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on Game Theory |
| By: | Iñarra García, María Elena; Serrano, Roberto; Shimomura, Ken-Ichi |
| Abstract: | One of David Schmeidler’s many important contributions in his distinguished career was the introduction of the nucleolus, one of the central single-valued solution concepts in cooperative game theory. This paper is an updated survey on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set. As a first approach to these concepts, we refer the reader to the great survey by Maschler (1992); see also the relevant chapters in Peleg and Sudholter (2003). Building on the notes of four lectures on the nucleolus and the kernel delivered by one of the authors at the Hebrew University of Jerusalem in 1999, we have updated Maschler’s survey by adding more recent contributions to the literature. Following a similar structure, we have also added a new section that covers the bargaining set. The nucleolus has a number of desirable properties, including nonemptiness, uniqueness, core selection, and consistency. The first way to understand it is based on an egalitarian principle among coalitions. However, by going over the axioms that characterize it, what comes across as important is its connection with coalitional stability, as formalized in the notion of the core. Indeed, if one likes a single-valued version of core stability that always yields a prediction, one should consider the nucleolus as a recommendation. The kernel, which contains the nucleolus, is based on the idea of “bilateral equilibrium” for every pair of players. And the bargaining set, which contains the kernel, checks for the credibility of objections coming from coalitions. In this paper, section 2 presents preliminaries, section 3 is devoted to the nucleolus, section 4 to the kernel, and section 5 to the bargaining set. |
| Keywords: | nucleolus, kernel, bargaining, set |
| JEL: | C71 C72 |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:34464&r=all |
| By: | Sebastiano Della Lena (Department of Economics, University Of Venice Cà Foscari); Pietro Dindo (Department of Economics, University Of Venice Cà Foscari) |
| Abstract: | In a heterogeneous population divided into two cultural groups, we investigate the intergenerational dynamics of norms, modeled as preferences over actions, as depending on strategic environments. We find that environments with strategic complementarity or substitutability lead to different long-run norms and horizontal socializations. When players face many games within the same class, under complementarity agents converge to the same norm and socialization is high, under substitutability norms may diverge or become neutral and socialization is low. However, for specific games, partial convergence can arise under complementarity, providing an explanation to cultural heterogeneity, and partial divergence can arise under substitutability. |
| Keywords: | Evolution of Norms, Cultural Transmission, Endogenous preferences, Cultural Heterogeneity |
| JEL: | C7 D9 I20 J15 Z1 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2019:16&r=all |
| By: | Giovanni Compiani (University of California, Berkeley, Haas School of Business); Philip A. Haile (Cowles Foundation, Yale University); Marcelo Sant'Anna (FGV EPGE) |
| Abstract: | In a "common values" environment, some market participants have private information relevant to others' assessments of their own valuations or costs. Economic theory shows that this type of informational asymmetry can have important implications for market performance and market design. Yet even for the classic example of an oil lease auction, formal evidence on the presence and strength of common values has been limited by the problem of auction-level unobserved heterogeneity that is likely to affect both participation in an auction and bidders' willingness to pay. Here we develop an empirical approach for first-price sealed bid auctions with affiliated values, unobserved heterogeneity, and endogenous bidder entry. We show that important features of the model are nonparametrically identified and apply a semiparametric estimation approach to data from U.S. offshore oil and gas lease auctions. Our empirical results show that common values, affiliated private information, and unobserved heterogeneity - three distinct phenomena with different implications for policy and empirical work - are all present. Failing to account for unobserved heterogeneity obscures the empirical evidence of common values. We examine the implications of our estimates for the classic revenue ranking of sealed bid auction designs, and for the interaction between affiliation, the winner's curse, and the number of bidders in determining the aggressiveness of bidding and seller revenue. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2137r&r=all |
| By: | Bas Dietzenbacher (National Research University Higher School of Economics); Elena Yanovskaya (National Research University Higher School of Economics) |
| Abstract: | This paper axiomatically studies the equal split-o set [Branzei, Dimitrov, Tijs 2006) as a solution for cooperative games with transferable utility. This solution extends the well-known [Dutta Ray 1989] solution for convex games to arbitrary games. By deriving several characterizations, we explore the relation of the equal split-o set with various consistency notions. |
| Keywords: | transferable utility games; egalitarianism; equal split-o set; consistency |
| JEL: | C71 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:215/ec/2019&r=all |
| By: | Korpela, Ville; Lombardi, Michele |
| Abstract: | Agents are farsighted when they consider the ultimate results to which their own actions may lead to. We re-examine the classical questions of implementation theory under complete information in a setting with transfers where farsighted coalitions are regarded as fundamental behavioral units and the equilibrium outcomes of their interactions are predicted via the stability notion of the largest consistent set. The designer's exercise consists of designing a rights structure, which formalizes the idea of power distribution in society. His or her challenge lies in designing a rights structure in which the equilibrium behavior of agents always coincides with the recommendation given by a social choice function. We show that (Maskin) monotonicity fully identifies the class of social choice functions that are implementable by a rights structure. We also discuss how this result changes when social choice correspondences are considered. |
| Keywords: | Farsightedness; implementation; transfers; rights structures; coaltions; largest consistent set; monotonicity |
| JEL: | C71 D71 D82 |
| Date: | 2019–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:94436&r=all |
| By: | Pogorelskiy. Kirill (University of Warwick); Shum, Matthew (Caltech) |
| Abstract: | More voters than ever get political news from their friends on social media platforms. Is this bad for democracy? Using context-neutral laboratory experiments, we find that biased (mis)information shared on social networks affects the quality of collective decisions relatively more than does segregation by political preferences on social media. Two features of subject behavior underlie this finding: 1) they share news signals selectively, revealing signals favorable to their candidates more often than unfavorable signals; 2) they naıvely take signals at face value and account for neither the selection in the shared signals nor the differential informativeness of news signals across different sources. |
| Keywords: | news sharing ; social networks ; voting ; media bias ; fake news ; polarization ; filter bubble ; lab experiments |
| JEL: | C72 C91 C92 D72 D83 D85 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1199&r=all |
| By: | Kazuya Kikuchi; Yukio Koriyama |
| Abstract: | This paper considers collective decision-making when individuals are partitioned into groups (e.g., states or parties) endowed with voting weights. We study a game in which each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members’ preferences. We show that under quite general conditions, the game is a Prisoner’s Dilemma: while the winner-take-all rule is a dominant strategy, the equilibrium is Pareto dominated. We also show asymptotic Pareto dominance of the proportional rule. Our numerical computation for the US Electoral College verifies the sensibility of the asymptotic results. |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1059&r=all |
| By: | Attar, Andrea; Campioni, Eloisa; Piaser, Gwenaël |
| Abstract: | We study games in which principals simultaneously post mechanisms in the presence of several agents. We evaluate the role of principals’ communication in these settings. As in Myerson (1982), each principal may generate incomplete information among agents by sending them private signals. We show that this channel of communication, which has not been considered in standard approaches to competing mechanisms, has relevant strategic effects. Specifically, we construct an example of a complete information game in which (multiple) equilibria are sustained as in Yamashita (2010) and none of them survives in games in which all principals can send private signals to agents. The corresponding sets of equilibrium allocations are therefore disjoint. The role of private communication we document may hence call for extending the construction of Epstein and Peters (1999) to incorporate this additional element. |
| Keywords: | Competing Mechanisms; Private Communication |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:123148&r=all |
| By: | Zachary Schaller (Department of Economics, University of California-Irvine); Stergios Skaperdas (Department of Economics, University of California-Irvine) |
| Abstract: | We examine settings—such as litigation, labor relations, or arming and war -- in which players first make non-contractible up-front investments to improve their bargaining position and gain advantage for possible future conflict. Bargaining is efficient ex post, but we show that a player may prefer Conflict ex ante if there are sufficient asymmetries in strength. There are two sources of this finding. First, up-front investments are more dissimilar between players under Con- flict, and they are lower than under Bargaining when one player is much stronger than the other. Second, the probability of the stronger player winning in Conflict is higher than the share received under Nash bargaining. We thus provide a rationale for conflict to occur under complete information that does not depend on long-term commitment problems. Greater balance in institutional support for different sides is more likely to maintain peace and settlements. |
| Keywords: | Power asymmetries; War; Litigation; Contests |
| JEL: | C70 D74 J53 K41 |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:irv:wpaper:181909&r=all |
| By: | Chen, Yongmin; Li, Jianpei; Schwartz, Marius |
| Abstract: | This paper analyzes welfare under differential versus uniform pricing across oligopoly markets that differ in costs of service. We establish necessary and sufficient conditions on demand properties---cross/own elasticities and curvature---for differential pricing by symmetric firms to raise aggregate consumer surplus, profit, and total welfare. The analysis reveals intuitively why differential pricing is generally beneficial though not always---including why profit can fall, unlike for monopoly---and why it is more beneficial than oligopoly third-degree price discrimination. When firms have asymmetric costs, however, differential pricing can reduce profit or consumer surplus even with `simple' demands such as linear. |
| Keywords: | differential pricing, price discrimination, demand curvature, cross-price elasticity, pass-through, oligopoly |
| JEL: | D4 D43 L1 L11 L13 L4 |
| Date: | 2019–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:94381&r=all |
| By: | Olaizola Ortega, María Norma; Valenciano Llovera, Federico |
| Abstract: | We consider a natural generalization of Jackson and Wolinsky s (1996) connections model where the quality or strength of a link depends on the amount invested in it and is determined by a non-decreasing function of that amount. The information that the nodes receive through the network is the revenue from investments in links. We prove that in this most general version of the connections model, the only possibly nonempty efficient networks, in the sense of maximizing the aggregate proffit, are still the all-encompassing star and the complete network, with the sole and rare exception of a highly particular case where there is a draw between the all-encompassing star, the complete network and a whole range of a particular type of nested split graph structures intermediate between them. |
| Keywords: | network, formation, connecions, model, nested, split, graph, efficiency |
| JEL: | A14 C7 D85 |
| Date: | 2019–05–09 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:34463&r=all |
| By: | Christian Bontemps (ENAC - Ecole Nationale de l'Aviation Civile); Bezerra Sampaio |
| Abstract: | In this paper we review the literature on static entry games and show how they can be used to estimate the market structure of the airline industry. The econometrics challenges are presented, in particular the problem of multiple equilibria and some solutions used in the literature are exposed. We also show how these models, either in the complete information setting or in the incomplete information one, can be estimated from i.i.d. data on market presence and market characteristics. We illustrate it by estimating a static entry game with heterogeneous firms by Simulated Maximum Likelihood on European data for the year 2015. |
| Keywords: | multiple equilibria,airlines,estimation,industrial organization,entry |
| Date: | 2019–05–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02137358&r=all |
| By: | Tushar Vaidya; Thiparat Chotibut; Georgios Piliouras |
| Abstract: | We propose new Degroot-type social learning models with feedback in a continuous time, to investigate the effect of a noisy information source on consensus formation in a social network. Unlike the standard Degroot framework, noisy information models destroy consensus formation. On the other hand, the noisy opinion dynamics converge to the equilibrium distribution that encapsulates correlations among agents' opinions. Interestingly, such an equilibrium distribution is also a non-equilibrium steady state (NESS) with a non-zero probabilistic current loop. Thus, noisy information source leads to a NESS at long times that encodes persistent correlated opinion dynamics of learning agents. |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1906.11481&r=all |
| By: | Midjord, Rune; Rodríguez Barraquer, Tomás; Valasek, Justin (Dept. of Economics, Norwegian School of Economics and Business Administration) |
| Abstract: | Numerous theoretical studies have shown that information aggregation through voting is fragile. We consider a model of information aggregation with vote-contingent payoffs and generically characterize voting behavior in large committees. We use this characterization to identify the set of vote-contingent payoffs that lead to a unique outcome that robustly aggregates information. Generally, it is not sufficient to simply reward agents for matching their vote to the true state of the world. Instead, robust and unique information aggregation can be achieved with vote-contingent payoffs whose size varies depending on which option the committee chooses, and whether the committee decision is correct |
| Keywords: | Information aggregation; Voting; Vote-contingent payoffs. |
| JEL: | D71 D72 |
| Date: | 2019–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhheco:2019_012&r=all |
| By: | Mikhail Anufriev (University of Technology Sydney); John Duffy (Department of Economics, University of California-Irvine); Valentyn Panchenko (UNSW Business School, Sydney) |
| Abstract: | We introduce a planar beauty contest game where agents must simultaneously guess two, endogenously determined variables, a and b. The system of equations determining the actual values of a and b is a coupled system; while the realization of a depends on the average forecast for a, a, as in a standard beauty contest game, the realization of b depends on both a and on the average forecast for b, b. Our aim is to better understand the conditions under which agents learn the steady state of such systems and whether the eigenvalues of the system matter for the convergence or divergence of this learning process. We find that agents are able to learn the steady state of the system when the eigenvalues are both less than 1 in absolute value (the sink property) or when the steady state is saddlepath stable with the one root outside the unit circle being negative. By contrast, when the steady state exhibits the source property (two unstable roots) or is saddlepath stable with the one root outside the unit circle being positive, subjects are unable to learn the steady state of the system. We show that these results can be explained by either an adaptive learning model or a mixed cognitive levels model, while other approaches, e.g., naive or homogeneous level-k learning, do not consistently predict whether subjects converge to or diverge away from the steady state. |
| Keywords: | Beauty contest; Learning; Stability; Simultaneous equation systems, Level-k cognitive theory |
| JEL: | C30 C92 D83 D84 |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:irv:wpaper:181907&r=all |
| By: | Gomis-Porqueras, Pedro; Sun, Ching-jen |
| Abstract: | This paper studies different welfare-enhancing roles that fiat money can have. To do so, we consider an indivisible monetary framework where agents are randomly and bilaterally matched and the government has weak enforcement powers. Within this environment, we analyze state contingent monetary policies and characterize the resulting equilibria under different government record-keeping technologies. We show that a threat of injecting fiat money, conditional on private actions, can improve allocations and achieve efficiency. This type of state contingent policy is effective even when the government cannot observe any private trades and agents can only communicate with the government through cheap talk. In all these equilibria fiat money and self-enforcing credit are complements in the off equilibrium. Finally, this type of equilibria can also emerge even when the injection of fiat money is not a public signal. |
| Keywords: | cheap talk; record-keeping; fiat money. |
| JEL: | E40 E52 |
| Date: | 2019–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:94327&r=all |
| By: | Stark, Oded; Budzinski, Wiktor; Kosiorowski, Grzegorz |
| Abstract: | We use queuing-related behavior as an instrument for assessing the social appeal of alternative cultural norms. Specifically, we study the behavior of rational and sophisticated individuals who stand in a given queue waiting to be served, and who, in order to speed up the process, consider switching to another queue. We look at two regimes that govern the possible order in which the individuals stand should they switch to the other queue: a regime in which cultural convention, social norms, and basic notions of fairness require that the order in the initial queue is preserved, and a regime without such cultural inhibitions, in which case the order in the other queue is random, with each configuration or sequence being equally likely. We seek to find out whether in these two regimes the aggregate of the behaviors of self-interested individuals adds up to the social optimum defined as the shortest possible total waiting time. To do this, we draw on a Nash Equilibrium setting. We find that in the case of the preserved order, the equilibrium outcomes are always socially optimal. However, in the case of the random order, unless the number of individuals is small, the equilibrium outcomes are not socially optimal. |
| Keywords: | Political Economy, Public Economics, Research Methods/ Statistical Methods |
| Date: | 2019–07–02 |
| URL: | http://d.repec.org/n?u=RePEc:ags:ubzefd:290417&r=all |