
on Microeconomics 
By:  Jetlir Duraj; Kevin He 
Abstract:  A benevolent sender communicates noninstrumental information over time to a Bayesian receiver who experiences gainloss utility over changes in beliefs ("news utility"). We show how to inductively compute the optimal dynamic information structure for arbitrary newsutility functions. With diminishing sensitivity over the magnitude of news, contrary to piecewiselinear newsutility models, oneshot resolution of uncertainty is strictly suboptimal under commonly used functional forms. We identify additional conditions that imply the sender optimally releases good news in small pieces but bad news in one clump. By contrast, information structures featuring the opposite skewness  i.e., delivering bad news gradually  are never optimal. A sender lacking commitment power can only credibly convey partial good news when the receiver is sufficiently loss averse. With diminishing sensitivity but no loss aversion, the babbling equilibrium is essentially unique. Contrary to the commitment case, a sender without commitment may generate higher equilibrium newsutility for receivers with higher loss aversion. 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.00084&r=all 
By:  Geoffroy de Clippel; Kfir Eliaz; Daniel Fershtman; Kareen Rozen 
Abstract:  Each period, a principal must assign one of two agents to some task. Profit is stochastically higher when the agent is qualified for the task. The principal cannot observe qualification. Her only decision is which of the two agents to assign, if any, given the public history of selections and profits. She cannot commit to any rule. While she maximizes expected discounted profits, each agent maximizes his expected discounted selection probabilities. We fully characterize when the principal's firstbest payoff is attainable in equilibrium, and identify a simple strategy profile achieving this firstbest whenever feasible. We propose a new refinement for dynamic mechanisms (without transfers) where the designer is a player, under which we show the principal's nextbest, when the firstbest is unachievable, is the oneshot Nash. We show how our analysis extends to variations on the game accommodating more agents, caring about one's own performance, cheap talk and losses. 
Keywords:  Dynamic allocation, mechanism design without transfers, mechanism design without commitment 
JEL:  D82 D86 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_116&r=all 
By:  Frick, Mira (Yale University); Iijima, Ryota (Yale University); Le Yaouanq, Yves (LMU Munich) 
Abstract:  We propose a class of multipleprior representations of preferences under ambiguity where the belief the decisionmaker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM\'s ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, as well as to represent contextdependent negative and positive ambiguity attitudes documented in experiments. We prove that our baseline representation, Boolean expected utility (BEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni and Marinacci, 2004), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler, 1989), while extensions of BEU allow for more general departures from independence. 
Keywords:  multiple priors; ambiguity; dualself models; 
JEL:  D81 
Date:  2019–07–30 
URL:  http://d.repec.org/n?u=RePEc:rco:dpaper:173&r=all 
By:  Deniz Kattwinkel; Jan Knoepfle 
Abstract:  A principal has to take a binary decision. She relies on information privately held by a completely biased agent. The principal cannot incentivize with transfers but can learn the agent's information at a cost. Additionally, the principal privately observes a signal correlated with the agent's type. Transparent mechanisms are optimal: unlike in standard results with correlation, the principal's payoff is the same as if her signal was public. They take a simple cutoff form: favorable signals ensure the agent's preferred action. Signals below this cutoff lead to the nonpreferred action unless the agent appeals. An appeal always triggers type verification. 
Keywords:  Mechanism Design without Transfers, Costly Verification, Robust Mechanism Design, Transparency 
JEL:  D61 D82 K40 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_114&r=all 
By:  Vasudha Jain; Mark Whitmeyer 
Abstract:  Firms strategically disclose product information in order to attract consumers, but recipients often find it costly to process all of it, especially when products have complex features. We study a model of competitive information disclosure by two senders, in which the receiver may garble each sender's experiment, subject to a cost increasing in the informativeness of the garbling. As long as attention costs are not too low, there is an interval of prior means over which it is an equilibrium for both senders to offer full information, which interval expands as attention costs grow. Information on one sender substitutes for information on the other, which allows the receiver to nullify the profitability of a deviation. We thus provide a novel channel through which competition encourages information disclosure. 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1907.09255&r=all 
By:  Ben Amiet; Andrea Collevecchio; Marco Scarsini 
Abstract:  Nash equilibria are a central concept in game theory and have applications in fields such as economics, evolutionary biology, theoretical computer science, and many others. Mixed equilibria exist in any finite game, but pure equilibria may fail to exist. We consider the existence of pure Nash equilibria in games where the payoffs are drawn at random. In particular, we consider games where a large number of players can each choose one of two possible actions, and the payoffs are i.i.d. with the possibility of ties. We provide asymptotic results about the random number of pure Nash equilibria, such as fast growth and a central limit theorem. Moreover, we establish a new link between percolation models and game theory to shed light on various aspects of Nash equilibria. Through this connection, we describe in detail the geometry of Nash equilibria and show that, when the probability of ties is small, a bestresponse dynamics reaches a Nash equilibrium with a probability that quickly approaches one as the number of players grows. We show a multitude of phase transitions depending on a single parameter of the model, that is, the probability of having ties. 
Date:  2019–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1905.10758&r=all 
By:  Ronald Stauber 
Abstract:  The term “belief function” is generally used to refer to a class of capacities that can be viewed as representing ambiguity averse preferences. This paper introduces a definition of equilibrium for normalform games with ambiguous beliefs, where belief functions are used to describe strategic uncertainty. To capture independence of strategies and beliefs, a novel notion of a “strategic product integral” is introduced for belief functions, based on the Möbius transform of a capacity, and shown to be different from the Choquet integral of an appropriate product capacity. A characterization of the integral in terms of maxmin expected utility expressed relative to elements of the cores of the respective belief functions, is also presented. The resulting equilibrium notion relies on the Möbius transform to embed objectively chosen probabilistic mixed strategies into ambiguous beliefs of opponents about these strategies, while incorporating stronger consistency requirements than those imposed by previous definitions of equilibria under ambiguity. ClassificationC72, D81 
Keywords:  Belief functions; Product capacities; Equilibrium under ambiguity; Strategic uncertainty 
Date:  2019–04 
URL:  http://d.repec.org/n?u=RePEc:acb:cbeeco:2019668&r=all 
By:  Armstrong, Mark; Vickers, John 
Abstract:  We explore patterns of competitive interaction by studying mixedstrategy equilibrium pricing in oligopoly settings where consumers vary in the set of suppliers they consider for their purchase. In the case of "nested reach" we find equilibria, unlike those in existing models, in which price competition is segmented: small firms offer only low prices and large firms only offer high prices. We characterize equilibria in the threefirm case using correlation measures of competition between pairs of firms. We then contrast them with equilibria in the parallel model with capacity constraints. A theme of the analysis is how patterns of consumer consideration matter for competitive outcomes. 
Keywords:  BertrandEdgeworth competition, price dispersion, consideration sets, mixed strategies, captive customers 
JEL:  D43 D83 L11 L13 L15 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:95336&r=all 
By:  Chiara Fumagalli; Massimo Motta 
Abstract:  This paper shows that vertical foreclosure can have a dynamic rationale. By refusing to supply an efficient downstream rival, a vertically integrated incumbent sacrifices current profits but can exclude the rival by depriving it of the critical profits it needs to be successful. In turn, monopolising the downstream market may prevent the incumbent from losing most of its future profits because: (a) it allows the incumbent to extract more rents from an efficient upstream rival if future upstream entry cannot be discouraged; or (b) it also deters future upstream entry by weakening competition for the input and reducing the postentry profits of the prospective upstream competitor. 
Keywords:  Inefficient foreclosure, Refusal to supply, Scale economies, Exclusion, Monopolisation 
JEL:  K21 L41 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:baf:cbafwp:cbafwp1899&r=all 
By:  Claudia Cerrone (Max Planck Institute for Research on Collective Goods, Bonn); Francesco Feri (Royal Holloway, Department of Economics); Philip R. Neary (Royal Holloway, Department of Economics) 
Abstract:  Existing models of regret aversion assume that individuals can make an expost comparison between their choice and a foregone alternative. Yet in many situations such a comparison can be made only if someone else chose the alternative option. We develop a model where regretaverse agents must decide between the status quo and a new risky option that outperforms the status quo in expectation, and learn the outcome of the risky option, if unchosen, with a probability that depends on the choices of others. This turns what was previously a series of singleperson decision problems into a coordination game. Most notably, regret can facilitate coordination on the status quo { an action that would not be observed if the agents were acting in isolation or had standard preferences. We experimentally test the model and find that regretaverse agents behave as predicted by our theory. 
Keywords:  regret aversion, coordination games, information 
JEL:  C72 C92 D81 D91 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:mpg:wpaper:2019_10&r=all 
By:  Philippe Jehiel (PJSE  Paris Jourdan Sciences Economiques  UP1  Université PanthéonSorbonne  ENS Paris  École normale supérieure  Paris  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics, UCL  University College of London [London]) 
Abstract:  I consider multiround cheap talk communication environments in which, after a lie, the informed party has no memory of the content of the lie. I characterize the equilibria with forgetful liars in such settings assuming that a liar.s expectation about his past lie coincides with the equilibrium distribution of lies aggregated over all possible realizations of the states. The approach is used to shed light on when the full truth is almost surely elicited, when multiple lies can arise in equilibrium, and when inconsistencies trigger harmful consequences. 
Keywords:  forgetful liars,lie detection,analogybased expectations,cheap talk 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:halshs02183313&r=all 
By:  Simina Br\^anzei; Yuval Peres 
Abstract:  The stochastic multiarmed bandit problem is a classic model illustrating the tradeoff between exploration and exploitation. We study the effects of competition and cooperation on this tradeoff. Suppose there are $k$ arms and two players, Alice and Bob. In every round, each player pulls an arm, receives the resulting reward, and observes the choice of the other player but not their reward. Alice's utility is $\Gamma_A + \lambda \Gamma_B$ (and similarly for Bob), where $\Gamma_A$ is Alice's total reward and $\lambda \in [1,1]$ is a cooperation parameter. At $\lambda = 1$ the players are competing in a zerosum game, at $\lambda = 1$, they are fully cooperating, and at $\lambda = 0$, they are neutral: each player's utility is their own reward. The model is related to the economics literature on strategic experimentation, where usually the players observe each other's rewards. In the discounted setting, the Gittins index reduces the oneplayer problem to the comparison between a risky arm, with a prior $\mu$, and a predictable arm with success probability $p$. The value of $p$ where the player is indifferent between the arms is the Gittins index $g(\mu,\beta) > m$, where $m$ is the mean of the risky arm and $\beta$ the discount factor. We show that competing players explore less than a single player: there is $p^* \in (m, g(\mu, \beta))$ so that for all $p > p^*$, the players stay at the predictable arm. However, the players are not completely myopic: they still explore for some $p > m$. On the other hand, cooperating players explore more than a single player. Finally, we show that neutral players learn from each other, receiving strictly higher total rewards than they would playing alone, for all $ p\in (p^*, g(\mu,\beta))$, where $p^*$ is the threshold above which competing players do not explore. We show similar phenomena in the finite horizon setting. 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1908.01135&r=all 