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on Economic Design |
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Issue of 2022‒12‒12
nine papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| 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=des |
| 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=des |
| By: | Andrew Tai |
| Abstract: | Consider the object allocation (one-sided matching) model of Shapley and Scarf (1974). When final allocations are observed but agents' preferences are unknown, can the allocation be in the core? This is a one-sided analogue of Echenique, Lee, Shum, and Yenmez (2013). I build a model in which the strict core is testable ("rationalizability") based on types of agents who share preferences. I find if and only if conditions for an allocation to be rationalizable. The main theorem also partially identifies the set of preferences which rationalize an allocation when possible. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.14388&r=des |
| 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=des |
| 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=des |
| By: | Bhattacherjee, Sanjay; Chakravarty, Satya R.; Sarkar, Palash |
| Abstract: | This article introduces a general model for voting games with multiple weight vectors. Each weight vector characterises a parameter representing a distinct aspect of the voting mechanism. Our main innovation is to model the winning condition by an arbitrary dichotomous function which determines whether a coalition is winning based on the weights that the coalition has for the different parameters. Previously studied multi-parameter games are obtained as particular cases of the general model. We identify a new and interesting class of games, that we call hyperplane voting games, which are compactly expressible in the new model, but not necessarily so in the previous models. For the general model of voting games that we introduce, we describe dynamic programming algorithms for determining various quantities required for computing different voting power indices. Specialising to the known classes of multi-parameter games, our algorithms provide unified and simpler alternatives to previously proposed algorithms. |
| Keywords: | weighted majority voting game, multi-parameter games, Boolean formula, voting power, dynamic programming |
| JEL: | C71 |
| Date: | 2022–11–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115407&r=des |
| 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=des |
| By: | Rosato, Antonio; Tymula, Agnieszka |
| Abstract: | We present experimental evidence on bidding in second-price auctions with real objects. Our novel design, combining a second-price auction with an individual-specific binary choice task based on the outcome of the auction, allows us to directly identify over and under-bidding. We analyze bidding in real-object and induced-value auctions, and find significant deviations from truthful bidding in both. Overall, under-bidding is somewhat more prevalent than over-bidding; yet, the latter has a bigger magnitude, especially with induced values. At the individual level, we find no relation between the tendency to deviate from truthful bidding in induced-value vs. real-object auctions. |
| Keywords: | Second-price Auctions; Overbidding; Consumer Surplus. |
| JEL: | D44 D81 D91 D92 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115427&r=des |
| By: | Ewa Zawojska (University of Warsaw, Faculty of Economic Sciences); Michał Krawczyk (University of Warsaw, Faculty of Economic Sciences) |
| Abstract: | Stated preferences should ideally be elicited in ways providing respondents with economic incentives to report them truthfully—that is, in incentive-compatible conditions. This study aims at testing empirically a novel theoretical approach, which allows for incentive-compatible elicitation of preferences. Choice-matching, proposed by Cvitanić et al. (2019), is applied here to elicit stated preferences towards a public good. While the approach has been originally designed for incentivizing responses to a multiple choice question, we illustrate its possible application to an open-ended question. We conduct an online experiment mirroring a standard stated preference survey as used for valuation of public goods. Two versions of the survey questionnaire are implemented: one employing the incentive-compatible choice-matching approach and another representing a common non-incentivized setting. We find that the open-ended willingness-to-pay values are statistically significantly higher when stated under choice-matching than when expressed in the non-incentivized conditions. |
| Keywords: | contingent valuation, choice-matching, incentive compatibility, open-ended elicitation, stated preferences |
| JEL: | D61 D82 H43 Q51 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2022-04&r=des |