by a monopolistic manufacturer for its branded product that is sold to final customers by a monopolistic retailer. The bargaining power of the downstream retailer is strengthened by offering also a vertically differentiated private label product whose production costs are known only incompletely to the upstream manufacturer. The model shows that the manufacturer can avoid double marginalization and implement the full information outcome by combining a quantity discount with a market-share discount where only a retailer with a strong private label retroactively receives an allowance. Under these circumstances it is unprofitable for the manufacturer to impose exclusive dealing on the retailer.

We examine multistage information transmission with voluntary monetary transfer in the framework of Crawford and Sobel (1982). In our model, an informed expert can send messages to an uninformed decision maker more than once, and the uninformed decision maker can pay money to the informed expert voluntarily whenever she receives a message. Our results are that under some conditions (i) the decision maker can obtain more detailed information from the expert than that in the Crawford and Sobel model and (ii) there exists an equilibrium whose outcome Pareto dominates all the equilibrium outcomes in the Crawford and Sobel model. Moreover, we find the upper bound of the receiver's equilibrium payoff, and provide a sufficient condition for it to be approximated by the receiver's payoff under a certain equilibrium. The 19th ISER-Moriguchi Prize (2016) Awarded Paper.

What is the strategic role of membership in an intergovernmental group with unanimity requirements if the group negotiates with an external player in a setting with incomplete information? Being in such a group has a strategic effect compared to negotiating as a stand-alone player and reduces the demands of the outside player. Group membership lends additional bargaining power. Negotiating as a group may also cause more inefficiencies due to bargaining failure, and this may harm also the intergovernmental group. We uncover the role of preference alignment and preference independence between members of the coalition group for equilibrium payoffs and welfare effects. In this analysis, we also distinguish between coalition groups with and without side payments. Overall, coalition groups tend to perform well for the members of the coalition group in comparison to fully decentralized negotiations, particularly if the objectives of the members of the coalition group are not always perfectly aligned. Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich / This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.

In unrestricted combinatorial auctions, we put forward a mechanism that guarantees a meaningful revenue benchmark based on the possibilistic beliefs that the players have about each other’s valuations. In essence, the mechanism guarantees, within a factor of two, the maximum revenue that the “best informed player” would be sure to obtain if he/she were to sell the goods to his/her opponents via take-it-or-leave-it offers. Our mechanism is probabilistic and of an extensive form. It relies on a new solution concept, for analyzing extensive-form games of incomplete information, which assumes only mutual belief of rationality. Moreover, our mechanism enjoys several novel properties with respect to privacy, computation and collusion., United States. Office of Naval Research (N00014-09-1-0597), National Science Foundation (U.S.) (CAREER award no. 1553385)

We study a college admissions problem in which colleges accept students by ranking students’ efforts in entrance exams. Students’ ability levels affect the cost of their efforts. We solve and compare the equilibria of “centralized college admissions” (CCA) where students apply to all colleges and “decentralized college admissions” (DCA) where students only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. Many predictions of the theory are supported by a lab experiment designed to test the theory, yet we find a number of differences that render DCA less attractive than CCA compared to the equilibrium benchmark.

We theoretically and experimentally study a college admissions problem in which colleges accept students by ranking students' efforts in entrance exams. Students hold private information regarding their ability level that affects the cost of their efforts. We assume that student preferences are homogeneous over colleges. By modeling college admissions as contests, we solve and compare the equilibria of "centralized college admissions" (CCA) in which students apply to all colleges, and "decentralized college admissions" (DCA) in which students can only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. The main qualitative predictions of the theory are supported by the experimental data, yet we find a number of behavioral differences between the mechanisms that render DCA less attractive than CCA compared to the equilibrium benchmark. (author's abstract)

We conduct a field experiment with 302 workers of the microcredit company in Russia to study the effects of the different designs of a contest for monetary prizes at the workplace. We consider a standard all-pay auction design with two and four prizes of different size and compare it to "parallel" contests with the same prizes, but where participants have to choose the prize prior to the start of the competition and then the winner is selected only among the players who chose the same prize. Despite the theoretical predictions, the parallel contests lead to higher efforts for all players, but mainly by lower-ability players. Division of prizes leads to the predicted effects. In parallel contests, too many players choose the higher prize than equilibrium suggests. Overall, the parallel version of contests appeared to be more profitable for the firm.

Two individuals are involved in a conflict situation in which preferences are ex ante uncertain. While they eventually learn their own preferences, they have to pay a small cost if they want to learn their opponent’s preferences. We show that, for sufficiently small positive costs of information acquisition, in any Bayesian Nash equilibrium of the resulting game of incomplete information the probability of getting informed about the opponent’s preferences is bounded away from zero and one.

Kolmogorov's extension theorem provides a natural mapping from the space of coherent hierarchies of an agent's first-order, second- order, etc. beliefs to the space of probability measures over the exogenous parameters and the other agents' belief hierarchies. Mertens and Zamir (1985) showed that, if the spaces of belief hierarchies are endowed with the product topology, then this mapping is a homeomorphism. This paper shows that this mapping is also a homeomorphism if the spaces of belief hierarchies are endowed with the uniform weak topology of Chen et al. (2010) or the universal strategic topology of Dekel et al. (2006), both of which ensure that strategic behaviour exhibits desirable continuity properties.

Work and trade relationships are often governed by relational contracts, in which incentives for cooperative action today stem from the prospective future benefits of the relationship. In this paper, we study how a lack of hard information about the costs of providing quality, and therefore about the financial consequences of actions, affects relational contracts in buyer-seller relationships. The absence of verifiable information can impede the joint understanding of what constitutes cooperative behavior, and may thus inject mistrust into relationships. Comparing seller-buyer relationships with hard (verifiable) and soft (non-verifiable) information about seller costs in the laboratory, we find that soft information affects the terms of relational contracts. Contractual terms are adjusted to the detriment of the uniformed party. However, the uniformed party does not reciprocate these adjustments with efficiency-reducing actions. We therefore find that asymmetric information only affects the distribution of rents, and not efficiency.

Game-theoretic models are a convenient tool to systematically analyze competitive situations. This makes them particularly handy in the field of security where a company or a critical infrastructure wants to defend against an attacker. When the optimal solution of the security game involves several pure strategies (i.e., the equilibrium is mixed), this may induce additional costs. Minimizing these costs can be done simultaneously with the original goal of minimizing the damage due to the attack. Existing models assume that the attacker instantly knows the action chosen by the defender (i.e., the pure strategy he is playing in the i-th round) but in real situations this may take some time. Such adversarial inertia can be exploited to gain security and save cost. To this end, we introduce the concept of information delay, which is defined as the time it takes an attacker to mount an attack. In this period it is assumed that the adversary has no information about the present state of the system, but only knows the last state before commencing the attack. Based on a Markov chain model we construct strategy policies that are cheaper in terms of maintenance (switching costs) when compared to classical approaches. The proposed approach yields slightly larger security risk but overall ensures a better performance. Furthermore, by reinvesting the saved costs in additional security measures it is possible to obtain even more security at the same overall cost.

Modern financial theory acknowledges that decision makers do not perfectly know the stochastic process of financial figures, in particular corporate cash flows. In other words, there is imperfect information in the sense of incomplete information. Incomplete information in the context of this thesis is modeled with the help of an unobservable underlying regime model, i.e., corporate dividends can assume several regimes. It is clear that incomplete information regarding dividends should be reflected in companies’ stock prices. It is not so clear how incomplete information translates into risk premia. Does incomplete information as a second source of risk in addition to “normal” stock price fluctuations (first source of risk) (i) automatically increase overall risk and, hence, call for an adequate compensation, or (ii) can incomplete information and “normal” stock price risk interact in a way that overall risk is reduced and risk premia decrease? Veronesi (2000) has shown that incomplete information leads to an unintuitive asset pricing outcome: the incomplete information risk premium (two sources of risk) is below its complete information counterpart (one source of risk) for typical values of risk aversion parameters. This result of Veronesi (2000) has been derived in a narrow model framework: CRRA utility, regimes in expectations only, and only one asset. This thesis analyzes the effect of incomplete information on asset prices in a more general framework (various types of utility functions, cash flow functions, regimes in both standard deviations and expectations, and several risky assets). The results can be summarized as follows: (i) Incomplete information exerts a substantial influence on risk premia for all models considered in this thesis - CARA and CRRA utility functions, richer class of regime processes, various forms of cash flow model, and more than one risky asset - as the analytical analyses demonstrate. Core of all pricing approaches is the covariance between stochastic discount factor and asset return. Incomplete information fundamentally alters this covariance. (ii) The numerical analyses illustrate that the theoretical pricing results are also relevant from an economic point of view: incomplete information risk premia are significantly different from complete information risk premia and the different model versions also translate into substantially different risk premia. By and large, the results found in Veronesi (2000) still hold in the more general setting that has been considered in this thesis.

We study the role that price transparency plays in determining the efficiency and surplus division in a sequential bargaining model of price formation with asymmetric information. Under natural assumptions on type distributions, and for any discount factor, we show that the unobservability of past negotiations leads to lower prices and faster trading. Unobservability therefore enhances the ``Coasian effect" by fostering efficiency and diverting more of the surplus to the player who possesses private information. In addition, we show that the equilibrium is unique and is in pure strategies in the non-transparent regime; this stands in sharp contrast to the existing literature and allows for a better understanding of the Coasian effect and price observability.

We scrutinize the scope of auctions in the presence of downstream interactions and information externalities by using the topical example of a firm acquisition. We show that no mechanism exists that allows an investor to acquire a low-cost firm under incomplete information: a separating auction implies adverse selection and relies substantially on commitment to allocation and transfer rules. A pooling auction serves as a commitment device against ex-post opportunistic behavior and alleviates adverse selection. It can earn the investor a higher expected payoff than a separating auction, even when consistency is required as to qualify for a sequential equilibrium.

This paper studies a contest in which players with unobservable types may form an alliance in a pre-stage of the game to join their forces and compete for a prize. We characterize the pure strategy equilibria of this game of incomplete information. We show that if the formation of an alliance is voluntary, players do not reveal private information in the process of alliance formation in any equilibrium. In this case there exists a pooling equilibrium without alliances with a unique effort choice in the contest and there exist equilibria in which all types prefer to form an alliance. If the formation of an alliance can be enforced by one player with positive probability there exists an equilibrium in which only the low types prefer to form an alliance. Der vorliegende Aufsatz untersucht ein Modell, in welchem Agenten mit unbeobachtbaren Typen ihre Kräfte in Allianzen vereinen können, bevor sie in einen Wettstreit um eine Ressource eintreten. Wir beschreiben die Gleichgewichte in reinen Strategien dieses Spiels unter unvollständiger Information. Für den Fall des freiwilligen Eintritts in eine Allianz zeigen wir, dass die Spieler in keinem Gleichgewicht private Information während der Bildung der Allianz offenbaren. In diesem Fall existiert ein vereinigendes Gleichgewicht ohne Allianz, in dem die Spieler eine eindeutige, typen-abhängige Investition im Wettstreit wählen. Es existieren auch vereinigende Gleichgewichte, in welchen es alle Spieler-Typen strikt bevorzugen, in eine Allianz einzutreten. Falls eine Allianz seitens eines Spielers mit positiver Wahrscheinlichkeit erzwungen werden kann, existiert ein trennendes Gleichgewicht, in welchem nur die schwachen Spieler-Typen in die Allianz eintreten wollen.

We study the strategic disclosure of demand information and product-market strategies of duopolists. In a setting where both firms receive information with some probability, we show that firms selectively disclose information in equilibrium in order to influence their competitor’s product-market strategy. Subsequently, we analyze the firms’ behavior in a laboratory experiment. We find that subjects often use selective disclosure strategies, and this finding appears to be robust to changes in the information structure, the mode of competition, and the degree of product differentiation. Moreover, in our experiment, subjects’ product-market conduct is largely consistent with theoretical predictions.

Cahier de Recherche du Groupe HEC Paris, n° 754; We study stochastic games with incomplete information on one side, in which the transition is controlled by one of the players. We prove that if the informed player also controls the transitions, the game has a value, whereas if the uninformed player controls the transitions, the max-min value as well as the min-max value exist, but they may differ. We discuss the structure of the optimal strategies, and provide extensions to the case of incomplete information on both sides.

We shed light on the function, properties and optimal size of austerity using the standard sovereign debt model augmented to include incomplete information about credit risk. Austerity is defined as the shortfall of consumption from the level desired by a country and supported by its repayment capacity. We find that austerity serves as a tool for securing a more favourable loan package; that it is associated with over-investment even when investment does not create collateral; and that low risk borrowers may favour more to less severe austerity. These findings imply that the amount of fresh funds obtained by a sovereign is not a reliable measure of austerity suffered; and that austerity may actually be associated with higher growth. Our analysis accommodates costly signaling for gaining credibility and also assigns a novel role to spending multipliers in the determination of optimal austerity.

The aim of this paper is to provide fresh empirical evidence on the mechanisms through which wage inequality affects worker satisfaction.Theoretically, the wages of others may affect workers’ utility for two main reasons: Workers may derive well-being from their social status (the comparison effect) and/or they may use others’ wages to help predict their own future wage (the information effect). The author tests both hypotheses. To do this, she models individual utility from pay as a function of a workers own wage and the earnings of all other workers within the same establishment, and she estimates the model using matched British employeremployee data. The author assumes incomplete information about others’ wages. She finds that the comparison effect matters. Interestingly, she also provides some evidence on a positive relation between well-being and inequality. Her results are robust to different specifications and different definitions of the reference group.

We shed light on the function, properties and optimal size of austerity using the standard sovereign debt model augmented to include incomplete information about credit risk. Austerity is defined as the shortfall of consumption from the level desired by a country and supported by its repayment capacity. We find that austerity serves as a tool for securing a more favourable loan package; that it is associated with over-investment even when investment does not create collateral; and that low risk borrowers may favour more to less severe austerity. These findings imply that the amount of fresh funds obtained by a sovereign is not a reliable measure of austerity suffered; and that austerity may actually be associated with higher growth. Our analysis accommodates costly signalling for gaining credibility and also assigns a novel role to spending multipliers in the determination of optimal austerity.

Motivated by trying to better understand the norms that govern pedestrian traffic, I study symmetric two-player coordination games with independent private values. The strategies of "always pass on the left" and "always pass on the right" are always equilibria of this game. Some such games, however, also have other (pure strategy) equilibria with a positive likelihood of mis-coordination. Perhaps sur- prisingly, in some such games, these Pareto-inefficient equilibria, with a positive likelihood of mis-coordination, are the only evolutionarily stable equilibria of the game.

In this paper, we describe a series of laboratory experiments that implement specific examples of a more general network structure and we examine equilibrium selection. Specifically, actions are either strategic substitutes or strategic complements, and participants have either complete or incomplete information about the structure of a random network. Since economic environments typically have a considerable degree of complementarity or substitutability, this framework applies to a wide variety of settings. The degree of equilibrium play is striking, in particular with incomplete information. Behavior closely resembles the theoretical equilibrium whenever this is unique; when there are multiple equilibria, general features of networks, such as connectivity, clustering, and the degree of the players, help to predict informed behavior in the lab. People appear to be strongly attracted to maximizing aggregate payoffs (social efficiency), but there are forces that moderate this attraction: 1) people seem content with (in the aggregate) capturing only the lion’s share of the efficient profits in exchange for reduced exposure to loss, and 2) uncertainty about the network structure makes it considerably more difficult to coordinate on a demanding, but efficient, equilibrium that is typically implemented with complete information.