
on Microeconomics 
By:  Chatterji, Shurojit (School of Economics, Singapore Management University); Kunimoto, Takashi (School of Economics, Singapore Management University); Salles Ramos, Paulo Daniel (School of Economics, 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:  2024–02–01 
URL:  http://d.repec.org/n?u=RePEc:ris:smuesw:2024_002&r=mic 
By:  Ori Haimanko (BGU) 
Keywords:  Allpay auctions, incomplete information, behavioral strategies, Bayesian Nash equilibrium, interdependent types. 
JEL:  C72 D44 D82 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:bgu:wpaper:2318&r=mic 
By:  Daniel (University of Pavia); 
Abstract:  Product design is studied in a simple duopoly where firms compete Ã la Cournot, goods are hedonically differentiated and consumers have preferences defined over characteristics. What we find is that, in equilibrium, firms choose the same product’s design. This results in horizontal product differentiation being minimal. 
Keywords:  Hedonic Product Differentiation, Horizontal Differentiation, Product Design, Cournot Competition 
JEL:  D43 L13 L20 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:pav:demwpp:demwp0216&r=mic 
By:  Giebe, Thomas (Department of Economics and Statistics); Gürtler, Oliver (Department of Economics, University of Cologne) 
Abstract:  In competitive settings, disparities in player strength are common. It is intuitively unclear whether a stronger player would opt for larger or smaller effort compared to weaker players. Larger effort could leverage their strength, while lower effort might be justified by their higher probability of winning regardless of effort. We analyze contests with three or more players, exploring when stronger players exert larger or lower effort. To rank efforts, it suffices to compare marginal utilities in situations where efforts are equal. Effort ranking depends on differences in hazard rates (which are smaller for stronger players) and reversed hazard rates (which are larger for stronger players). Compared to weaker players, stronger players choose larger effort in winnertakesall contests and lower effort in losergetsnothing contests. Effort rankings can be nonmonotonic in contests with several identical prizes, and they depend on the slopes of players’ pdfs in contests with linear prize structure. 
Keywords:  contest theory; heterogeneity; player strength 
JEL:  C72 D74 D81 
Date:  2024–03–06 
URL:  http://d.repec.org/n?u=RePEc:hhs:vxesta:2024_004&r=mic 
By:  Gehlbach, Scott; Luo, Zhaotian; Shirikov, Anton; Vorobyev, Dmitriy 
Abstract:  In his seminal work on the political economy of dictatorship, Ronald Wintrobe (1998) posited the existence of a "dictator's dilemma, " in which repression leaves an autocrat less secure by reducing information about discontent. We explore the nature and resolution of this dilemma with a formalization that builds on recent work in the political economy of nondemocracy. When the regime is sufficiently repressive, and the dictator's popularity correspondingly unclear to opposition as well as autocrat, the ruler faces two unattractive options: he can mobilize the repressive apparatus, even though there may be no threat to his rule, or he can refrain from mobilizing, even though the threat may be real. Semicompetitive elections can ease the dilemma through the controlled revelation of discontent. Depending on the ease of building a repressive apparatus, autocrats who manage information in this way may prefer more or less repression than Wintrobe's dilemma alone implies. 
Date:  2024–03–21 
URL:  http://d.repec.org/n?u=RePEc:osf:socarx:b94fc&r=mic 
By:  DziubiÅ„ski, M.; Goyal, S.; Zhou, J. 
Abstract:  We study a model of conflict with multiple battlefields and the possibility of investments spillovers between the battlefields. Results of conflicts at the individual battlefields are determined by the Tullock contest success function based on efforts assigned to a battlefield as well as efforts spilling over from the neighbouring battlefields. We characterize Nash equilibria of this model and uncover a network invariance result: equilibrium payoffs, equilibrium total expenditure, and equilibrium probabilities of winning individual battlefields are independent of the network of spillovers. We show that the network invariance holds for any contest success function that is homogeneous of degree zero and has the notie property. We define a network index that characterizes equilibrium efforts assignments of the players. We show that the index satisfies neighbourhood inclusion and can, therefore, be considered a network centrality. 
Keywords:  Conflict, Investments, Models, Networks 
Date:  2024–02–21 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2408&r=mic 
By:  Zhang Xu; Mingsheng Zhang; Wei Zhao 
Abstract:  As firms' pricing strategies increasingly rely on algorithms, two concerns have received much attention: algorithmic tacit collusion and price discrimination. This paper investigates the interaction between these two issues through simulations. In each period, a new buyer arrives with independently and identically distributed willingness to pay (WTP), and each firm, observing private signals about WTP, adopts Qlearning algorithms to set prices. We document two novel mechanisms that lead to collusive outcomes. Under asymmetric information, the algorithm with information advantage adopts a BaitandRestrainedExploit strategy, surrendering profits on some signals by setting higher prices, while exploiting limited profits on the remaining signals by setting much lower prices. Under a symmetric information structure, competition on some signals facilitates convergence to supracompetitive prices on the remaining signals. Algorithms tend to collude more on signals with higher expected WTP. Both uncertainty and the lack of correlated signals exacerbate the degree of collusion, thereby reducing both consumer surplus and social welfare. A key implication is that the overusage of data, both payoffrelevant and nonrelevant, by AIs in competitive contexts will reduce the degree of collusion and consequently lead to a decline in industry profits. 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2403.06150&r=mic 
By:  Simon Finster; Patrick Loiseau; Simon Mauras; Mathieu Molina; Bary Pradelski 
Abstract:  We study how pricing affects the division of surplus among buyers in auctions for multiple units. Our equity objective may be important, e.g., for competition concerns in downstream markets, complementing the longstanding debate on revenue and efficiency. We study a canonical model of auctions for multiple indivisible units with unit demand buyers and valuations with a private and a common component and consider all pricing rules that are a mixture (i.e., a convex combination) of payasbid and uniform pricing. We propose the winners' empirical variance (WEV), the expected empirical variance of surplus among the winners, as a metric for surplus equity. We show that, for a range of privatecommon value proportions, a strictly interior mix of payasbid and uniform pricing minimizes WEV. From an equity perspective, auctions with a higher private value component benefit from more price discrimination, whereas only auctions with a sufficiently high common value justify a more uniform pricing rule. We provide a criterion under which strictly mixed pricing dominates uniform pricing, a partial ranking of different mixed pricing formats, and bounds on the WEVminimizing pricing under the assumption of logconcave signal distributions. In numerical experiments, we further illustrate the WEVminimal pricing as a function of the privatecommonvalue mix. 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2403.07799&r=mic 
By:  NAKADA, Satoshi; SAKAMOTO, Norihito 
Abstract:  This paper investigates a class of socialwelfare orderings that satisfy the standard and acceptable axioms in the literature: anonymity, strong Pareto, separability, and PigouDalton transfer (or, convexity). Due to the lack of continuity, we show that the class of social welfare orderings typically has some thresholds satisfying the following property, which we call leveloligarchy: individuals whose utility is less than the value are prioritized over the other individuals whose utility is greater than the value. First, we provide the novel reduced form characterization that a social welfare ordering satisfies anonymity, strong Pareto, separability, and convexity must be either the weak generalized utilitarian or leveloligarchy. Next, by dropping convexity and instead requiring PigouDalton transfer and a mild continuity axiom, we characterize the new class of social welfare orderings, the multithreshold generalized sufficientarian orderings, which subsumes the leximin, generalized utilitarian, and criticallevel sufficientarian social welfare orderings as special cases. Therefore, we can provide a unified characterization for the important class of social welfare orderings only by the permissible axioms. In particular, although the social judgment from both classes of orderings seems quite different, our result implies that the difference between the utilitarian and leximin orderings just comes from the degree of continuity. 
Keywords:  Social welfare ordering, utilitarian, leximin, sufficientarianism, distributive justice 
JEL:  D31 D63 D70 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:hit:rcnedp:13&r=mic 
By:  Mert Kimya 
Abstract:  We provide the first axiomatic treatment of two of the most fundamental farsighted solution concepts. We then extend our analysis to include an axiomatization of the stable set to the extent that it is farsighted. In fi nite abstract games a solution is the largest consistent set if and only if it is maximally supportable and nonempty. In any abstract game a solution is the farsighted stable set if and only if it is minimally supportable, consistent, conversely consistent and nonempty in finite horizon games. We call the stable set that does not suffer from Harsanyi (1974)'s critique of myopia the Harsanyi stable set. In any abstract game a solution is the Harsanyi stable set if and only if it is simply supportable, consistent, weakly conversely consistent and it satisfi es restricted nonemptiness. The axioms of consistency and converse consistency are the adaptations of the frequently used principles of consistency and converse consistency to a farsighted framework. The axioms of maximal supportability, minimal supportability and simple supportability relate to the commonly held expectations that support these solutions as their stationary states. 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:syd:wpaper:202403&r=mic 
By:  Gisèle Umbhauer (BETA  Bureau d'Économie Théorique et Appliquée  AgroParisTech  UNISTRA  Université de Strasbourg  Université de HauteAlsace (UHA)  Université de HauteAlsace (UHA) Mulhouse  Colmar  UL  Université de Lorraine  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  This paper shows how minimax regret sheds new light on an old economic topic, marketexit games. It focuses on wars of attrition, namely overcrowded duopoly markets where the strategic variable is the exit time. The only symmetric Nash equilibrium (NE) of the game studied is a mixedstrategy equilibrium that leads to a null expected payoff, i.e., the payoff a firm gets when it immediately exits the market. This result is not convincing, both from a behavioral and from a strategic viewpoint. The minimax regret approach that builds upon opposite regrets — exiting the market too late and exiting the market too early — is more convincing and ensures that both firms obtain a strictly positive expected payoff. 
Keywords:  War of attrition, Minimax regret, Mixedstrategy Nash equilibrium, Maximin payoff, Overcrowded market 
Date:  2022–12–11 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal04491262&r=mic 
By:  Bramoullé, Y.; Ghiglino, C. 
Abstract:  We introduce loss aversion into a model of conspicuous consumption in networks. Agents allocate heterogeneous incomes between a conventional good and a status good. They interact over a connected network and compare their status consumption to their neighborsâ€™ average consumption. We find that aversion to lying below the social reference point has a profound impact. If loss aversion is large relative to income heterogeneity, a continuum of conformist Nash equilibria emerges. Agents have the same status consumption, despite differences in incomes and network positions, and the equilibrium is indeterminate. Otherwise, there is a unique Nash equilibrium and status consumption depends on the interplay between network positions and incomes. Our analysis extends to homothetic and heterogeneous preferences. 
Keywords:  Conspicuous Consumption, Loss Aversion, Social Networks 
Date:  2024–03–12 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2414&r=mic 
By:  Mitsunobu MIYAKE 
Abstract:  This note elaborates on Luce and Narens' (1978) axiomatic derivation of subjective probability, which generically satisfies the multiplicative law by removing requirement for the derived subjective probability to be nonatomic. For the two original sample spaces, we add the sample space defined by the direct product of the original sample spaces and the sample space of the auxiliary experiment. As a main result, the necessary and sufficient conditions are provided for the likelihood relation on the events of the sample spaces to be represented by the subjective probability satisfying the law with respect to the direct product, allowing atoms in the original sample spaces. 
Date:  2024–03–22 
URL:  http://d.repec.org/n?u=RePEc:toh:tergaa:481&r=mic 