
on Game Theory 
By:  Nathan Canen; Kyungchul Song 
Abstract:  Structural models that admit multiple reduced forms, such as gametheoretic models with multiple equilibria, pose challenges in practice, especially when parameters are setidentified and the identified set is large. In such cases, researchers often choose to focus on a particular subset of equilibria for counterfactual analysis, but this choice can be hard to justify. This paper proposes a refinement criterion for the identified set. Our criterion chooses a subset such that counterfactual predictions of outcomes are most stable against local perturbations of the reduced forms (e.g. the equilibrium selection rule). Our refinement has multiple appealing features, including an intuitive characterization, lower computational cost, and stable predictions. Focusing on moment inequality models, we propose bootstrap inference on the refinement and provide generic conditions under which the inference is uniformly asymptotically valid. We present and discuss results from our Monte Carlo study and an empirical application based on a model with topcoded data. 
Date:  2019–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1906.00003&r=all 
By:  GiménezGómez, José M (Universitat Rovira i Virgili); Peris, Josep E (University of Alicante, D. Quantitative Methods and Economic Theory); Subiza, Begoña (University of Alicante, D. Quantitative Methods and Economic Theory) 
Abstract:  A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source. Hence the question is how to fairly allocate the total cost among these agents. Our approach, reinterpreting the spanning tree cost allocation as a claims problem (O'Neill, 1982), defines a simple way to allocate the optimal cost with two main criteria: (1) each individual only pays attention to a few connection costs (the total cost of the optimal network and the cost of connecting by himself to the source); and (2) an egalitarian criteria is used to share costs or benefits. Then, by using claims rules, we define two egalitarian solutions so that the total cost is allocated equalizing either the payments in which agents incur, or the benefit that agents obtain throughout cooperation. Finally, through the axiomatic study of core selection, we obtain an alternative interpretation of the Folk solution. 
Keywords:  Minimum cost spanning tree; Egalitarian; Cost sharing; Core 
JEL:  C71 D63 D71 
Date:  2019–06–12 
URL:  http://d.repec.org/n?u=RePEc:ris:qmetal:2019_003&r=all 
By:  Long, Yan (New York University Abu Dhabi); Sethuraman, Jay (Columbia University); Xue, Jingyi (Singapore Management University) 
Abstract:  A group of agents have uncertain needs on a resource, and the resource has to be divided before uncertainty resolves. We propose a class of division rules we call equalquantile rules, parameterized by λ ∈ (0, 1]. The parameter λ is a common maximal probability of satisfaction — the probability that an agent’s realized need is no more than his assignment — imposed on all agents. Thus, the maximal assignment of each agent is his λquantile assignment. If the endowment of the resource exceeds the sum of the agents’ λquantile assignments, each agent receives his λquantile assignment and the resource is not fully allocated to the agents. Otherwise, the resource is fully allocated and the rule equalizes the probability of satisfaction across agents.We provide justifications for the class of equalquantile rules from two perspectives. First, each equalquantile rule maximizes a particular utilitarian social welfare function that involves an outside agent, who provides an alternative use of the resource, and aggregates linear individual utilities. Equivalently, it minimizes a particular utilitarian social cost function that is the sum of the aggregate expected waste and the aggregate expected deficit, weighted, respectively, by a unit waste cost and a unit deficit cost. Second, four familiar axioms, consistency, continuity, strict ranking, and ordinality, when extended to the uncertain context, characterize the class of equalquantile rules. Thus, requiring the four axioms is equivalent to imposing either of these utilitarian objective functions. 
Keywords:  Resource allocation; Fair division; Uncertain needs; Equalquantile rules; Utilitarian social welfare function; Waste; Deficit; Ordinality 
JEL:  D44 D63 D71 D82 
Date:  2019–05–09 
URL:  http://d.repec.org/n?u=RePEc:ris:smuesw:2019_011&r=all 
By:  Andrea Attar (CEIS & DEF University of Rome "Tor Vergata"); Eloisa Campioni (CEIS & DEF University of Rome "Tor Vergata"); Thomas Mariotti (Toulouse School of Economics, CNRS); Gwenael Piaser (IPAG Business School, Paris) 
Abstract:  We study competingmechanism games under exclusive competition: principals first simultaneously post mechanisms, then agents simultaneously choose to participate and communicate with at most one principal. In this setting, which is common to competingauction and competitivesearch applications, we develop two examples that question the relevance of the folk theorems for competingmechanism games documented in the literature. The first example shows that there can exist purestrategy equilibria in which some principal obtains a payoff below her minmax payoff, computed over all principals' decisions. Thus folktheorem results may have to involve a bound on principals' payoffs that depends on the spaces of messages available to the agents, and not only on the players' available actions. The second example shows that even this nonintrinsic approach is misleading when agents' participation decisions are strategic: there can exist incentivefeasible allocations in which principals obtain payoffs above their minmax payoffs, computed over arbitrary spaces of mechanisms, but which cannot be supported in equilibrium. 
Keywords:  Competing Mechanisms, Folk Theorems, Exclusive Competition 
JEL:  D82 
Date:  2019–06–06 
URL:  http://d.repec.org/n?u=RePEc:rtv:ceisrp:460&r=all 
By:  S. Nageeb Ali; Ce Liu 
Abstract:  We develop a theory of repeated interaction for coalitional behavior. We consider stage games where both individuals and coalitions may deviate. However, coalition members cannot commit to longrun behavior (on and off the path), and anticipate that today's actions influence tomorrow's behavior. We evaluate the degree to which historydependence can ward off coalitional deviations. If monitoring is perfect, every feasible and strictly individually rational payoff can be supported by historydependent conventions. By contrast, if players can make secret sidepayments to each other, every coalition achieves a coalitional minmax value, reducing the set of supportable payoffs to the core of the stage game. 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1906.00280&r=all 
By:  Makoto Hagiwara (PhD Student, Department of Industrial Engineering and Economics, Tokyo Institute of Technology, JAPAN) 
Abstract:  We consider the implementation problem under incomplete information and private values. We investigate double implementability of (singlevalued) mappings in dominant strategy equilibria and ex post equilibria. We call a mapping a "rule". We show that the notion of an ex post equilibrium is weaker than the notion of a dominant strategy equilibrium. Then, this double implementability notion is not trivial even under private values. We define a new strategic axiom that is stronger than "strategyproofness", but weaker than "secure strategyproofness". We call it "weak securestrategyproofness". We show that a rule is doubly implementable if and only if it is weakly securelystrategyproof. 
Keywords:  Double Implementation; Dominant Strategy Equilibrium; Ex Post Equilibrium; Weak Securestrategyproofness; Private Values 
JEL:  C72 D71 D78 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:kob:dpaper:dp201913&r=all 
By:  Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta 
Abstract:  Coarse correlated equilibria (CCE, Moulin and Vial, 1978) can be used to substantially improve upon the Nash equilibrium solution of the wellanalysed abatement game (Barrett, 1994). We show this by computing successively the CCE with the largest total utility, the one with the highest possible abatement levels and finally, the one with maximal abatement level while maintaining at least the level of utility from the Nash outcome. 
Keywords:  Abatement game, Coarse correlated equilibrium, Efficiency gain 
JEL:  C72 Q52 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:lan:wpaper:266042710&r=all 
By:  Thiparat Chotibut; Fryderyk Falniowski; Micha{\l} Misiurewicz; Georgios Piliouras 
Abstract:  We study a learning dynamic model of routing (congestion) games to explore how an increase in the total demand influences system performance. We focus on nonatomic routing games with two parallel edges of linear cost, where all agents evolve using Multiplicative Weights Updates with a fixed learning rate. Previous gametheoretic equilibrium analysis suggests that system performance is close to optimal in the large population limit, as seen by the Price of Anarchy reduction. In this work, however, we reveal a rather undesirable consequence of nonequilibrium phenomena driven by population increase. As the total demand rises, we prove that the learning dynamics unavoidably become nonequilibrating, typically chaotic. The Price of Anarchy predictions of nearoptimal performance no longer apply. To the contrary, the timeaverage social cost may converge to its worst possible value in the large population limit. Every system has a carrying capacity, above which the dynamics is nonequilibrating. If the equilibrium flow is a symmetric $5050\%$ split, the system exhibits one perioddoubling bifurcation. A single periodic attractor of period two replaces the attracting fixed point when the demand exceeds the carrying capacity. In general, for asymmetric equilibrium flows, increasing the demand destabilizes the system, so that the system eventually becomes LiYorke chaotic with positive topological entropy. This demanddriven instability emerges from any pair of linear cost functions. Remarkably, in any nonequilibrating regime, the timeaverage flows on the edges converge {\it exactly} to the equilibrium flows, a property akin to noregret learning in zerosum games. Our results extend to any sequence of shrinking learning rates, e.g., $1/\sqrt{T}$, by allowing for a dynamically increasing population size. 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1906.02486&r=all 
By:  Dietzenbacher, Bas (Tilburg University, Center For Economic Research); Yanovskaya, E. 
Abstract:  This paper axiomatically studies the equal splitoff set (cf. Branzei et al. (2006)) as a solution for cooperative games with transferable utility. This solution extends the wellknown Dutta and Ray (1989) solution for convex games to arbitrary games. By deriving several characterizations, we explore the relation of the equal splitoff set with various consistency notions. 
Keywords:  transferable utility games; egalitrianism; equal splitoff set; consistency 
JEL:  C71 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:2846ead571b54d0cbf0b59445287cfd1&r=all 
By:  Alex Garivaltis 
Abstract:  We consider a twoperson trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the `numerator player') picks $b$ so as to maximize $\mathbb{E}[V_t(b)/V_t(c)]$, while Player 2 (the `denominator player') picks $c$ so as to minimize it. In the unique Nash equilibrium, both players use the continuoustime Kelly rule $b^*=c^*=\Sigma^{1}(\mur\textbf{1})$, where $\Sigma$ is the covariance of instantaneous returns per unit time, $\mu$ is the drift vector of the stock market, and $\textbf{1}$ is a vector of ones. Thus, even over very short intervals of time $[0,t]$, the desire to perform well relative to other traders leads one to adopt the Kelly rule, which is ordinarily derived by maximizing the asymptotic exponential growth rate of wealth. Hence, we find agreement with Bell and Cover's (1988) result in discrete time. 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1906.02216&r=all 
By:  Tatsuyoshi Saijo (School of Economics and Management, Kochi University of Technology) 
Abstract:  This paper shows that second thoughts are not an innocent device in our daily life, but is human wisdom that plays an important role in resolving problems such as social dilemmas. We design a simple mechanism to achieve Pareto efficiency in social dilemmas, and then compare the performance of this mechanism with and without second thoughts. First, second thoughts change the payoff structure of the game in favor of cooperation. Second, this mechanism is robust even when players deviate from a payoff maximizing behavior. 
Keywords:  second thoughts, subgame perfection, social dilemma, cooperation, mechanism design 
JEL:  C72 C92 D74 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:kch:wpaper:sdes20196&r=all 
By:  Elena Iñarra (University of the Basque Country, Spain); Roberto Serrano (Brown university, U.S.A.); KenIchi Shimomura (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan) 
Abstract:  One of the many important contributions in David Schmeidler's distinguished career was the introduction of the nucleolus. This paper is an update on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set. 
Keywords:  Nucleolus; Kernel; Bargaining set 
JEL:  C71 C72 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:kob:dpaper:dp201912&r=all 
By:  Rubbenstroth, Bodo (Center for Mathematical Economics, Bielefeld University) 
Abstract:  This paper studies two player stopping games in a discrete time multiple prior framework with a finite time horizon. Optimal stopping times as well as recursive formulas for the value processes of the games are derived. These results are used to characterize the set of noarbitrage prices for a game option. The notion of a noarbitrage price for a game option is based on the idea to consider the payoff for fixed stopping times as an European option. 
Keywords:  Dynkin games, multiple priors, game options, incomplete Markets 
Date:  2019–06–13 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:619&r=all 
By:  Alonso, Ricardo; Câmara, Odilon 
Abstract:  We consider a persuasion model in which a sender influences the actions of a receiver by selecting an experiment (public signal) from a set of feasible experiments. We ask: does the sender benefit from becoming an expert — observing a private signal prior to her selection? We provide necessary and sufficient conditions for a sender to never gain by becoming informed. Our key condition (sequential redundancy) shows that the informativeness of public experiments can substitute for the sender's expertise. We then provide conditions for private information to strictly benefit or strictly hurt the sender. Expertise is beneficial when the sender values the ability to change her experimental choice according to her private information. When the sender does not gain from expertise, she is strictly hurt when different types cannot pool on an optimal experiment. 
Keywords:  information design; Bayesian persuasion; experts 
JEL:  D83 
Date:  2018–03–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:86370&r=all 
By:  Tasnádi, Attila 
Abstract:  We determine a symmetric mixedstrategy equilibrium of the productioninadvance type symmetric capacityconstrained BertrandEdgeworth duopoly game for the most challenging case of intermediate capacities, which was unknown so far. Based on the obtained equilibrium we show that economic surplus within the productiontoorder type environment is higher than in the respective productioninadvance type one, and therefore productiontoorder should be preferred to productioninadvance if the mode of production can be influenced by the government. 
Keywords:  Pricequantity games, BertrandEdgeworth competition 
JEL:  D43 L13 
Date:  2019–06–10 
URL:  http://d.repec.org/n?u=RePEc:cvh:coecwp:2019/06&r=all 
By:  Tsuyoshi Toshimitsu (School of Economics, Kwansei Gakuin University) 
Abstract:  We reconsider the excess entry theorem in the presence of network externalities under Cournot oligopoly. We demonstrate that if the strength of a network externality is larger (smaller) than a half, the number of firms under free entry is socially too small (too large), based on the secondbest criteria. 
Keywords:  Cournot oligopoly; free entry; excess entry theorem; network externality; a fulfilled equilibrium; passive expectations; responsive expectations 
JEL:  D21 D43 D62 L15 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:kgu:wpaper:195&r=all 
By:  Mikhail Anufriev (University of Technology, Sydney); John Duffy (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 levelk learning, do not consistently predict whether subjects converge to or diverge away from the steady state. 
Keywords:  Beauty Contest, Learning; Stability, Simultaneous Equation Systems, Levelk cognitive theory 
JEL:  C30 C92 D83 D84 
URL:  http://d.repec.org/n?u=RePEc:swe:wpaper:201906&r=all 
By:  Marius Schwartz (Department of Economics, Georgetown University); Daniel R. Vincent (Department of Economics, University of Maryland) 
Abstract:  We analyze competing strategic platforms setting fees to a local monopolist merchant and cashback rebates to end users, when the merchant may not surcharge platforms’ customers, a rule imposed by some credit card networks. Each platform has an incentive to gain transactions by increasing the spread between its merchant fee and user rebate above its rival’s spread. This incentive yields nonexistence of pure strategy equilibrium in many natural environments. In some circumstances, there is a mixed strategy equilibrium where platforms choose fee structures that induce the merchant to accept only one platform with equal probability, a form of monopolistic market allocation. 
Keywords:  Platform price competition; rebates; no surcharge; payment networks; credit cards. 
JEL:  L13 L41 L42 D43 
Date:  2019–06–11 
URL:  http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~191903&r=all 
By:  Paul Belleflamme; Martin Peitz 
Abstract:  We consider twosided platforms with the feature that some users on one or both sides of the market lack information about the price charged to participants on the other side of the market. With positive crossgroup external effects, such lack of price information makes demand less elastic. A monopoly platform does not benefit from opaqueness and optimally reveals price information. contrast, in a twosided singlehoming duopoly, platforms benefit from opaqueness and, thus, do not have an incentive to disclose price information. In competitive bottleneck markets, results are more nuanced: if one side is fully informed (for exogenous reasons), platforms may decide to inform users on the other side either fully, partially or not at all, depending on the strength of crossgroup external effects and the degree of horizontal differentiation. 
Keywords:  price transparency; twosided markets; competitive bottleneck; platform competition; price information; strategic disclosure 
JEL:  D43 L12 L13 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_099&r=all 
By:  Moreno, Alejandro; Viianto, Lari; García, Daniel 
Abstract:  We run an economic experiment in order to find out the preferences of altruism, envy, and guilt at individual level. We extend Andreoni and Miller’s (2002) series of Dictator Experiments and Fisman et al.’s (2007) graphical experiment in order to have additional and more precise data at individual level. We run 55 graphical dictator games including some with a positive relation between the money the Dictator and the Receiver obtain, in order to estimate individual preferences for envy and guilt. Our program is interactive, as it looks for the regions where individuals´ emotions change from altruist to envy, and altruism to guilt, and changes the form of the budget sets. We find that most individuals show the emotion of altruism when facing other individuals that have similar income as themselves. However, some individuals show the emotion of envy when facing other individuals with much higher payoffs than themselves. More surprisingly, some individuals reveal the emotion of guilt when they have much higher payoffs that other individuals. 
Keywords:  Altruism, Envy, Guilt, Experimental Economics 
JEL:  C79 C91 D64 
Date:  2019–05–19 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:94096&r=all 
By:  Roberto Galbiati (OSC  Observatoire sociologique du changement  Sciences Po  CNRS  Centre National de la Recherche Scientifique); Emeric Henry (ECON  Département d'économie  Sciences Po); Nicolas Jacquemet (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  How does the exposure to past institutions affect current cooperation? While a growing literature focuses on behavioral channels, we show how cooperationenforcing institutions affect rational learning about the group's value. Strong institutions, by inducing members to cooperate , may hinder learning about intrinsic values in the group. We show, using a lab experiment with independent interactions and random rematching, that participants behave in accordance with a learning model, and in particular react differently to actions of past partners whether they were played in an environment with coercive enforcement or not. 
Keywords:  Enforcement,social values,cooperation,learning,spillovers,persistence of insti tutions,repeated games,experiments 
Date:  2019–06–03 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs02145486&r=all 
By:  Daniel Lacker; Agathe Soret 
Abstract:  We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and consumption when compared to the averages among the other agents. We derive a closed form solution for the $n$player game and the corresponding mean field game. This solution is unique in the class of equilibria with constant investment and continuous timedependent consumption, both independent of the wealth of the agent. Compared to the classical Merton problem with one agent, the competitive model exhibits a wide range of highly nonlinear and nonmonotone dependence on the agents' risk tolerance and competitiveness parameters. Counterintuitively, competitive agents with high risk tolerance may behave like noncompetitive agents with low risk tolerance. 
Date:  2019–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1905.11782&r=all 
By:  YuJui Huang; Xiang Yu 
Abstract:  An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguityaverse an agent is. This inclusion of ambiguity attitude, via an $\alpha$maxmin nonlinear expectation, renders the stopping problem timeinconsistent. We look for subgame perfect equilibrium stopping policies, formulated as fixed points of an operator. For a onedimensional diffusion with drift and volatility uncertainty, we show that every equilibrium can be obtained through a fixedpoint iteration. This allows us to capture much more diverse behavior, depending on an agent's ambiguity attitude, beyond the standard worstcase (or bestcase) analysis. In a concrete example of real options valuation under volatility uncertainty, all equilibrium stopping policies, as well as the best one among them, are fully characterized. It demonstrates explicitly the effect of ambiguity attitude on decision making: the more ambiguityaverse, the more eager to stopso as to withdraw from the uncertain environment. The main result hinges on a delicate analysis of continuous sample paths in the canonical space and the capacity theory. To resolve measurability issues, a generalized measurable projection theorem, new to the literature, is also established. 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1906.01232&r=all 
By:  Paul Jusselin; Thibaut Mastrolia; Mathieu Rosenbaum 
Abstract:  We consider an auction market in which market makers fill the order book during a given time period while some other investors send market orders. We define the clearing price of the auction as the price maximizing the exchanged volume at the clearing time according to the supply and demand of each market participants. Then we derive in a semiexplicit form the error made between this clearing price and the fundamental price as a function of the auction duration. We study the impact of the behavior of market takers on this error. To do so we consider the case of naive market takers and that of rational market takers playing a Nash equilibrium to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are found to be usually suboptimal. However, in term of our metric, they only moderately impair the quality of price formation process. Order of magnitude of optimal auction durations is from 2 to 10 minutes. 
Date:  2019–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1906.01713&r=all 