
on Economic Design 
By:  Tal Alon; Paul D\"utting; Yingkai Li; Inbal TalgamCohen 
Abstract:  We study a generalization of both the classic singledimensional mechanism design problem, and the hiddenaction principalagent 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 commonlyused contract form in practice. We establish that in Bayesian settings, under natural smalltail 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 smoothedanalysis style argument. We thus obtain a strong worstcase 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 nonmonotonicity 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 multidimensional 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 (onesided 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 onesided 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 higherorder beliefs. We assume that â€œall agents are selfishâ€ 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 incentivecompatible 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 multiparameter 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 multiparameter games, our algorithms provide unified and simpler alternatives to previously proposed algorithms. 
Keywords:  weighted majority voting game, multiparameter 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 realworld 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 decisionmakers utilities by viewing them as a collection of normalform games where uncertainty about types persist in all game stages. Instead of searching for the BayesNash equilibrium, we consider the question of how uncertainty in utilities is reflected in uncertainty of strategic play. We introduce $\alpha$Rankcollections as a solution concept that extends $\alpha$Rank, a new solution concept for normalform games, to Bayesian games. This allows us to analyze the strategic play in, for example, (nonstrategyproof) matching markets, for which we do not have appropriate solution concepts so far. $\alpha$Rankcollections characterize a range of strategyprofiles emerging from replicator dynamics of the game rather than equilibrium point. We prove that $\alpha$Rankcollections 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 secondprice auctions with real objects. Our novel design, combining a secondprice auction with an individualspecific binary choice task based on the outcome of the auction, allows us to directly identify over and underbidding. We analyze bidding in realobject and inducedvalue auctions, and find significant deviations from truthful bidding in both. Overall, underbidding is somewhat more prevalent than overbidding; 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 inducedvalue vs. realobject auctions. 
Keywords:  Secondprice 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 incentivecompatible conditions. This study aims at testing empirically a novel theoretical approach, which allows for incentivecompatible elicitation of preferences. Choicematching, 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 openended 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 incentivecompatible choicematching approach and another representing a common nonincentivized setting. We find that the openended willingnesstopay values are statistically significantly higher when stated under choicematching than when expressed in the nonincentivized conditions. 
Keywords:  contingent valuation, choicematching, incentive compatibility, openended elicitation, stated preferences 
JEL:  D61 D82 H43 Q51 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:war:wpaper:202204&r=des 