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on Microeconomics |
| By: | Hitoshi Matsushima (Department of Economics, University of Tokyo) |
| Abstract: | We investigate the implementation of social choice functions with asymmetric information concerning the state from an epistemological perspective. Although agents are either selfish or honest, they do not expect other participants to be honest. However, an honest agent may exist not among participants but in their higher-order beliefs. We assume that “all agents are selfish†never happens to be common knowledge. We show a positive result in general asymmetric information environments, demonstrating that with a minor restriction on signal correlation called information diversity, any incentive-compatible social choice function, whether ethical or nonethical, is uniquely implementable in the Bayesian Nash equilibrium. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf548&r=mic |
| By: | Marco de Pinto; Laszlo Goerke; Alberto Palermo |
| Abstract: | We consider a principal-agent relationship with adverse selection. Principals pay informational rents due to asymmetric information and sell their output in a homogeneous Cournot-oligopoly. We find that asymmetric information may mitigate or more than compensate the welfare reducing impact of market power, irrespective of whether the number of firms is given exogenously or determined endogenously by a profit constraint. We further show that welfare in a setting with adverse selection may be higher than the maximized welfare level attainable in a world with perfect observability. |
| Keywords: | adverse selection, oligopoly, welfare |
| JEL: | D43 D82 L51 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10003&r=mic |
| By: | Tal Alon; Paul D\"utting; Yingkai Li; Inbal Talgam-Cohen |
| Abstract: | We study a generalization of both the classic single-dimensional mechanism design problem, and the hidden-action principal-agent problem of contract theory. In this setting, the principal seeks to incentivize an agent with a private Bayesian type to take a costly action. The goal is to design an incentive compatible menu of contracts which maximizes the expected revenue. Our main result concerns linear contracts, the most commonly-used contract form in practice. We establish that in Bayesian settings, under natural small-tail conditions, linear contracts provide an $O(1)$-approximation to the optimal, possibly randomized menu of contracts. This constant approximation result can also be established via a smoothed-analysis style argument. We thus obtain a strong worst-case approximation justification of linear contracts. These positive findings stand out against two sets of results, which highlight the challenges of obtaining (near-)optimal contracts with private types. First, we show that the combination of private type and hidden action makes the incentive compatibility constraints less tractable: the agent's utility has to be convex (as without hidden action), but it also has to satisfy additional curvature constraints. Second, we show that the optimal menu of contracts can be complex and/or exhibit undesirable properties - such as non-monotonicity of the revenue in the type distribution. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.06850&r=mic |
| By: | Chatterji, Shurojit (Singapore Management University); Kunimoto, Takashi (Singapore Management University); Ramos, Paulo (Singapore Management University) |
| Abstract: | A social choice function (SCF) is said to be Nash implementable if there exists a mechanism in which every Nash equilibrium outcome coincides with that specified by the SCF. The main objective of this paper is to assess the impact of considering mixed strategy equilibria in Nash implementation. To do this, we focus on environments with two agents and restrict attention to finite mechanisms. We call a mixed strategy equilibrium “compelling” if its outcome Pareto dominates any pure strategy equilibrium outcome. We show that if the finite environment and the SCF to be implemented jointly satisfy what we call Condition P+M, we construct a finite mechanism which Nash implements the SCF in pure strategies and possesses no compelling mixed strategy equilibria. This means that the mechanism might possess mixed strategy equilibria which are “not” compelling. Our mechanism has several desirable features: transfers can be completely dispensable; only finite mechanisms are considered; integer games are not invoked; and players’ attitudes toward risk do not matter. |
| Keywords: | implementation; compelling equilibria; ordinality; mixed strategies[Nash equilibrium |
| JEL: | C72 D78 D82 |
| Date: | 2022–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2022_010&r=mic |
| By: | Fabian R. Pieroth; Martin Bichler |
| Abstract: | Game theory largely rests on the availability of cardinal utility functions. In contrast, only ordinal preferences are elicited in fields such as matching under preferences. The literature focuses on mechanisms with simple dominant strategies. However, many real-world applications do not have dominant strategies, so intensities between preferences matter when participants determine their strategies. Even though precise information about cardinal utilities is unavailable, some data about the likelihood of utility functions is typically accessible. We propose to use Bayesian games to formalize uncertainty about decision-makers utilities by viewing them as a collection of normal-form games where uncertainty about types persist in all game stages. Instead of searching for the Bayes-Nash equilibrium, we consider the question of how uncertainty in utilities is reflected in uncertainty of strategic play. We introduce $\alpha$-Rank-collections as a solution concept that extends $\alpha$-Rank, a new solution concept for normal-form games, to Bayesian games. This allows us to analyze the strategic play in, for example, (non-strategyproof) matching markets, for which we do not have appropriate solution concepts so far. $\alpha$-Rank-collections characterize a range of strategy-profiles emerging from replicator dynamics of the game rather than equilibrium point. We prove that $\alpha$-Rank-collections are invariant to positive affine transformations, and that they are efficient to approximate. An instance of the Boston mechanism is used to illustrate the new solution concept. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.10317&r=mic |
| By: | Gerrit Bauch; Frank Riedel |
| Abstract: | We investigate the allocation of a co-owned company to a single owner using the Texas Shoot-Out mechanism with private valuations. We identify Knightian Uncertainty about the peer's distribution as a reason for its deterrent effect of a premature dissolving. Modeling uncertainty by a distribution band around a reference distribution $F$, we derive the optimal price announcement for an ambiguity averse divider. The divider hedges against uncertainty for valuations close to the median of $F$, while extracting expected surplus for high and low valuations. The outcome of the mechanism is efficient for valuations around the median. A risk neutral co-owner prefers to be the chooser, even strictly so for any valuation under low levels of uncertainty and for extreme valuations under high levels of uncertainty. If valuations are believed to be close, less uncertainty is required for the mechanism to always be efficient and reduce premature dissolvements. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.10089&r=mic |
| By: | Ben Abramowitz; Nicholas Mattei |
| Abstract: | We consider the problem of aggregating binary votes from an ensemble of experts to reveal an underlying binary ground truth where each expert votes correctly with some independent probability. We focus on settings where the number of agents is too small for asymptotic results to apply, many experts may vote correctly with low probability, and there is no central authority who knows the experts' competences, or their probabilities of voting correctly. Our approach is to designate a second type of agent -- a judge -- to weight the experts to improve overall accuracy. The catch is that the judge has imperfect competence just like the experts. We demonstrate that having a single minimally competent judge is often better than having none at all. Using an ensemble of judges to weight the experts can provide a better weighting than any single judge; even the optimal weighting under the right conditions. As our results show, the ability of the judge(s) to distinguish between competent and incompetent experts is paramount. Lastly, given a fixed set of agents with unknown competences drawn i.i.d. from a common distribution, we show how the optimal split of the agents between judges and experts depends on the distribution. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.08494&r=mic |
| By: | Gagnon-Bartsch, Tristan; Rosato, Antonio |
| Abstract: | We study how misperceptions of others’ tastes influence beliefs, demand, and prices in a market with observational learning. Consumers infer the commonly-valued quality of a good based on the quantity demanded and price paid by other consumers. When consumers exaggerate the degree to which others’ tastes resemble their own, such “taste projection” leads to erroneous and disparate quality perceptions across consumers (i.e., “quality is in the eye of the beholder”). In particular, a consumer’s biased estimate of the good’s quality is negatively related to her own taste. Moreover, consumers’ quality estimates are increasing in the observed price, even when the price would have no influence on the beliefs of rational consumers. These biased beliefs result in perceived valuations that exhibit too little dispersion relative to rational learning and a demand function that is excessively price sensitive. We then analyze how a sophisticated monopolist optimally sets prices when facing short-lived taste-projecting consumers. Projection leads to a declining price path: the seller uses an excessively high price early on to inflate future buyers’ perceptions (e.g., creating “hype”), and then lowers the price to induce a larger-than-rational share to buy. When consumers can instead time their purchase, projection causes late buyers to under-appreciate selection effects, thereby exposing them to systematic disappointment. A final application examines how projection of risk preferences distorts portfolio choice when learning from asset prices. |
| Keywords: | Social Learning; Dynamic Pricing; Projection Bias; False-Consensus Effect. |
| JEL: | D42 D82 D83 D91 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115426&r=mic |
| By: | Kohei Daido (School of Economics, Kwansei Gakuin University); Takeshi Murooka (Osaka School of International Public Policy, Osaka University) |
| Abstract: | We study multitasking problems where an agent engages in both a contractible task and a non-contractible task, which are substitutes. The agent has private information on the value of the non-contractible task, and there are followers who can also contribute to this task. We highlight a new mechanism by incorporating leading-by-example (Hermalin, 1998) in a multitasking model. To prevent excessive effort by the agent with low value on the non-contractible task, the principal provides high-powered incentives for the contractible task. We discuss its organizational implications to pay for performance, incentives to help colleagues, and prevention of overwork. |
| Keywords: | Multitasking, Signaling, Leadership, Pay for Performance, Help, Overwork |
| JEL: | D82 D86 J33 M52 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:osp:wpaper:22e005&r=mic |
| By: | Jason D. Hartline; Liren Shan; Yingkai Li; Yifan Wu |
| Abstract: | This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest, Krysta, and V\"ocking, 2005, Singer, 2010) and it is foundational to applying algorithmic mechanism design to the classroom. The paper identifies two simple families of scoring rules that guarantee constant approximations to the optimal scoring rule. The truncated separate scoring rule is the sum of single dimensional scoring rules that is truncated to the bounded range of feasible scores. The threshold scoring rule gives the maximum score if reports exceed a threshold and zero otherwise. Approximate optimality of one or the other of these rules is similar to the bundling or selling separately result of Babaioff, Immorlica, Lucier, and Weinberg (2014). Finally, we show that the approximate optimality of the best of those two simple scoring rules is robust when the agent's choice of effort is made sequentially. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.03302&r=mic |
| By: | Banghua Zhu; Stephen Bates; Zhuoran Yang; Yixin Wang; Jiantao Jiao; Michael I. Jordan |
| Abstract: | We study the hidden-action principal-agent problem in an online setting. In each round, the principal posts a contract that specifies the payment to the agent based on each outcome. The agent then makes a strategic choice of action that maximizes her own utility, but the action is not directly observable by the principal. The principal observes the outcome and receives utility from the agent's choice of action. Based on past observations, the principal dynamically adjusts the contracts with the goal of maximizing her utility. We introduce an online learning algorithm and provide an upper bound on its Stackelberg regret. We show that when the contract space is $[0,1]^m$, the Stackelberg regret is upper bounded by $\widetilde O(\sqrt{m} \cdot T^{1-C/m})$, and lower bounded by $\Omega(T^{1-1/(m+2)})$. This result shows that exponential-in-$m$ samples are both sufficient and necessary to learn a near-optimal contract, resolving an open problem on the hardness of online contract design. When contracts are restricted to some subset $\mathcal{F} \subset [0,1]^m$, we define an intrinsic dimension of $\mathcal{F}$ that depends on the covering number of the spherical code in the space and bound the regret in terms of this intrinsic dimension. When $\mathcal{F}$ is the family of linear contracts, the Stackelberg regret grows exactly as $\Theta(T^{2/3})$. The contract design problem is challenging because the utility function is discontinuous. Bounding the discretization error in this setting has been an open problem. In this paper, we identify a limited set of directions in which the utility function is continuous, allowing us to design a new discretization method and bound its error. This approach enables the first upper bound with no restrictions on the contract and action space. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.05732&r=mic |
| By: | Jacob K Goeree |
| Abstract: | I introduce a concave function of allocations and prices -- the economy's potential -- which measures the difference between utilitarian social welfare and its dual. I show that Walrasian equilibria correspond to roots of the potential: allocations maximize weighted utility and prices minimize weighted indirect utility. Walrasian prices are "utility clearing" in the sense that the utilities consumers expect at Walrasian prices are just feasible. I discuss the implications of this simple duality for equilibrium existence, the welfare theorems, and the interpretation of Walrasian prices. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.14437&r=mic |
| By: | Drobner, Christoph (Technical University of Munich); Goerg, Sebastian J. (Technische Universität München) |
| Abstract: | We study belief updating about relative performance in an ego-relevant task. Manipulating the perceived ego-relevance of the task, we show that subjects update their beliefs optimistically because they derive direct utility flows from holding positive beliefs. This finding provides a behavioral explanation why and how overconfidence can evolve in the presence of objective information. Moreover, we document that subjects, who received more bad signals, downplay the ego-relevance of the task. Taken together, these findings suggest that subjects use two alternative strategies to protect their ego when presented with objective information. |
| Keywords: | motivated beliefs, optimistic belief updating, overconfidence, direct belief utility, Bayes' rule, ex-post rationalization |
| JEL: | C91 D83 D84 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15682&r=mic |
| By: | Avidit Acharya (Stanford University, and the Hoover Institution Author-Name: Edoardo Grillo; University of Padova); Takuo Sugaya (Stanford University); Eray Turkel (Stanford University) |
| Abstract: | We develop a model of electoral campaigns as dynamic contests in which two office-motivated candidates allocate their budgets over time to affect their odds of winning. We measure the candidates’ evolving odds of winning using a state variable that tends to decay over time, and we refer to it as the can- didates’ “relative popularity.†In our baseline model, the equilibrium ratio of spending by each candidate equals the ratio of their initial budgets; spending is independent of past realizations of relative popularity; and there is a positive relationship between the strength of decay in the popularity process and the rate at which candidates increase their spending over time as election day ap- proaches. We use this relationship to recover estimates of the perceived decay rate in popularity leads in actual U.S. subnational elections. |
| Keywords: | campaigns, dynamic allocation problems, contests |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:pad:wpaper:0293&r=mic |