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on Game Theory |
| By: | Dan Levin; Luyao Zhang |
| Abstract: | We introduce NLK, a model that connects the Nash equilibrium (NE) and Level-K. It allows a player in a game to believe that her opponent may be either less or as sophisticated as, she is, a view supported in psychology. We apply NLK to data from five published papers on static, dynamic, and auction games. NLK provides different predictions than those of the NE and Level-K; moreover, a simple version of NLK explains the experimental data better in many cases, with the same or lower number of parameters. We discuss extensions to games with more than two players and heterogeneous beliefs. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.12292&r= |
| By: | Noga Alon (Princeton University); Kirill Rudov (Princeton University); Leeat Yariv (Princeton University) |
| Abstract: | We study the effectiveness of iterated elimination of strictly dominated actions in random two-player games. We show that dominance solvability of games is vanishingly small as the number of at least one player’s actions grows. Furthermore, conditional on dominance solvability, the number of iterations required to converge to Nash equilibrium grows rapidly as action sets grow. Nonetheless, at least when one of the players has a small action set, iterated elimination simplifies the game substantially by ruling out a sizable fraction of actions. This is no longer the case as both players’ action sets expand. With more than two players, iterated elimination becomes even less potent in altering the game players need to consider. Technically, we illustrate the usefulness of recent combinatorial methods for the analysis of general games. |
| Keywords: | Random Games, Dominance Solvability, Iterated Elimination |
| JEL: | C70 C79 |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-84&r= |
| By: | M. Beatrice Lignola (Università di Napoli Federico II); Jacqueline Morgan (Università di Napoli Federico II and CSEF) |
| Abstract: | We consider a two-stage game with k leaders having pessimistic attitude and one follower common to all leaders. Such a game, called CF game, may fail to have pessimistic solutions, even if the leader payoffs are linear and the optimal reaction of the follower to the leaders strategies is unique. So, we introduce two classes of games, called weighted value-potential and weighted potential CF games, and we illustrate their inherent difficulties and properties. For the more tractable class of weighted potential CF games, suitable approximate and viscosity solutions are introduced and are proven to exist under appropriate conditions, in line with what done for one-leader-one-follower games. |
| Date: | 2022–03–10 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:639&r= |
| By: | Sylvain Chassang (Princeton University); Lucia Del Carpio (INSEAD); Samuel Kapon (New York University) |
| Abstract: | Limits on a government’s capacity to enforce laws can result in multiple equilibria. If most agents comply, limited enforcement is sufficient to dissuade isolated agents from misbehaving. If most agents do not comply, overstretched enforcement capacity has a minimal impact on behavior. We study the extent to which divide-and-conquer enforcement strategies can help select a high compliance equilibrium in the presence of realistic compliance frictions. We study the role of information about the compliance of others both in theory and in lab experiments. As the number of agents gets large, theory indicates that providing information or not is irrelevant in equilibrium. In contrast, providing individualized information has a first order impact in experimental play by increasing convergence to equilibrium. This illustrates the value of out-of-equilibrium information design. |
| Keywords: | government capacity, limited enforcement, divide and conquer, common knowledge enforcement priorities, tax collection, bounded rationality, information design |
| JEL: | C72 C73 C92 D73 D82 D86 H26 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2020-7&r= |
| By: | Christian Bontemps (ENAC - Ecole Nationale de l'Aviation Civile, TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Raquel Menezes Bezerra Sampaio (UFRN - Universidade Federal do Rio Grande do Norte [Natal]) |
| 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: | Estimation,Airlines,Multiple equilibria,Entry,Industrial organization |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-02137358&r= |
| By: | Fan-chin Kung; Ping Wang; Quan Wen |
| Abstract: | We develop a framework of group corruption via back-door negotiations between an outside initiator and an authority of decision-makers in a hierarchical organization. We examine the role played by the architecture of a multi-tier authority and determine under such a structure how bargaining proceeds, in what order, and when it breaks down. We verify that equilibrium bargaining sequence proceeds as a chain through decision-making agents, regardless of the hierarchy of the organization. We prove the existence of a compromised equilibrium, where the decision of the authority is compromised, and establish sufficient conditions under which the most natural bottom-up bargaining configuration arises in equilibrium where a proposer negotiates with an immediately higher ranked respondent, starting with the initiator bargaining with the lowest ranked decision-maker in the organization. We then show the circumstances under which a top-down or a non-monotonic equilibrium configuration may emerge, and those under which the deal may break down. This enables us to capture a rich array of group corruptive configurations as observed. We conclude by investigating the extension to multi-tier authorities with multiple agents of the same rank in each tier, such as in a tree hierarchy. |
| JEL: | C78 D23 D73 L22 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29759&r= |
| By: | Jonathan Libgober; Xiaosheng Mu |
| Abstract: | This paper studies durable good monopoly without commitment under an informationally robust objective. A seller cannot commit to future prices and does not know the information arrival process available to a representative buyer. We consider the case where the seller chooses prices to maximize her profit guarantee against a time-consistent worst-case information structure. In the gap case, the solution to this model is payoff-equivalent to a particular known-values environment, immediately delivering a sharp characterization of the equilibrium price paths. Furthermore, for a large class of environments, arbitrary (possibly time-inconsistent) information arrival processes would not lower the seller's profit as long as these prices are chosen. We call a price path with this property a reinforcing solution. As certain versions of the informationally robust objective under limited commitment may very well involve time-inconsistency, we posit that the notion of a reinforcing solution may be useful for researchers seeking to tractably analyze these settings. To highlight the non-triviality of these conclusions, we comment that while the analogy to known values can hold under an equilibrium selection in the no-gap case, it does not hold more generally. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.04616&r= |
| By: | Jibang Wu; Zixuan Zhang; Zhe Feng; Zhaoran Wang; Zhuoran Yang; Michael I. Jordan; Haifeng Xu |
| Abstract: | In today's economy, it becomes important for Internet platforms to consider the sequential information design problem to align its long term interest with incentives of the gig service providers. This paper proposes a novel model of sequential information design, namely the Markov persuasion processes (MPPs), where a sender, with informational advantage, seeks to persuade a stream of myopic receivers to take actions that maximizes the sender's cumulative utilities in a finite horizon Markovian environment with varying prior and utility functions. Planning in MPPs thus faces the unique challenge in finding a signaling policy that is simultaneously persuasive to the myopic receivers and inducing the optimal long-term cumulative utilities of the sender. Nevertheless, in the population level where the model is known, it turns out that we can efficiently determine the optimal (resp. $\epsilon$-optimal) policy with finite (resp. infinite) states and outcomes, through a modified formulation of the Bellman equation. Our main technical contribution is to study the MPP under the online reinforcement learning (RL) setting, where the goal is to learn the optimal signaling policy by interacting with with the underlying MPP, without the knowledge of the sender's utility functions, prior distributions, and the Markov transition kernels. We design a provably efficient no-regret learning algorithm, the Optimism-Pessimism Principle for Persuasion Process (OP4), which features a novel combination of both optimism and pessimism principles. Our algorithm enjoys sample efficiency by achieving a sublinear $\sqrt{T}$-regret upper bound. Furthermore, both our algorithm and theory can be applied to MPPs with large space of outcomes and states via function approximation, and we showcase such a success under the linear setting. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.10678&r= |
| By: | Rohit Lamba |
| Abstract: | This paper analyzes repeated version of the bilateral trade model where the independent payoff relevant private information of the buyer and the seller is correlated across time. Using this setup it makes the following five contributions. First, it derives necessary and sufficient conditions on the primitives of the model as to when efficiency can be attained under ex post budget balance and participation constraints. Second, in doing so, it introduces an intermediate notion of budget balance called interim budget balance that allows for the extension of liquidity but with participation constraints for the issuing authority interpreted here as an intermediary. Third, it pins down the class of all possible mechanisms that can implement the efficient allocation with and without an intermediary. Fourth, it provides a foundation for the role of an intermediary in a dynamic mechanism design model under informational constraints. And, fifth, it argues for a careful interpretation of the "folk proposition" that less information is better for efficiency in dynamic mechanisms under ex post budget balance and observability of transfers. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.04201&r= |
| By: | Ran Eilat (University of the Negev); Kfir Eliaz Eliaz (Tel-Aviv University and the University of Utah); Xiaosheng Mu (Princeton University) |
| Abstract: | Modern information technologies make it possible to store, analyze and trade unprecedented amounts of detailed information about individuals. This has led to public discussions on whether individuals’ privacy should be better protected by restricting the amount or the precision of information that is collected by commercial institutions on their participants. We contribute to this discussion by proposing a Bayesian approach to measure loss of privacy in a mechanism. Specifically, we define the loss of privacy associated with a mechanism as the difference between the designer’s prior and posterior beliefs about an agent’s type, where this difference is calculated using Kullback-Leibler divergence, and where the change in beliefs is triggered by actions taken by the agent in the mechanism. We consider both ex-post (for every realized type, the maximal difference in beliefs cannot exceed some threshold k) and ex-ante (the expected difference in beliefs over all type realizations cannot exceed some threshold k) measures of privacy loss. Using these notions we study the properties of optimal privacy-constrained mechanisms and the relation between welfare/profits and privacy levels. |
| Keywords: | Privacy, mechanism-design, relative entropy, social networks |
| JEL: | D47 D82 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-65&r= |
| By: | Paolo Garella (Department of Economics, Management and Quantitative Methods (DEMM) - UNIMI - Università degli Studi di Milano [Milano]); Didier Laussel (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Joana Resende (Cef.up, Economics Department, University of Porto) |
| Abstract: | We study price personalization in a two period duopoly with vertically differentiated products. In the second period, a firm not only knows the purchase history of all customers, as in standard Behavior Based Price Discrimination models, but it also collects detailed information on its old customers, using it to engage in price personalization. The analysis reveals that there exists a natural market for each firm, defined as the set of customers that cannot be poached by the rival in the second period. The equilibrium is unique, except when firms are ex-ante almost identical. In equilibrium, only the firm with the largest natural market poaches customers from the rival. This firm has highest profits but not necessarily the largest market share. Aggregate profits are lower than under uniform pricing. All consumers gain, total welfare is higher herein than under uniform pricing if firms' natural markets are sufficiently asymmetric. The low quality firm chooses the minimal quality level and a quality differential arises, though the exact choice for the high quality depends upon the cost specification. |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03263513&r= |