nep-gth New Economics Papers
on Game Theory
Issue of 2016‒10‒02
twenty-one papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. Static versus Dynamic Deferred Acceptance in School Choice: Theory and Experiment By Flip Klijn; Joana Pais; Marc Vorsatz
  2. A "Pencil-Sharpening" Algorithm for Two Player Stochastic Games with Perfect Monitoring By Abreu, Dilip; Brooks, Benjamin; Sannikov, Yuliy
  3. Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance By Herings, P. Jean-Jacques; Mauleon, Ana; Vannetelbosch, Vincent
  4. Allocation rules for coalitional network games By Jean-François Caulier; Ana Mauleon; Vincent Vannetelbosch
  5. Fair Allocation of Disputed Properties By Biung-Ghi Ju; Juan D. Moreno-Ternero
  6. On K-Class discounted stochastic games By Frank Page
  7. Analyzing Games with Ambiguous Player Types Using the MINthenMAX Decision Model By Ilan Nehama
  8. Stationary Markov equilibria for approximable discounted stochastic games By Frank Page
  9. Bases and Transforms of Set Functions By Michel Grabisch
  10. On symbols and cooperation By Tom Potoms; Tom Truyts
  11. Evolutionarily Stable Strategies of Random Games and the Facets of Random Polytopes By Ohad Navon
  12. Collective Action in an Asymmetric World By Chen, Cuicui; Zeckhauser, Richard
  13. Systemic risk and the dynamics of temporary financial networks By Rui Gong; Frank Page
  14. Fluid intelligence and cognitive reflection in a strategic environment: evidence from dominance-solvable games By Nobuyuki Hanaki; Nicolas Jacquemet; Stéphane Luchini; Adam Zylbersztejn
  15. Women ask for less (only from men): Evidence from alternating-offer bargaining in the field By Hernandez-Arenaz, Iñigo; Iriberri, Nagore
  16. Environmental awareness: The case of climate change By Hans, Wiesmeth; Weber, Shlomo
  17. Ranking Languages in the European Union:Before and after Brexit By Ginsburgh, Victor; Juan, Moreno-Ternero; Weber, Shlomo
  18. Immigration Policies, Labor Complementarities, Population Size and Cultural Frictions: Theory and Evidence By Thomas, Osang; Weber, Shlomo
  19. Groups and trust: Distributive Justice with Production and the Social Contract. An Experimental study By Giacomo Degli Antoni; Marco Faillo; Lorenzo Sacconi; Pedro Francés-Gomez
  20. Optimality, Equilibrium, and Curb Sets in Decision Problems without Commitment By Herings, Jean-Jacques; Meshalkin, Andrey; Predtetchinski, Arkadi
  21. Regional (In)Stability in Europe: a Quantitative Model of State Fragmentation By Vanschoonbeek, Jakob

  1. By: Flip Klijn; Joana Pais; Marc Vorsatz
    Abstract: In the context of school choice, we experimentally study how behavior and outcomes are affected when, instead of submitting rankings in the student proposing or receiving deferred acceptance (DA) mechanism, participants make decisions dynamically, going through the steps of the underlying algorithms. Our main results show that, contrary to theory, (a) in the dynamic student proposing DA mechanism, participants propose to schools respecting the order of their true preferences slightly more often than in its static version while, (b) in the dynamic student receiving DA mechanism, participants react to proposals by always respecting the order and not accepting schools in the tail of their true preferences more often than in the corresponding static version. As a consequence, for most problems we test, no significant differences exist between the two versions of the student proposing DA mechanisms in what stability and average payoffs are concerned, but the dynamic version of the student receiving DA mechanism delivers a clear improvement over its static counterpart in both dimensions. In fact, in the aggregate, the dynamic school proposing DA mechanism is the best performing mechanism.
    Keywords: dynamic school choice, deferred acceptance, stability, efficiency
    JEL: C78 C91 C92 D78 I20
    Date: 2016–09
  2. By: Abreu, Dilip (Princeton University); Brooks, Benjamin (University of Chicago); Sannikov, Yuliy (Princeton University)
    Abstract: We study the subgame perfect equilibria of two player stochastic games with perfect monitoring and geometric discounting. A novel algorithm is developed for calculating the discounted payoffs that can be attained in equilibrium. This algorithm generates a sequence of tuples of payoffs vectors, one payoff for each state, that move around the equilibrium payoff sets in a clockwise manner. The trajectory of these "pivot" payoffs asymptotically traces the boundary of the equilibrium payoff correspondence. We also provide an implementation of our algorithm, and preliminary simulations indicate that it is more efficient than existing methods. The theoretical results that underlie the algorithm also yield a bound on the number of extremal equilibrium payoffs.
    JEL: C63 C72 C73 D90
    Date: 2016–04
  3. By: Herings, P. Jean-Jacques (General Economics 1 (Micro)); Mauleon, Ana (saint louis university brussels; university of louvain, louvain la neuve); Vannetelbosch, Vincent (university of louvain, louvain la neuve)
    Abstract: We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty, meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominance has to be replaced by path dominance along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise myopic vNM set and the myopic vNM set, respectively. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core. We also show that the pairwise and coalitional analogues of the level-1 farsighted set yield the core as the unique prediction.
    Keywords: Mathematical economics, Microeconomics, Operations research and management science
    JEL: C70 C78
  4. By: Jean-François Caulier (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Ana Mauleon (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain, CEREC - Université Saint-Louis - Bruxelles); Vincent Vannetelbosch (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain, CEREC - Université Saint-Louis - Bruxelles)
    Abstract: Coalitional network games are real-valued functions defined on a set of players organized into a network and a coalition structure. We adopt a flexible approach assuming that players organize themselves the best way possible by forming the efficient coalitional network structure. We propose two allocation rules that distribute the value of the efficient coalitional network structure: the atom-based flexible coalitional network allocation rule and the player-based flexible coalitional network allocation rule.
    Keywords: cooperative game theory, allocation rules,Coalition, Networks
    Date: 2015–11
  5. By: Biung-Ghi Ju (Department of Economics, Seoul National University, Korea); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide, Spain, and CORE, Université catholique de Louvain, Belgium)
    Abstract: We model problems of allocating disputed properties as generalized exchange economies. Therein, agents have preferences and claims over multiple goods, and the social endowment of each good may not be sufficient to satisfy all individual claims. We focus on market-based allocation rules that impose a two-step procedure: assignment of rights based on claims first, and voluntary exchange based on the assigned rights afterwards. We characterize three focal egalitarian rights-assignment rules that guarantee that the allocation rules are fair. We apply our results to problems of greenhouse gas emissions and contested water rights.
    Keywords: fairness, claims, no-envy, individual rationality, egalitarianism, efficiency, Walrasian exchange
    JEL: D63 D71
    Date: 2016–09–28
  6. By: Frank Page
    Abstract: For a discounted stochastic game with an uncountable state space and compact metric action spaces, we show that if the measurable-selection-valued, Nash payoff selection correspondence of the underlying one-shot game contains a sub-correspondence having the K- limit property (i.e., if the Nash payoff selection sub-correspondence contains its K-limits and therefore is a K correspondence), then the discounted stochastic game has a stationary Markov equilibrium. Our key result is a new fixed point theorem for measurable-selection-valued correspondences having the K-limit property. We also show that if the discounted stochastic game is noisy (Duggan, 2012), or if the underlying probability space satisfies the G-nonatomic condition of Rokhlin (1949) and Dynkin and Evstigneev (1976) (and therefore satisfies the coaser transition kernel condition of He and Sun, 2014), then the Nash payoff selection correspondence contains a sub-correspondence having the K-limit property.
    Keywords: approximate Caratheodory selections; fixed points of nonconvex valued correspondences; measurable selection valued correspondences; Komlos limits; Komlos’ Theorem; weak star convergence; discounted stochastic games; stationary Markov equilibria
    JEL: C7
    Date: 2016–07
  7. By: Ilan Nehama
    Abstract: In many common interactive scenarios, participants lack information about other participants, and specifically about the preferences of other participants. In this work, we model an extreme case of incomplete information, which we term games with type ambiguity, where a participant lacks even information enabling him to form a belief on the preferences of others. Under type ambiguity, one cannot analyze the scenario using the commonly used Bayesian framework, and therefore one needs to model the participants using a different decision model. To this end, we present the MINthenMAX decision model under ambiguity. This model is a refinement of Wald’s MiniMax principle, which we show to be too coarse for games with type ambiguity. We characterize MINthenMAX as the finest refinement of the MiniMax principle that satisfies three properties we claim are necessary for games with type ambiguity. This prior-less approach we present here also follows the common practice in computer science of worst-case analysis. Finally, we define and analyze the corresponding equilibrium concept, when all players follow MINthenMAX. We demonstrate this equilibrium by applying it to two common economic scenarios: coordination games and bilateral trade. We show that in both scenarios, an equilibrium in pure strategies always exists, and we analyze the equilibria.
    Date: 2016–08
  8. By: Frank Page
    Abstract: We identify a new class of uncountable-compact discounted stochastic games for which existence of stationary Markov equilibria can be established and we prove two new existence results for this class. Our approach to proving existence in both cases is new – with both proofs being based upon continuous approximation methods. For our first result we use approximation methods involving measurable-selection-valued continuous functions to establish a new fixed point result for Nash payoff selection correspondences - and more generally for measurable-selection-valued correspondences having nonconvex values. For our second result, we again use approximation methods, but this time involving player action-profile-valued continuous functions to establish a new measurable selection result for upper Caratheodory Nash payoff correspondences. Because conditions which guarantee approximability - the presence of sub-correspondences taking contractible values (or more generally, Rd-values) - are the very conditions which rule out Nash equilibria homeomorphic to the unit circle, we conjecture that for uncountable-compact discounted stochastic games, the approximable class is the widest class for which existence of stationary Markov equilibria can be established.
    Keywords: tationary Markov equilibria; discounted stochastic games; fixed point
    JEL: C7
    Date: 2016
  9. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)
    Abstract: The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic dual-ity between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral.
    Keywords: set function, capacity, basis, transform, Moebius transform, Choquet integral
    Date: 2016
  10. By: Tom Potoms; Tom Truyts
    Abstract: How are group symbols (e.g., a flag, a Muslim veil, a clothing style) helpful in sustaining cooperation and social norms? We study the role of symbols in an infinitely repeated public goods game with random matching, endogenous partnership termination, limited information ‡flows and endogenous symbol choice. We characterize an efficient segregating equilibrium, in which players only cooperate with others bearing the same symbol. In this equilibrium, players bearing a scarcer symbol face a longer expected search time to find a cooperative partner upon partnership termination, and this sacrifice of outside options allows them to sustain higher levels of cooperation. We compare this equilibrium to other equilibria in terms of renegotiation proofness, and we discuss the relation this has to the evolution of intolerance.
    Date: 2016–09
  11. By: Ohad Navon
    Abstract: An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (mutant) strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the question of what happens when the size of the game increases: does an ESS exist for almost every” large game? We let the entries of an n × n game matrix be independently randomly chosen according to a symmetrical subexponential distribution F, and study the expected number of ESS with support of size d as n ? ?. In a previous paper by Hart, Rinott and Weiss [6] it was shown that this limit is 1 2 for d = 2. This paper deals with the case of d ? 4, and proves the conjecture in [6] (Section 6,c), that the expected number of ESS with support of size d ? 4 is 0. Furthermore, it discusses the classic problem of the number of facets of a convex hull of n random points in Rd, and relates it to the above ESS problem. Given a collection of i.i.d. random points, our result implies that the expected number of facets of their convex hull converges to 2d as n ? ?.
    Date: 2016–09
  12. By: Chen, Cuicui (Harvard University); Zeckhauser, Richard (Harvard University)
    Abstract: A central authority possessing tax and expenditure responsibilities can readily provide an efficient level of a public good. Absent a central authority, the case with climate change mitigation, voluntary arrangements must replace coercive arrangements; significant under-provision must be expected. Potential contributors have strong incentives to free ride, or to ride cheaply. International public goods are particularly challenging. The players--the nations of the world--are many and they start in quite different circumstances. Voluntary arrangements that might emerge from negotiations fall short for two reasons: First, players frame negotiations from their own standpoint, making stalemate likely. Second, the focal-point solution where contributions are proportional to benefits clashes with the disproportionate incentives little players have to ride cheaply. We identify a solution, the Cheap-Riding Efficient Equilibrium, which defines the relative contributions of players of differing size (or preference intensity) to reflect cheap riding incentives, yet still achieves Pareto optimality. Players start by establishing the Alliance/Nash Equilibrium as a base point. From that point they apply either the principles of the Lindahl Equilibrium or the Nash Bargaining Solution to proceed to the Pareto frontier. The former benefits from its focal-point properties; the latter is a standard analytic tool addressing bargaining. We apply our theory to climate change by first examining the Nordhaus Climate Club proposal. We then test the Alliance Equilibrium model using individual nations' Intended Nationally Determined Contributions pledged at the Paris Climate Change Conference. As hypothesized, larger nations made much larger pledges in proportion to their Gross National Incomes.
    JEL: C72 F53 H87
    Date: 2016–04
  13. By: Rui Gong; Frank Page
    Abstract: This paper has two main objectives: first, to provide a formal definition of endogenous systemic risk that is firmly grounded in equilibrium dynamics of temporary financial networks (i.e., short-term lending and investment networks); and second, to construct a discounted stochastic game (DSG) model of the emergence of equilibrium network dynamics that fully takes into account the feedback between network structure, strategic behavior, and risk. Based on our definition of systemic risk we also propose a formal definition of tipping points. Using these tools we provide a strategic approach to making global assessments of systemic risk in temporary financial networks. Our approach is based on three key facts: (1) the equilibrium dynamics which emerge from the game of network formation generate finitely many disjoint basins of attraction as well as finitely many ergodic measures (implying that, starting from any temporary financial network, in finite time with probability one, the dynamic sequence of networks arrives at one of these basins, and once there, stays there), (2) each basin of attraction is homogenous with respect to its default characteristics (meaning that if a basin contains networks having a particular set of defaulted players, then all networks contained in this basin have the same set of defaulted players), and (3) the unique profile of basins generated by the equilibrium dynamics carries with it a unique set of tipping points (special networks) - and these tipping points provide an early warning of network failure.
    Keywords: systemic risk; counter-party risk; financial networks; supernetworks; tipping points; default cascades; basins of attraction; Pareto optimal stationary Markov equilibrium; first passage probabilities; hitting times; hitting time probabilities.
    JEL: C7
    Date: 2016–07
  14. By: Nobuyuki Hanaki (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - CNRS - Centre National de la Recherche Scientifique); Nicolas Jacquemet (PSE - Paris School of Economics); Stéphane Luchini (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales - Université Paul Cézanne - Aix-Marseille 3 - Université de la Méditerranée - Aix-Marseille 2 - CNRS - Centre National de la Recherche Scientifique); Adam Zylbersztejn (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - UCBL - Université Claude Bernard Lyon 1 - UL2 - Université Lumière - Lyon 2 - Université Jean Monnet - Saint-Etienne - PRES Université de Lyon - ENS Lyon - École normale supérieure - Lyon)
    Abstract: Dominance solvability is one of the most straightforward solution concepts in game theory. It is based on two principles: dominance (according to which players always use their dominant strategy) and iterated dominance (according to which players always act as if others apply the principle of dominance). However, existing experimental evidence questions the empirical accuracy of dominance solvability. In this study, we study the relationships between the key facets of dominance solvability and two cognitive skills, cognitive reection and uid intelligence. We provide evidence that the behaviors in accordance with dominance and one-step iterated dominance are both predicted by one's uid intelligence rather than cognitive reection. Individual cognitive skills, however, only explain a small fraction of the observed failure of dominance solvability. The accuracy of theoretical predictions on strategic decision making thus not only depends on individual cognitive characteristics, but also, perhaps more importantly, on the decision making environment itself.
    Keywords: Raven's test,experiment,Dominance solvability,cognitive skills,CRT
    Date: 2016
  15. By: Hernandez-Arenaz, Iñigo; Iriberri, Nagore
    Abstract: We study gender differences and gender interaction effects in bargaining. Data from a TV show offer a unique opportunity to observe both bargaining outcomes and behavior, with sizable stakes. The matching between male proposers (strong position) and female responders (weak position) is different from all other matchings. No differences are observed in opening offers, but women demand less from men than from women. This differential behavior yields bargaining outcomes that are more favorable for men and less favorable for women when male proposers encounter female responders.
    Keywords: Alternating-offer bargaining; field data.; gender differences; gender interaction effects
    JEL: C72 J16 J31
    Date: 2016–09
  16. By: Hans, Wiesmeth; Weber, Shlomo
    Abstract: The extent of provision of a public good often relies on social awareness and public support for it. This applies, in particular, to global reduction of greenhouse gases and its relevance for mitigating climate change. We examine the concept of "public awareness" by introducing a formal model that analyzes efforts to mitigate climate change in a setting with heterogeneous countries. In the theoretical part we examine the Nash equilibrium of the contribution game. The effects of awareness and economic parameters on mitigation efforts can be disentangled, raising the possibility of linking awareness of climate change with economic wealth. The second part provides some empirical observations and offers the rankings of countries regarding awareness for climate change, as well as an empirical relationship between awareness and economic wealth.
    Keywords: diversity; Environmental awareness; Kyoto protocol; Public Goods; regional economics
    JEL: C72 D74 H41 H87 Q42 Q54
    Date: 2016–09
  17. By: Ginsburgh, Victor; Juan, Moreno-Ternero; Weber, Shlomo
    Abstract: This article presents a framework for evaluation of the impact of languages in multilingual societies. We consider several ranking methods grounded on various principles, including minimal disenfranchisement, communicative benefits, utilitarianism, and the game-theoretical concept of the Shapley Value. We use data from the Special Barometer survey to apply these methods to languages within the European Union. Although the methods we consider are driven by distinct normative grounds, they generate quite similar results. Finally, we analyse the impact of Brexit on the rankings, especially if English forfeits its status as an ocial language in the Union.
    Keywords: Communicative benefits; European Union; linguistic disenfranchisement; official languages; Ranking methods
    JEL: C71 D71 Z18
    Date: 2016–09
  18. By: Thomas, Osang; Weber, Shlomo
    Abstract: In this paper we consider a simple model of international migration developed in Fujita and Weber (2010). There are two countries A and B, that differ in population size, degree of labor complementarity between natives and immigrants, as well as cultural attitudes towards immigrants. The countries select immigration quotas for the world population of immigrants. We apply the existence result of Fujita-Weber and show that in equilibrium the larger country attracts more immigrants, while choosing a lower quota than its smaller counterpart. It also turns out that higher degree of labor complementarity between natives and immigrants and a lower degree of cultural friction between two groups yield higher immigration quota. Finally, we test the empiricalvalidity of the model using time-series country-level data and demonstrate that both cross-section and panel data approaches support several of the key theoretical findings.
    Keywords: cultural frictions; fixed effects; Immigration quotas; labor complementarity; Nash equilibrium; panel data
    JEL: C72 F22 O3 R1
    Date: 2016–09
  19. By: Giacomo Degli Antoni (University of Parma, Department of Law); Marco Faillo (University of Trento); Lorenzo Sacconi (University of Trento); Pedro Francés-Gomez (University of Granada)
    Abstract: Drawing on the theoretical and experimental literature on distributive justice, we put some assumptions of the contractarian argument to an empirical test by means of an experiment which investigates the influence that explicit agreement under the veil of ignorance may have on individuals' conception of justice and its implementation in a context of the production and distribution of a common output. One crucial characteristic of our experiment is that subjects are assigned unequal endowments for which they are not responsible; the assignment is random. At the same time, their work naturally generates unequal levels of earnings. Do the subjects involved in this interaction distinguish between the two types of inequality? Do they try to reduce the arbitrary one, while accepting the one generated through effort? Do they elaborate other distributive criteria? Does their choice ex-ante, when they are behind the veil, differ from their choice ex-post once the veil has been lifted and they know the outcome of the production phase? The main result is that the agreement under a veil of ignorance induces subjects to accept a liberal egalitarian division rule not only in the ex-ante agreement, but also in the actual implementation of the pie division, even if this contradicts their self-interest and some common economic assumptions about reciprocal expectations of rationality. In addition, our results show that deliberating through open discussion increases the level of ex-post compliance.
    Keywords: Trust; Distributive justice, social contract, fairness, dictator game, contractarian business ethics
    JEL: C72 C91 D02 D63
  20. By: Herings, Jean-Jacques (General Economics 1 (Micro)); Meshalkin, Andrey (General Economics 1 (Micro)); Predtetchinski, Arkadi (General Economics 1 (Micro))
    Abstract: The paper considers a class of decision problems with infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. We introduce the notions of Nash equilibrium, subgame perfect equilibrium, and curb sets for decision problems. An optimal policy at the initial history is a Nash equilibrium but not vice versa. Both subgame perfect equilibria and curb sets are equivalent to subgame optimal policies. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.
    JEL: C61 C62 C73
  21. By: Vanschoonbeek, Jakob
    Abstract: Despite a rich theoretical literature on regional (in)stability, little is known about its empirical validity. This paper presents simulated experimental findings on spatial heterogeneity in regional (in)stability accross 264 regions belonging to 26 European countries. To do so, it develops a broad model of state fragmentation that reconciles the views of the dominant strands in the literature. In order to apply the model, a novel indicator of regional political distinctiveness is proposed, rooted in the discrepancy between regional and national electoral behavior. Calibrating our model to the current European situation, we find that Cataluña, Flanders and the Basque country are the regions currently most likely to break away. In line with these results, governments in all three regions have consistently vocalized demands for increased autonomy - or even secession - in recent years. Denmark, Hungary and Slovenia show up as the most secession-robust European countries.
    Keywords: Political heterogeneity, European Union, state fragmentation, secession and unification
    JEL: C63 C70 H77
    Date: 2016–09–23

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