|
on Game Theory |
| By: | Ziv Hellman (Bar-Ilan University); Ilan Nehama (Bar-Ilan University); Omer Edhan |
| Abstract: | We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even with linkage disequilibrium) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified underlying theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual, and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:biu:wpaper:2020-05&r=all |
| By: | Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We consider a class of comprehensive compact convex polyhedra called _Cephoids_. A Cephoid is a Minkowski sum of finitely many standardized simplices ("deGua Simplices''). The Pareto surface of Cephoids consists of certain translates of simplices, algebraic sums of subsimplices etc. The peculiar shape of such a Pareto surface raises the question as to how far results for Cephoids can be carried over to general comprehensive compact convex bodies by approximation. We prove that to any comprehensive compact convex body Γ , given a set of finitely many points on its surface, there is a Cephoid Π that coincides with Γ in exactly these preset points. As a consequence, Cephoids are dense within the set of comprehensive compact convex bodies with respect to the Hausdorff metric. Cephoids appear in Operations Research (Optimization |10|, |3|), in Mathematical Economics (Free Trade theory |7|, |8|), and in Cooperative Game Theory (the Maschler--Perles solution |6|). More generally in the context of Cooperative Game Theory, the notion of a Cephoid serves to construct "solutions'' or "values'' for bargaining problems and non--side payment games (|9|). Therefore, the results of this paper open up an avenue for the extension of solution concepts from Cephoids to general compact convex bodies. |
| Date: | 2020–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:640&r=all |
| By: | Ziv Hellman (Bar-Ilan University); Yehuda John Levy |
| Abstract: | We study dynamic properties of the group action on the simplex that is induced by Bayesian updating. We show that generically the orbits are dense in the simplex, although one must make use of the entire group, hence departing from straightforward Bayesian updating. We demonstrate also the necessity of the genericity of the signalling structure, a relationship to descriptive set theoretical concepts and applications thereof to repeated games of incomplete information, as well a strengthening concerning the group action on itself. |
| Keywords: | Bayesian updating, group actions, descriptive set theory, repeated games. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:biu:wpaper:2020-04&r=all |
| By: | Wu, Haoyang |
| Abstract: | In mechanism design theory, a designer would like to implement a social choice function which specifies her favorite outcome for each possible profile of agents' private types. The revelation principle asserts that if a social choice function can be implemented by a mechanism in equilibrium, then there exists a direct mechanism that can truthfully implement it. This paper aims to propose a failure of the revelation principle. At first we point out that in any game the format of each agent's strategy is either an abstract message or a real action. For any given social choice function, if the mechanism which implements it in Bayesian Nash equilibrium has action-format strategies, then ``honest and obedient'' will not be an equilibrium strategy in the corresponding direct mechanism. Consequently, the revelation principle fails. |
| Keywords: | Mechanism design; Revelation principle. |
| JEL: | D71 |
| Date: | 2020–11–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104171&r=all |
| By: | Nicolas Fugger; Vitali Gretschko; Helene Mass; Achim Wambach |
| Abstract: | Procurement regulation aimed at curbing discrimination requires equal treatment of sellers. However, Deb and Pai show that such regulation imposes virtually no restrictions on the ability to discriminate. We propose a simple rule - imitation perfection - that restricts discrimination significantly. It ensures that in every equilibrium bidders with the same valuation distribution and the same valuation earn the same expected utility. If all bidders are homogeneous, revenue and social surplus optimal auctions consistent with imitation perfection exist. For heterogeneous bidders, however, it is incompatible with revenue and social surplus optimization. Thus, a trade-off between non-discrimination and optimality exists. |
| Keywords: | Discrimination, symmetric auctions, procurement regulation |
| JEL: | D44 D73 D82 L13 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_225v2&r=all |
| By: | Kang, Liying; Khmelnitskaya, Anna; Shan, Erfang; Talman, A.J.J. (Tilburg University, Center For Economic Research); Zhang, Guang (Tilburg University, Center For Economic Research) |
| Keywords: | TU game; hypergraph communication structure; average tree value; component fairness |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:54b390b3-2713-4a64-874c-84d3974c7e5d&r=all |
| By: | Adam Zylbersztejn; Zakaria Babutsidze (Observatoire français des conjonctures économiques); Nobuyuki Hanaki (Université Côte d'Azur (UCA)) |
| Abstract: | We experimentally investigate how much value people put in observable information about others in strategic interactions. The incentivized experimental task is to predict an unknown target player’s trustworthiness in an earlier hidden action game. In Experiment 1, we vary the source of information about the target player (neutral picture, neutral video, video containing strategic content). The observed prediction accuracy rates then serve as an empirical measure of the objective value of information. In Experiment 2, we elicit the subjective value of information using the standard stated preferences method (“willing- ness to accept”). While the elicited subjective values are ranked in the same manner as the objective ones, subjects attach value to information which does not help predict target behavior, and exaggerate the value of helpful information. |
| Keywords: | Prediction; Observable information; Individual characteristics; Stated preferences; Willingness to accept; Experiment |
| JEL: | C72 D83 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/3r19808hvq8dlb97k36cbcqihj&r=all |
| By: | Azevedo, Eduardo M.; Gottlieb, Daniel |
| Abstract: | Rothschild and Stiglitz [1976] proposed a model of a competitive market with adverse selection and showed that a (pure strategy) Nash equilibrium may not exist. Among the solutions proposed to deal with this problem, a particularly influential one is the notion of Riley (or reactive) equilibrium [Riley, 1979]. We give an example that shows that a Riley equilibrium may not exist if consumers are not ordered. |
| Keywords: | adverse selection; equilibrium; insurance |
| JEL: | D86 D82 |
| Date: | 2019–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:102566&r=all |
| By: | Olivier Bos; Tom Truyts |
| Abstract: | We study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders’ types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in the second-price auction and the English auction. We establish there is no equivalence between these two auction designs, neither in bidding strategies nor in expected revenue. This is because the presence or absence of an increasing price clock, affects signaling incentives differently in both auction formats, and thereby also the bidders’ incentives to overbid their types. This leads to a strictly higher expected revenue in the second-price auction than in the English auction. Our analysis is completed by a comparison with other disclosure policies. Applications include art auctions and charity auctions. |
| Keywords: | costly signalling, D1 criterion, social status, art auctions, charity auctions |
| JEL: | D44 D82 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8650&r=all |
| By: | Lea Heursen; Eva Ranehill; Roberto A. Weber |
| Abstract: | We study whether one reason behind female underrepresentation in leadership is that female leaders are less effective at coordinating action by followers. Two experiments using coordination games investigate whether female leaders are less successful than males in persuading followers to coordinate on efficient equilibria. Group performance hinges on higher-order beliefs about the leader’s capacity to convince followers to pursue desired actions, making beliefs that women are less effective leaders potentially self-confirming. We find no evidence that such bias impacts actual leadership performance, identifying a precisely-estimated null effect. We show that this absence of an effect is surprising given experts’ priors. |
| Keywords: | Gender, coordination games, leadership, experiment |
| JEL: | D23 C72 C92 J1 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:368&r=all |
| By: | Jeongbin Kim; Wooyoung Lim; Sebastian Schweighofer-Kodritsch |
| Abstract: | We generalize the Rubinstein (1982) bargaining model by disentangling payoff delay from bargaining delay. We show that our extension is isomorphic to generalized discounting with dynamic consistency and characterize the unique equilibrium. Using a novel experimental design to control for various confounds, we then test comparative statics predictions with respect to time discounting. All bargaining takes place within a single experimental session, so bargaining delay is negligible and dynamic consistency holds by design, while payoff delay per disagreement round is significant and randomized transparently at the individual level (week/month, with/without front-end delay). In contrast to prior experiments, we obtain strong behavioral support for the basic predictions that hold regardless of the details of discounting. Testing differential predictions of different forms of discounting, we strongly reject exponential discounting in favor of present-biased discounting. |
| Keywords: | alternating-offers bargaining, time preferences, present bias, laboratory experiments |
| JEL: | C78 C91 D03 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8683&r=all |
| By: | Moshe Babaioff; Yoav Kolumbus; Eyal Winter |
| Abstract: | We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to him, and at the same time, raise capital for his firm own enterprise from other agents he is linked to. Failing to raise sufficient capital results with the firm defaulting, being unable to invest in others. Our main objective is to examine the role of collaterals in handling the strategic risk that can propagate to a systemic risk throughout the network in a cascade of defaults. We take a mechanism design approach and solve for the optimal scheme of collateral contracts that capital raisers offer their investors. These contracts aim at sustaining the efficient level of investment as a unique Nash equilibrium, while minimizing the total collateral. Our main results contrast the network environment with its non-network counterpart (where the sets of investors and capital raisers are disjoint). We show that for acyclic investment networks, the network environment does not necessitate any additional collaterals, and systemic risk can be fully handled by optimal bilateral collateral contracts between capital raisers and their investors. This is, unfortunately, not the case for cyclic investment networks. We show that bilateral contracting will not suffice to resolve systemic risk, and the market will need an external entity to design a global collateral scheme for all capital raisers. Furthermore, the minimum total collateral that will sustain the efficient level of investment as a unique equilibrium may be arbitrarily higher, even in simple cyclic investment networks, compared with its corresponding non-network environment. Additionally, we prove computational-complexity results, both for a single enterprise and for networks. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2011.06247&r=all |
| By: | von Auer, Ludwig; Pham, Tu Anh |
| Abstract: | A model-based derivation of an effective antitrust policy requires an economic framework that includes three actors: a cartel, a group of competing fringe firms, and a welfare maximizing antitrust authority. In existing models of cartel behavior, at least one of these actors is always missing. By contrast, the present paper's oligopoly model includes all three actors. The cartel is the Stackelberg quantity leader and the fringe firms are in Cournot competition with respect to the residual demand. Taking into account that the antitrust policy instruments (effort, fine, and leniency program) are not costless for society, an optimal policy is derived. |
| Keywords: | antitrust,stability,Cournot fringe,oligopoly,leniency |
| JEL: | L13 L41 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc20:224521&r=all |
| By: | Minoru Osawa; Takashi Akamatsu; Yosuke Kogure |
| Abstract: | We consider a model of urban spatial structure proposed by Harris and Wilson (Environment and Planning A, 1978). The model consists of fast dynamics, which represent spatial interactions between locations by the entropy-maximizing principle, and slow dynamics, which represent the evolution of the spatial distribution of local factors that facilitate such spatial interactions. One known limitation of the Harris and Wilson model is that it can have multiple locally stable equilibria, leading to a dependence of predictions on the initial state. To overcome this, we employ equilibrium refinement by stochastic stability. We build on the fact that the model is a large-population potential game and that stochastically stable states in a potential game correspond to global potential maximizers. Unlike local stability under deterministic dynamics, the stochastic stability approach allows a unique and unambiguous prediction for urban spatial configurations. We show that, in the most likely spatial configuration, the number of retail agglomerations decreases either when shopping costs for consumers decrease or when the strength of agglomerative effects increases. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2011.06778&r=all |
| By: | Fortuna Casoria (Univ Lyon, CNRS, GATE UMR 5824, F-69130 Ecully, France); Ernesto Reuben (New York University Abu Dhabi, Center for Behavioral Institutional Design; Luxembourg Institute of Socio-Economic Research); Christina Rott (Vrije Universiteit Amsterdam, 1081HV Amsterdam, The Netherlands) |
| Abstract: | We investigate the effects of group identity on hiring decisions with adverse selection problems. We run a laboratory experiment in which employers cannot observe a worker's ability nor verify the veracity of the ability the worker claims to have. We evaluate whether sharing an identity results in employers discriminating in favor of ingroup workers, and whether it helps workers and employers overcome the adverse selection problem. We induce identities using the minimal group paradigm and study two settings: one where workers cannot change their identity and one where they can. Although sharing a common identity does not make the worker's claims more honest, employers strongly discriminate in favor of ingroup workers when identities are fixed. Discrimination cannot be explained by employers' beliefs and hence seems to be taste-based. When possible, few workers change their identity. However, the mere possibility of changing identities erodes the employers' trust towards ingroup workers and eliminates discrimination. |
| Keywords: | Labor, Discrimination, Identity, Economics: Game Theory and Bargaining Theory, Hiring |
| JEL: | C9 D82 J71 M51 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:2033&r=all |
| By: | Mantas Radzvilas; Francesco De Pretis; William Peden; Daniele Tortoli; Barbara Osimani |
| Abstract: | Despite the tremendous successes of science in providing knowledge and technologies, the Replication Crisis has highlighted that scientific institutions have much room for improvement. Peer-review is one target of criticism and suggested reforms. However, despite numerous controversies peer review systems, plus the obvious complexity of the incentives affecting the decisions of authors and reviewers, there is very little systematic and strategic analysis of peer-review systems. In this paper, we begin to address this feature of the peer-review literature by applying the tools of game theory. We use simulations to develop an evolutionary model based around a game played by authors and reviewers, before exploring some of its tendencies. In particular, we examine the relative impact of double-blind peer-review and open review on incentivising reviewer effort under a variety of parameters. We also compare (a) the impact of one review system versus another with (b) other alterations, such as higher costs of reviewing. We find that is no reliable difference between peer-review systems in our model. Furthermore, under some conditions, higher payoffs for good reviewing can lead to less (rather than more) author effort under open review. Finally, compared to the other parameters that we vary, it is the exogenous utility of author effort that makes an important and reliable difference in our model, which raises the possibility that peer-review might not be an important target for institutional reforms. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2011.07797&r=all |
| By: | Domenico Buccella; Luciano Fanti; Luca Gori |
| Abstract: | Is it profitable to include an environmental ("green") incentive in a managerial contract when a dirty technology causes pollution externality, and the government levies an emissions tax? This research considers a non-cooperative Cournot duopoly game in which owners choose whether to delegate output and the abatement choices to their managers to address the above question. When the societal (or public) evaluation of the environmental damage is sufficiently low, two symmetric equilibria emerge (both firms are either "green" or "polluting"); when the public environmental concern becomes larger, the "green" delegation is the unique Nash equilibrium, which is Pareto inefficient (resp. efficient) for intermediate (resp. high) values of the government’s weight towards the environment. Differently, in a managerial duopoly where owners delegate only sales or sales and abatement, sales delegation arises in equilibrium; however, firms face a Prisoner’s Dilemma because "green" delegation yields higher profits. |
| Keywords: | Green managerial delegation, Abatement, Emissions tax, Cournot duopoly |
| JEL: | H23 L1 M5 Q58 |
| Date: | 2020–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:pie:dsedps:2020/262&r=all |
| By: | Domenico Buccella; Luciano Fanti; Luca Gori |
| Abstract: | This research analyses the firms’ strategic choice of adopting an abatement technology in an environment with pollution externalities when the government levies an emission tax (to incentivise firms undertaking emission-reducing actions). A set of different Nash equilibria – ranging from dirty to green production – arises in both quantity-setting (Cournot) and price-setting (Bertrand) duopolies depending on the societal awareness towards environmental quality and the relative importance of technological progress in abatement adopted by firms. A synthesis of the main results is the following: if the awareness of the society towards a clean environment is relatively low (resp. high) and the index measuring the relative cost of abatement is relatively high (resp. low), the strategic interaction between two independent, competing and selfish (profit maximising) firms playing the abatement game leads to not to abate [NA] (resp. to abate [A]) as the Pareto efficient outcome: no conflict exists between self-interest and mutual benefit to do not undertake (resp. to undertake) emission-reducing actions. Multiple Nash equilibria or a "green" prisoner’s dilemma may also emerge in pure strategies. When the choice of adopting a green technology is a deadlock (anti-prisoner’s dilemma), the society is better off as social welfare under A is always larger than under NA because pollution and environmental damage are higher in the latter scenario. These findings suggest that living in a sustainable environment challenges and the improvement of public education systems to achieve an eco-responsible attitude and the development of clean technologies through ad hoc R&D. |
| Keywords: | Green production, Abatement, Emissions tax, Cournot and Bertrand duopolies |
| JEL: | H23 L1 M5 Q58 |
| Date: | 2020–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:pie:dsedps:2020/261&r=all |
| By: | Jana Friedrichsen; Katharina Momsen; Stefano Piasenti |
| Abstract: | Intentions play a fundamental role in many situations characterized by nonsimultaneous interaction from principal-agent settings in firms to the international task of protecting the environment and the climate. We experimentally investigate how decision makers (DMs) respond to perceived intentions of a matched partner and a stochastic, imperfectly informative outcome when choosing a reciprocating action. We vary if the DM observes their partner's action or only the outcome before taking their own decision. Observing no evidence of an outcome bias, we find that the DM reciprocates good intentions under full information. However, reciprocity of DMs is lower in the treatment where information on the partner's action is hidden. Our analysis suggests that this is driven by the partners? behavior. DMs select into being informed or uninformed based on their inclination to behave more or less prosocially. While information avoidance is frequent, we do not find evidence for moral wiggling. In line with the absence of moral wiggling, an analysis of subjects' beliefs speaks against strategic cynicism. |
| Keywords: | information avoidance, dictator game, public good game, moral wiggle room, intentions, reciprocity |
| JEL: | D91 C91 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2020-31&r=all |
| By: | Charles de Beauffort (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES)) |
| Abstract: | What does central bank independence imply for the optimal conduct of time-consistent fiscal and monetary policy in a liquidity trap? To provide an answer, I consider a stochastic noncooperative game in which the lower bound on nominal rates is an occasionally binding constraint and in which government debt serves as a tool to influence future policy trade-offs. I show that a transitory consolidation of debt in the liquidity trap optimally reduces expected real rates and stimulates current consumption and inflation via an expectation channel. The reaction function of the independent central bank outside the lower bound is pivotal in obtaining this result - considering instead coordinated policy produces the opposite effect of an optimal increase in debt. Lengthening the debt maturity allows to mitigate issues related to lack of coordination. |
| Keywords: | Optimal Time-Consistent Policy, Distortionary Taxation, Liquidity Trap, Fiscal and Monetary Policy Interactions |
| Date: | 2020–11–10 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvir:2020033&r=all |