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on Game Theory |
| By: | Levy, Gilat; Moreno de Barreda, Inés; Razin, Ronny |
| Abstract: | We consider an information design problem in which a sender tries to persuade a receiver that has "correlation neglect", i.e. fails to understand that signals might be correlated. We show that a sender with unlimited number of signals can fully manipulate the receiver. Specifically, the sender can induce the receiver to hold any state-dependent posterior she wishes to. If the sender only wishes to induce a state-independent posterior, she can use fully correlated signals, but generally she needs to design more involved correlation structures. |
| JEL: | J1 |
| Date: | 2021–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:111551&r= |
| By: | Ghislain H. Demeze-Jouatsa; Roland Pongou; Jean-Baptiste Tondji |
| Abstract: | Frequent violations of fair principles in real-life settings raise the fundamental question of whether such principles can guarantee the existence of a self-enforcing equilibrium in a free economy. We show that elementary principles of distributive justice guarantee that a pure-strategy Nash equilibrium exists in a finite economy where agents freely (and non-cooperatively) choose their inputs and derive utility from their pay. Chief among these principles is that: 1) your pay should not depend on your name, and 2) a more productive agent should not earn less. When these principles are violated, an equilibrium may not exist. Moreover, we uncover an intuitive condition -- technological monotonicity -- that guarantees equilibrium uniqueness and efficiency. We generalize our findings to economies with social justice and inclusion, implemented in the form of progressive taxation and redistribution, and guaranteeing a basic income to unproductive agents. Our analysis uncovers a new class of strategic form games by incorporating normative principles into non-cooperative game theory. Our results rely on no particular assumptions, and our setup is entirely non-parametric. Illustrations of the theory include applications to exchange economies, surplus distribution in a firm, contagion and self-enforcing lockdown in a networked economy, and bias in the academic peer-review system. Keywords: Market justice; Social justice; Inclusion; Ethics; Discrimination; Self-enforcing contracts; Fairness in non-cooperative games; Pure strategy Nash equilibrium; Efficiency. JEL Codes: C72, D30, D63, J71, J38 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2107.12870&r= |
| By: | Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yuhta Ishii (Department of Economics at Pennsylvania State University) |
| Abstract: | We study settings in which, prior to playing an incomplete information game, players observe many draws of private signals about the state from some information structure. Signals are i.i.d. across draws, but may display arbitrary correlation across players. For each information structure, we deï¬ ne a simple learning efficiency index, which only considers the statistical distance between the worst-informed player’s marginal signal distributions in different states. We show, ï¬ rst, that this index characterizes the speed of common learning (Cripps, Ely, Mailath, and Samuelson, 2008): In particular, the speed at which players achieve approximate common knowledge of the state coincides with the slowest player’s speed of individual learning, and does not depend on the correlation across players’ signals. Second, we build on this characterization to provide a ranking over information structures: We show that, with sufficiently many signal draws, information structures with a higher learning efficiency index lead to better equilibrium outcomes, robustly for a rich class of games and objective functions. We discuss implications of our results for constrained information design in games and for the question when information structures are complements vs. substitutes. |
| Keywords: | Common learning, Learning efficiency, Comparison of information structures |
| JEL: | D80 D83 C70 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2299&r= |
| By: | Jingfeng Lu; Zongwei Lu; Christian Riis |
| Abstract: | We study a model in which before a conflict between two parties escalates into a war (in the form of an all-pay auction), a party can offer a take-it-or-leave-it bribe to the other one for a peaceful settlement. We distinguish between various degrees of peace prospects--implementability, weak security and strong security. We first characterize the necessary and sufficient conditions for peace implementability and weak security. We then show that weak security implies strong security. We also consider a requesting-a-bribe game and characterize the necessary and sufficient conditions for existence of a robust peaceful equilibrium. We find that all such robust peaceful equilibria share the same request. |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2107.11575&r= |
| By: | Alex Garivaltis |
| Abstract: | To protect his teaching evaluations, an economics professor uses the following exam curve: if the class average falls below a known target, $m$, then all students will receive an equal number of free points so as to bring the mean up to $m$. If the average is above $m$ then there is no curve; curved grades above $100\%$ will never be truncated to $100\%$ in the gradebook. The $n$ students in the course all have Cobb-Douglas preferences over the grade-leisure plane; effort corresponds exactly to earned (uncurved) grades in a $1:1$ fashion. The elasticity of each student's utility with respect to his grade is his ability parameter, or relative preference for a high score. I find, classify, and give complete formulas for all the pure Nash equilibria of my own game, which my students have been playing for some eight semesters. The game is supermodular, featuring strategic complementarities, negative spillovers, and nonsmooth payoffs that generate non-convexities in the reaction correspondence. The $n+2$ types of equilibria are totally ordered with respect to effort and Pareto preference, and the lowest $n+1$ of these types are totally ordered in grade-leisure space. In addition to the no-curve ("try-hard") and curved interior equilibria, we have the "$k$-don't care" equilibria, whereby the $k$ lowest-ability students are no-shows. As the class size becomes infinite in the curved interior equilibrium, all students increase their leisure time by a fixed percentage, i.e., $14\%$, in response to the disincentive, which amplifies any pre-existing ability differences. All students' grades inflate by this same (endogenous) factor, say, $1.14$ times what they would have been under the correct standard. |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2108.03709&r= |
| By: | Xu, Yongsheng; Yoshihara, Naoki |
| Abstract: | This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on resource allocations. A framework in such a context is developed and the egalitarian solution to standard bargaining problems is reformulated and axiomatically characterized. |
| Keywords: | Opportunity sets, bargaining over opportunity assignments, egalitarian solution |
| JEL: | C71 C78 D60 D63 D70 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:725&r= |
| By: | Azacis, Helmuts (Cardiff Business School); Vida, Peter (Corvinus Institute for Advanced Studies, Corvinus University of Budapest) |
| Abstract: | A competition authority has an objective, which specifies what output profile firms need to produce as a function of production costs. These costs change over time and are only known by the firms. The objective is implementable if in equilibrium, the firms cannot collude on their reports to the competition authority. Assuming that the firms can only report prices and quantities, we characterize what objectives are one-shot and repeatedly implementable. We use this characterization to identify conditions when the competitive output is implementable. We extend the analysis to the cases when a buyer also knows the private information of firms and when the firms can supply hard evidence about their costs. |
| Keywords: | Collusion, Antitrust, (Repeated) Implementation, Monotonicity, Price-Quantity Mechanism, Hard Evidenc |
| JEL: | C72 C73 D71 D82 L41 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2021/19&r= |
| By: | Jin Yeub Kim (Yonsei Univ) |
| Abstract: | This paper considers social contracts (or mechanisms) in negotiations with incomplete information in which an outside option is a probabilistic conflict and a peaceful agreement is ex ante efficient. Applications include partnership, labor-management bargaining, pretrial negotiations, and international negotiations. I compute the set of interim incentive efficient mechanisms, the ex ante incentive efficient mechanism, as well as the neutral bargaining solution. I numerically illustrate that the focus on the ex ante incentive efficient mechanism as the most reasonable prediction is not robust. This paper justifies the neutral bargaining solution as the unique, robust solution among all interim incentive efficient mechanisms. |
| Keywords: | Negotiation; Social contracts; Incomplete information; Incentive efficiency; Neutral bargaining solution |
| JEL: | C78 D74 D82 F51 J52 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2021rwp-187&r= |
| By: | Martin Herdegen; Johannes Muhle-Karbe; Florian Stebegg |
| Abstract: | We study one-shot Nash competition between an arbitrary number of identical dealers that compete for the order flow of a client. The client trades either because of proprietary information, exposure to idiosyncratic risk, or a mix of both trading motives. When quoting their price schedules, the dealers do not know the client's type but only its distribution, and in turn choose their price quotes to mitigate between adverse selection and inventory costs. Under essentially minimal conditions, we show that a unique symmetric Nash equilibrium exists and can be characterized by the solution of a nonlinear ODE. |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2107.12094&r= |
| By: | Charlson, G. |
| Abstract: | A platform holds information on the demographics of its users and wants maximise total surplus. The data generates a probability over which of two products a buyer prefers, with different data segmentations being more or less informative. The platform reveals segmentations of the data to two firms, one popular and one niche, preferring to reveal no information than completely revealing the consumer's type for certain. The platform can improve profits by revealing to both firms a segmentation where the niche firm is relatively popular, but still less popular than the other firm, potentially doing even better by revealing information asymmetrically. The platform has an incentive to provide more granular data in markets in which the niche firm is particularly unpopular or in which broad demographic categories are not particularly revelatory of type, suggesting that the profit associated with big data techniques differs depending on market characteristics. |
| Keywords: | Strategic interaction, network games, interventions, industrial organisation, platforms, hypergraphs |
| JEL: | D40 L10 L40 |
| Date: | 2021–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2159&r= |
| By: | Martin Richardson |
| Abstract: | We suppose that expert witnesses are, generically, either honest in their assessment of a fact situation or are mercenary ‘hired guns’ that advocate for their retaining party. The type of a witness is known to law firms, who engage with them repeatedly, but not to courts. If the only way an honest witness can credibly reveal their type to a court is by siding with the opposing party then the question arises of why a law firm would ever retain an honest expert. We show that it can act as a signaling device in a game between the law firms to communicate private information regarding a party’s confidence in winning the case. Our results indicate, amongst other things, that the ‘English’ rule of costs allocation can make a socially desirable separating equilibrium less likely, compared to the ‘American’ rule. |
| Keywords: | expert witnesses, signaling, litigation |
| JEL: | K41 D82 C72 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2021-678&r= |
| By: | Ian Ball (Department of Economics, MIT); Jose-Antonio Espin-Sanchez (Cowles Foundation, Yale University) |
| Abstract: | We introduce experimental persuasion between Sender and Receiver. Sender chooses an experiment to perform from a feasible set of experiments. Receiver observes the realization of this experiment and chooses an action. We characterize optimal persuasion in this baseline regime and in an alternative regime in which Sender can commit to garble the outcome of the experiment. Our model includes Bayesian persuasion as the special case in which every experiment is feasible; however, our analysis does not require concaviï¬ cation. Since we focus on experiments rather than beliefs, we can accommodate general preferences including costly experiments and non-Bayesian inference. |
| Keywords: | Experiments, Beliefs, Decision Making, Information, Bayesian |
| JEL: | D81 D82 D83 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2298&r= |
| By: | Xiaotie Deng; Yotam Gafni; Ron Lavi; Tao Lin; Hongyi Ling |
| Abstract: | We study competition among contests in a general model that allows for an arbitrary and heterogeneous space of contest design, where the goal of the contest designers is to maximize the contestants' sum of efforts. Our main result shows that optimal contests in the monopolistic setting (i.e., those that maximize the sum of efforts in a model with a single contest) form an equilibrium in the model with competition among contests. Under a very natural assumption these contests are in fact dominant, and the equilibria that they form are unique. Moreover, equilibria with the optimal contests are Pareto-optimal even in cases where other equilibria emerge. In many natural cases, they also maximize the social welfare. |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2107.13363&r= |
| By: | Moshe Babaioff; Ruty Mundel; Noam Nisan |
| Abstract: | In the early $20^{th}$ century, Pigou observed that imposing a marginal cost tax on the usage of a public good induces a socially efficient level of use as an equilibrium. Unfortunately, such a "Pigouvian" tax may also induce other, socially inefficient, equilibria. We observe that this social inefficiency may be unbounded, and study whether alternative tax structures may lead to milder losses in the worst case, i.e. to a lower price of anarchy. We show that no tax structure leads to bounded losses in the worst case. However, we do find a tax scheme that has a lower price of anarchy than the Pigouvian tax, obtaining tight lower and upper bounds in terms of a crucial parameter that we identify. We generalize our results to various scenarios that each offers an alternative to the use of a public road by private cars, such as ride sharing, or using a bus or a train. |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2107.12023&r= |
| By: | Nobuyuki Hanaki; Takashi Hayashi; Michele Lombardi; Kazuhito Ogawa |
| Abstract: | This study experimentally evaluates the performance of partial equilibrium mechanisms when different sectors run their mechanisms separately, despite the existence of complementarity between them. In our simple laboratory experiment setting that includes two sectors, each sector runs the top-trading-cycle mechanism. There is a Pareto-dominant equilibrium, but it requires coordination across sectors. Our results show that coordination failure occurs more frequently when there is asymmetry between the two sectors compared with the one-sector benchmark, even without inter-sectoral complementarity. When mechanisms are run sequentially across the two sectors, such failure is substantially reduced, compared with when they are run simultaneously. |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1138&r= |