
on Game Theory 
By:  Demuynck, Thomas (universite libre de bruxelles); Herings, P. JeanJacques (General Economics 1 (Micro)); Saulle, Riccardo (General Economics 1 (Micro)); Seel, Christian (General Economics 1 (Micro)) 
Abstract:  We introduce a new solution concept for models of coalition formation, called the myopic stable set (MSS). The MSS is defined for a general class of social environments and allows for an infinite state space. An MSS exists and, under minor continuity assumptions, it is also unique. The MSS generalizes and unifies various results from more specific applications. It coincides with the coalition structure core in coalition function form games when this set is nonempty; with the set of stable matchings in the GaleShapley matching model; with the set of Pareto optimal allocations in the ShapleyScarf housing matching model; with the set of pairwise stable networks and closed cycles in models of network formation; with the set of pure strategy Nash equilibria in pseudopotential games and finite supermodular games; and with the set of mixed strategy Nash equilibria in several classes of twoplayer games. 
Keywords:  Social environments, group formation, stability, Nash equilibrium 
JEL:  C70 C71 
Date:  2018–02–01 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2018001&r=gth 
By:  Ronald Peeters (Department of Economics, University of Otago, New Zealand); Marc Vorsatz (Departamento de An´alisis Econ´omico, Universidad Nacional de Educaci´on a Distancia, Calle Senda del Rey, Madrid, Spain) 
Abstract:  We introduce simple guilt into a generic prisoner’s dilemma (PD) game and solve for the equilibria of the resulting psychological game. It is shown that for all guilt parameters, it is a pure strategy equilibrium that both players defect. But, if the guilt parameter surpasses a threshold, a mixed strategy equilibrium and a pure strategy equilibrium in which both players cooperate emerge. We implement three payoff constellations of the PD game in a laboratory experiment and find in line with our equilibrium analysis that first and secondorder beliefs are highly correlated and that the probability of cooperation depends positively on these beliefs. Finally, we provide numerical evidence on the degree of guilt cooperators experience 
Keywords:  Psychological game theory, Guilt, Prisoner’s dilemma 
JEL:  C72 C91 
Date:  2018–01 
URL:  http://d.repec.org/n?u=RePEc:otg:wpaper:1801&r=gth 
By:  Takashi Yamada (Faculty of Global and Science Studies, Yamaguchi University); Nobuyuki Hanaki (UNS  Université Nice Sophia Antipolis  UCA  Université Côte d'Azur , GREDEG  Groupe de Recherche en Droit, Economie et Gestion  UNS  Université Nice Sophia Antipolis  UCA  Université Côte d'Azur  CNRS  Centre National de la Recherche Scientifique  UCA  Université Côte d'Azur , UCA  Université Côte d'Azur) 
Abstract:  We experimentally study Lowest Unique Integer Games (LUIGs). In a LUIG, N (>= 3) players submit a positive integer up to M and the player choosing the smallest number not chosen by anyone else wins. LUIGs are simplified versions of real systems such as lottery games and Lowest/Highest Unique Bid Auctions that have been attracting attention from scholars, yet experimental studies are still scarce. Here, we consider four LUIGs with N={3,4} and M={3,4}. We find that (a) choices made by a majority of subjects over 50 rounds of a LUIG were not significantly different from that in the symmetric mixedstrategy Nash equilibrium (MSE) of the LUIG; however, (b) those subjects who behaved significantly differently from what the MSE predicts won the game more frequently than those who behaved similarly to what the MSE predicts. 
Keywords:  Laboratory Experiment,Lowest Unique Integer Game 
Date:  2016–12–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01204814&r=gth 
By:  Engwerda, Jacob (Tilburg University, School of Economics and Management) 
Abstract:  This paper reconsiders existence of worstcase Nash equilibria in noncooperative multiplayer differential games, this, within an openloop information structure. We show that these equilibria can be obtained by determining the openloop Nash equilibria of an associated differential game with an additional initial state constraint. For the special case of linearquadratic differential games, we derive both necessary and sufﬁcient conditions for solvability of the ﬁnite planning horizon problem. In particular, we demonstrate that, unlike in the standard linearquadratic differential game setting, uniqueness of equilibria may fail to hold. A both necessary and sufﬁcient condition under which there is a unique equilibrium is provided. A sufﬁcient existence condition for a unique equilibrium is derived in terms of a Riccati differential equation. Consequences for control policies are demonstrated in a simple debt stabilization game. 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutis:9032e90c3a094132848b465c443c2174&r=gth 
By:  Engwerda, Jacob (Tilburg University, School of Economics and Management) 
Abstract:  In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables. 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutis:0442b2031b924be3ba607b68374d14b5&r=gth 
By:  Dietzenbacher, Bas (Tilburg University, School of Economics and Management); Borm, Peter (Tilburg University, School of Economics and Management); Hendrickx, Ruud (Tilburg University, School of Economics and Management) 
Abstract:  Using network control structures, this paper introduces a general class of network communication games and studies their decomposition into unanimity games. We obtain a relation between the dividends in any network communication game and its underlying transferable utility game, which depends on the structure of the communication network. Moreover,we introduce a new class of network control values which contains both the Myerson value and the position value. The decomposition results are used to explicitly express these values in terms of dividends. 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutis:ab795ba7d30244bfba6af3612f1b8867&r=gth 
By:  Mohamed Belhaj (AixMarseille Univ., CNRS, EHESS, Centrale Marseille, AMSE); Frédéric Deroïan (InSHSCNRS and AixMarseille Univ., CNRS, EHESS, Centrale Marseille, AMSE) 
Abstract:  We consider a network game with local complementarities. A policymaker, aiming at minimizing or maximizing aggregate effort, contracts with a single agent on the network to trade effort change against transfer. The policymaker has to find the best agent and the optimal contract to offer. Our study shows that for all utilities with linear bestresponses, it only takes two statistics about the position of each agent on the network to identify the key player: the Bonacich centrality and a weighted measure of the number of closed walks originating from the agent. We also characterize key players under linear quadratic utilities for various contractual arrangements. 
Keywords:  key player, Network, Linear Interaction, incentives, contract, limited budget 
JEL:  C72 D85 
Date:  2018–02 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:1804&r=gth 
By:  Saglam, Ismail 
Abstract:  In this paper we borrow from Ciarreta and GutierrezHita (2012) a duopolistic industry structure with cost asymmetry and demand uncertainty, and using this structure we build a bargaining model to study the division of collusion profits obtained from the joint selection of supply functions under the possibility of side payments. In our model, we consider potential disagreement points obtained from the noncooperative equilibrium of either the quantity competition or the supply function competition, and potential bargaining solutions splitting the gains from agreement either equally or proportionally according to the relative disagreement payoffs of the duopolists. Given any of these disagreement points and any of these bargaining solutions, we find that each duopolist has always incentive to join a collusive agreement. On the other hand, irrespective of whether the bargaining solution splits the gains from agreement equally or proportionally respecting the relative disagreement payoffs, the more efficient firm (the less efficient firm) in the cartel always obtains a higher agreement payoff when the disagreement point is obtained from the equilibrium of supply function competition (quantity competition). Given the studied disagreement points and bargaining solutions, we also find that bargaining over collusion profits always makes the more efficient firm worse off and the less efficient firm better off in comparison to a collusive agreement equalizing the marginal costs of these two firms. 
Keywords:  Duopoly; collusion; bargaining; Cournot competition; supply function competition; uncertainty 
JEL:  D43 L13 
Date:  2018–01–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:84007&r=gth 
By:  Duan, Lian 
Abstract:  I discuss the optimal degree of privatization in a mixed oligopoly in which multiple public enterprises exist. I find that the optimal degree of privatization is increasing in the number of private firms n and independent of the number of public firms m. These results suggest that no matter how many public firms exist, an increase in the number of private firms would increase the optimal degree of privatization as long as all public firms are partially privatized at the same degree. 
Keywords:  Quantitysetting; Partial privatization; Mixed oligopoly 
JEL:  C72 H42 L13 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:82896&r=gth 
By:  Yuhta Ishii (Centro de Investigaci´on Econ´omica, Mexico); Aniko Ory (Cowles Foundation, Yale University); Adrien Vigier (BI Norwegian Business School) 
Abstract:  In many labor markets, e.g., for lawyers, consultants, MBA students, and professional sport players, workers get offered and sign longterm contracts even though waiting could reveal significant information about their capabilities. This phenomenon is called unraveling. We examine the link between wage bargaining and unraveling. Two firms, an incumbent and an entrant, compete to hire a worker of unknown talent. Informational frictions prevent the incumbent from always observing the entrant’s arrival, inducing unraveling in all equilibria. We analyze the extent of unraveling, surplus shares, the average talent of employed workers, and the distribution of wages within and across firms. 
Keywords:  Unraveling, Talent, Wage Bargaining, Competition, Uncertainty 
JEL:  C7 D8 J3 
Date:  2018–02 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:3019&r=gth 
By:  Cason, Timothy; Masters, William; Sheremeta, Roman 
Abstract:  This study provides a unified framework to compare three canonical types of contests: winnertakeall contests won by the best performer, winnertakeall lotteries where probability of success is proportional to performance, and proportionalprize contests in which rewards are shared in proportion to performance. We derive equilibria and observe outcomes from each contest in a laboratory experiment. Equilibrium and observed efforts are highest in winnertakeall contests. Lotteries and proportionalprize contests have the same Nash equilibrium, but empirically, lotteries induce higher efforts and lower, more unequal payoffs. Behavioral deviations from theoretical benchmarks in different contests are caused by the same underlying attributes, such as riskaversion and the utility of winning. Finally, we find that subjects exhibit consistent behavior across different types of contests, with subjects exerting higher effort in one contest also exerting higher effort in another contest. 
Keywords:  contests, rentseeking, lotteries, incentives in experiments, risk aversion 
JEL:  C72 D72 D74 J33 
Date:  2018–01–29 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:84246&r=gth 
By:  Shuige Liu 
Abstract:  We define a modification of the standard Kripke model, called the ordered Kripke model, by introducing a linear order on the set of accessible states of each state. We first show this model can be used to describe the lexicographic belief hierarchy in epistemic game theory, and perfect rationalizability can be characterized within this model. Then we show that each ordered Kripke model is the limit of a sequence of standard probabilistic Kripke models with a modified (common) belief operator, in the senses of structure and the (epsilon)permissibilities characterized within them. 
Date:  2018–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1801.08767&r=gth 
By:  SangChul Suh (Department of Economics, University of Windsor); Yuntong Wang (Department of Economics, University of Windsor) 
Abstract:  The global economy under climate change is represented by countries, each of whom owns a technology that emits GHGs to produce output and privately owns a certain amount of permits. The permits are treated as the only input that is perfectly transferable among the countries, unlike regular factor inputs such as labor or capital. First, we axiomatically characterize a series of solutions called the proportional solutions. We hypothetically separate countries into two groups, permit contributors and technology contributors, and identify solutions under which countries receive rewards systematically according to the two types of contribution they provide (Separation Principle). Two other main axioms (NART and NARP), saying that no group of countries benefit from rearranging their contributions of technologies or permits among themselves, are used in characterizing the proportional solutions. Second, we introduce another axiom called Voluntary Participation to the solutions of sharing the surplus produced beyond the autarky economy output. This addition of Voluntary Participation leads to an interesting result; the surplus must be shared equally between the two groups, the permit (input) contributors and technology contributors. Hence the equal share proportional solution is uniquely characterized. 
Keywords:  Proportional Solution, Pollution Permits, Axioms, Voluntary Participation, Separation Principle 
JEL:  D51 D63 D71 F51 Q54 
Date:  2018–02 
URL:  http://d.repec.org/n?u=RePEc:wis:wpaper:1802&r=gth 
By:  Francisco B. Galarza (Universidad del Pací fico) 
Abstract:  We use experimental data to examine the effect of ethnicity (foreign, indigenous, and mestizo) and gender on trust and trustworthiness in Peru. We find that, compared to the foreign group, the indigenous group is more trusted (positive discrimination), while the mestizo group is less trustworthy (negative discrimination). Likewise, subjects reciprocate more in favor of males. We further analyze whether cognitive ability, the Big Five Personality Traits, and the social dominance orientation scale (SODS) can predict trust and trustworthiness. We find that the Cognitive Reflection Test score is positively correlated with trust, while the cumulative college GPA is negatively correlated with trustworthiness. And neuroticism is correlated with trusting behavior, while the SODS is (negatively) correlated with the trustworthiness ratio. 
Keywords:  Trust, trustworthiness, cognitive reection, personality traits, social dominance, discrimination, experiments 
JEL:  C72 C91 J15 
Date:  2018–01 
URL:  http://d.repec.org/n?u=RePEc:apc:wpaper:117&r=gth 
By:  Martin Hellwig (Max Planck Institute for Research on Collective Goods) 
Abstract:  For a countable product of complete separable metric spaces with a topology induced by a uniform metric, the set of Borel probability measures coincides with the set of completions of probability measures on the product σalgebra. Whereas the product space with the uniform metric is nonseparable, the support of any Bofrel measure is separable, and the topology of weak convergence on the space of Borel measures is metrizable by both the Prohorov metric and the bounded Lipschitz metric. 
Keywords:  Borel measures, product spaces with uniform metrics, completions of product σalgebras, universal type space, separability of supports, metrizability of weak convergence 
JEL:  C02 C72 
Date:  2017–05 
URL:  http://d.repec.org/n?u=RePEc:mpg:wpaper:2017_06&r=gth 
By:  Olivier Gossner (CREST; CNRS; Ecole polytechnique; Université ParisSaclay; London School of Economics); Christoph Kuzmics (University of Graz) 
Abstract:  A decision maker (DM) makes choices from different sets of alternatives. The DM is initially ignorant of the payoff associated to each alternative, and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option once payoffs are learned, the optimal choice rule from sets of alternatives is one that is as if the DM had strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are “right”. 
Keywords:  consistency, rationality, weak axiom of revealed preferences, strict preference 
JEL:  C73 D01 D11 
Date:  2017–12–31 
URL:  http://d.repec.org/n?u=RePEc:crs:wpaper:201752&r=gth 
By:  Frédéric Gavrel (CREM  Centre de recherche en économie et management  UNICAEN  Université de Caen Normandie  NU  Normandie Université  UR1  Université de Rennes 1  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  In the same vein as Blanchard and Tirole (2008) First Pass, this note shows that, under the condition for equilibrium stability, the partial implementation of layoff taxes invariably increases firms' profits as well as workers' utilities by lowering payroll taxes. It also proves that requiring stability does not raise any equilibrium existence issue per se: since the budget constraint of unemployment compensation induces multiple equilibria, the condition for stability simply permits the selection of one of these equilibria. These insights could favor the introduction of firing taxes, which in practice would probably be a gradual process 
Keywords:  Layoff taxes,payroll taxes,public policy efficiency 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01462917&r=gth 
By:  Paula Eugenia Gobbi; Juliane Parys; Gregor Schwerhoff 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ulb:ulbeco:2013/265950&r=gth 
By:  Goyal, S. 
Abstract:  This chapter shows that networks can have large and differentiated effects on behavior and then argues that social and economic pressures facilitate the formation of heterogenous networks. Thus networks can play an important role in understanding the wide diversity in human behaviour and in economic outcomes. 
Date:  2018–02–06 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:1812&r=gth 