
on Game Theory 
By:  René van den Brink (Department of Econometrics and OR, VU University and Tinbergen Institute Amsterdam, The Netherlands) 
Abstract:  In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that arise from restricted communication and hierarchies. This survey discusses several models of hierarchy restrictions and their relation with communication restrictions. In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize exisiting solutions for TUgames. In this survey we mainly focus on axiomatizations of the Shapley value in different models of games with a hierarchically structured player set, and their applications. Not only do these axiomatizations provide insight in the Shapley value for these models, but also by considering the types of axioms that characterize the Shapley value, we learn more about different network structures. A central model of games with hierarchies are the games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players that need permission from other players before they are allowed to cooperate. This permission structure is represented by a directed graph. Generalizations of this model are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications, in particular auction games and hierarchically structured firms. 
Keywords:  Cooperative TUgame; hierarchy; permission structure; antimatroid; local permission structure; applications. 
JEL:  C71 
Date:  2017–01–30 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20170016&r=gth 
By:  Thomas Demuynck; JeanJacques Herings; Riccardo Saulle; Christian Seel 
Abstract:  We introduce a new solution concept for models of coalition formation, called the myopic stable set. The myopic stable set is defined for a very general class of social environments and allows for an infinite state space. We show that the myopic stable set exists and is nonempty. Under minor continuity conditions, we also demonstrate uniqueness. Furthermore, the myopic stable set is a superset of the core and of the set of pure strategy Nash equilibria in noncooperative games. Additionally, the myopic stable set generalizes and unifies various results from more specific environments. In particular, the myopic stable set coincides with the coalition structure core in coalition function form games if the coalition structure core is nonempty; with the set of stable matchings in the standard onetoone matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria infinite supermodular games, finite potential games, and aggregative games. We illustrate the versatility of our concept by characterizing the myopic stable set in a model of Bertrand competition with asymmetric costs, for which the literature so far has not been able to fully characterize the set of all (mixed) Nash equilibria. 
Keywords:  social environments; group formation; stability; Nash equilibrium 
JEL:  C70 C71 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/244778&r=gth 
By:  Bettina Klaus; Flip Klijn 
Abstract:  We study manytomany matching markets in which agents from a set A are matched to agents from a disjoint set B through a twostage nonrevelation mechanism. In the first stage, Aagents, who are endowed with a quota that describes the maximal number of agents they can be matched to, simultaneously make proposals to the Bagents. In the second stage,Bagents sequentially, and respecting the quota, choose and match to available Aproposers. We study the subgame perfect Nash equilibria of the induced game. We prove that stable matchings are equilibrium outcomes if all Aagents' preferences are substitutable. We also show that the implementation of the set of stable matchings is closely related to the quotas of the Aagents. In particular, implementation holds when Aagents' preferences are substitutable and their quotas are nonbinding. 
Keywords:  implementation; matching; mechanisms; stability; substitutability 
JEL:  C78 D78 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:lau:crdeep:17.01&r=gth 
By:  Fabrizio Germano; Jonathan Weinstein; Peio ZuazoGarin 
Abstract:  Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989) Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICRx, where x is a sequence whose nth term is the probability players attach to (n  1)thorder belief in rationality. We find that Weinstein and Yildiz's discontinuity holds when higherorder belief in rationality remains above some threshold (constant x), but fails when higherorder belief in rationality eventually becomes low enough (x converging to 0). 
Keywords:  Robustness, rationalizability, bounded rationality, incomplete information, belief hierarchies. 
JEL:  C72 D82 D83 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:upf:upfgen:1548&r=gth 
By:  Konstantinos Georgalos; Sonali Sen Gupta; Indrajit Ray 
Abstract:  In a coarse correlated equilibrium (Moulin and Vial 1978), each player finds it optimal to commit ex ante to the future outcome from a probabilistic correlation device instead of playing any strategy of their own. In this paper, we consider a specific twoperson game with unique pure Nash and correlated equilibrium and test the concept of coarse correlated equilibrium with a device which is an equally weighted lottery over three symmetric outcomes in the game including the Nash equilibrium, with higher expected payoff than the Nash payoff (as in Moulin and Vial 1978). We also test an individual choice between a lottery over the same payoffs with equal probabilities and the sure payoff as in the Nash equilibrium of the game. Subjects choose the individual lottery, however, they do not commit to the device in the game and instead coordinate to play the Nash equilibrium. We explain this behaviour as an equilibrium in the game. 
Keywords:  Correlation, Coordination, Lottery 
JEL:  C72 C91 C92 D63 D83 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:lan:wpaper:151235570&r=gth 
By:  Duman, Papatya (Center for Mathematical Economics, Bielefeld University); Trockel, Walter (Center for Mathematical Economics, Bielefeld University) 
Abstract:  The alternating offers game due to Rubinstein (1982) had been used by Binmore (1980) and by Binmore et.al. (1986) to provide via its unique subgame perfect equilibrium an approximate noncooperative support for the Nash bargaining solution of associated cooperative twoperson bargaining games. These results had strengthened the prominent role of the Nash bargaining solution in cooperative axiomatic bargaining theory and its application, for instance in labor markets, and have often even be interpreted as a mechanism theoretical implementation of the Nash solution. Our results in the present paper provide exact noncooperative foundations first, in our Proposition, via weakly subgame perfect equilibria of a game that is a modification of RubinsteinÂ´s game, then in our Theorem, via subgame perfect equilibria of a game that is a further modification of our first game. Moreover, they provide a general rule how to transform approximate support results into exact ones. Finally, we discuss the relation of the above mentioned support results, including our present ones, with mechanism theoretic implementation in (weakly) subgame perfect equilibrium of the Nash solution. There we come to the conclusion that a sound interpretation as an implementation can hardly be found except in very rare cases of extremely restricted domains of playersÂ´ preferences. 
Keywords:  Nash program, Noncooperative foundation, Implementation, Nash solution, Rubinstein game, Subgame perfect equilibrium 
Date:  2016–01–15 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:550&r=gth 
By:  Decerf, Benoit (Center for Mathematical Economics, Bielefeld University); Riedel, Frank (Center for Mathematical Economics, Bielefeld University) 
Abstract:  Riedel and Sass (2013) study complete information normal form games in which ambiguity averse players use ambiguous randomization strategies, in addition to pure and mixed strategies. The solution concept they propose, the Ellsberg equilibrium, is a coarsening of the classical Nash equilibrium. We provide a foundation of the new equilibrium concept in the spirit of Harsanyi. We prove an extension of the Purification Theorem for 2x2 normal form games. Our result implies that any Ellsberg equilibrium of such game is the limit case of a mixed strategy equilibrium in a disturbed version of the game for which payoffs are ambiguously disturbed. 
Keywords:  Knightian uncertainty, Ellsberg games, Ambiguity aversion, Purification, Disambiguation 
Date:  2016–03–03 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:554&r=gth 
By:  Brunner, Christoph; Kauffeldt, T. Florian; Rau, Hannes 
Abstract:  In many experiments, the Nash equilibrium concept seems not to predict well. One reason may be that players have nonselfish preferences over outcomes. As a consequence, even when they are told what the material payoffs of the game are, mutual knowledge of preferences may not be satisfied. We experimentally examine several 2x2 games and test whether revealing players' preferences leads to more equilibrium play. For that purpose, we elicit subjects' preferences over outcomes before the games are played. It turns out that subjects are significantly more likely to play an equilibrium strategy when other players' preferences are revealed. We discuss a noisy version of the Bayesian Nash equilibrium and a model of strategic ambiguity to account for observed subject behavior. 
Keywords:  Behavioral Game Theory; Epistemic Game Theory; Nash Equilibrium; Games of Incomplete Information 
Date:  2017–01–30 
URL:  http://d.repec.org/n?u=RePEc:awi:wpaper:0629&r=gth 
By:  de Angelis, Tiziano (Center for Mathematical Economics, Bielefeld University); Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University) 
Abstract:  In this paper we establish a new connection between a class of 2player nonzerosum games of optimal stopping and certain 2player nonzerosum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of singular control. Moreover a differential link between the players' value functions holds across the two games. 
Keywords:  games of singular control, games of optimal stopping, Nash equilibrium, onedimensional diffusion, HamiltonJacobiBellman equation, verification theorem 
Date:  2016–07–21 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:565&r=gth 
By:  Cheremukhin, Anton A. (Federal Reserve Bank of Dallas); RestrepoEchavarria, Paulina (Federal Reserve Bank of St. Louis); Tutino, Antonella (Federal Reserve Bank of Dallas) 
Abstract:  We endogenize the degree of randomness in the matching process by proposing a model where agents have to pay a search cost to locate potential matches more accurately. The model features a tension between an agent’s desire to find a more productive match and to maximize the odds of finding a match. This tension drives a wedge between the shape of sorting patterns and the shape of the underlying match payoff function. We show the empirical relevance of the latter prediction by applying the model to the U.S. marriage market. 
Keywords:  Matching; sorting; assignment; search 
JEL:  C78 D83 E24 J64 
Date:  2016–05–20 
URL:  http://d.repec.org/n?u=RePEc:fip:feddwp:1610&r=gth 
By:  Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) 
Abstract:  Within this paper we conclude the treatise of vNMStable Sets for (cooperative) linear production games with a continuum of players. The paper resumes a series of presentations of this topic, for Part I, II, III, IV, see IMW 483, IMW 498, IMW 500, IMW 534. The framework has been outlined previously. The coalitional function is generated by r+1 â€œproduction factors'' (non atomic measures). r factors are given by orthogonal probabilities ("cornered'' production factors) establishing the core of the game. Factor r+1 (the "central'' production factor) is represented by a nonantomic measure with carrier â€œacross the corners'' of the market. I.e., this factor is available in excess and the representing measure is no element of the core of the game. Generalizing our setup, we assume now that the ``central'' production factor is represented by an arbitrary measure not necessarily of step function character. Then the existence theorem is achieved by an approximation procedure. Again it turns out that there is a (not necessarily unique) imputation outside of the core which, together with the core generates the vNMStable Set as the convex hull. Significantly, this additional imputation can be seen as a truncation of the ``central'' distribution, i.e., the r+1^st production factor. Hence, there is a remarkable similarity mutatis mutandis regarding the Characterization Theorem that holds true for the â€œpurely orthogonal case'' Rosenmüller and Shitoviz (2000). This justifies to use the term â€œStandard vNMStable Set'' in the presence of a central production factor. 
Date:  2016–02–24 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:552&r=gth 
By:  Külpmann, Philipp (Center for Mathematical Economics, Bielefeld University); Khantadze, Davit (Center for Mathematical Economics, Bielefeld University) 
Abstract:  We investigate the effect of absence of common knowledge on the outcomes of coordination games in a laboratory experiment. Using cognitive types, we can explain coordination failure in pure coordination games while differentiating between coordination failure due to first and higherorder beliefs. In our experiment, around 76% of the subjects have chosen the payoffdominant equilibrium strategy despite the absence of common knowledge. However, 9% of the players had firstorder beliefs that lead to coordination failure and another 9% exhibited coordination failure due to higherorder beliefs. Furthermore, we compare our results with predictions of commonly used models of higherorder beliefs. 
Keywords:  Higherorder beliefs, coordination failure, cognitive abilities, experimental economics, game theory 
Date:  2016–09–26 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:567&r=gth 
By:  de Angelis, Tiziano (Center for Mathematical Economics, Bielefeld University); Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Moriarty, John (Center for Mathematical Economics, Bielefeld University) 
Abstract:  This paper analyses twoplayer nonzerosum games of optimal stopping on a class of regular diffusions with singular boundary behaviour (in the sense of Itô and McKean (1974) [19], p. 108). We prove that Nash equilibria are realised by stopping the diffusion at the first exit time from suitable intervals whose boundaries solve a system of algebraic equations. Under mild additional assumptions we also prove uniqueness of the equilibrium. 
Keywords:  nonzerosum Dynkin games, Nash equilibrium, smoothfit principle, regular diffusions, free boundary problems 
Date:  2016–07–21 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:563&r=gth 
By:  Dunia LópezPintado (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain) 
Abstract:  We survey a series of theoretical contributions on diffusion in random networks. We start with a benchmark contagion process, referred in the epidemiology literature as the SusceptibleInfectedSusceptible model, which describes the spread of an infectious disease in a population. To make this model tractable, the interaction structure is considered as a heterogeneous sampling process characterized by the degree distribution. Within this framework, we distinguish between the case of unbiaseddegree networks and biaseddegree networks. We focus on the characterization of the diffusion threshold; that is, a condition on the primitives of the model that guarantees the spreading of the product to a significant fraction of the population, and its persistence. We also extend the analysis introducing a general diffusion model with features that are more appropriate for describing the diffusion of a new product, idea, behavior, etc. 
Keywords:  degree distribution, random networks, diffusion threshold, endemic state, homophily. 
JEL:  C73 L14 O31 O33 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:pab:wpaper:16.10&r=gth 
By:  Sun, Lan (Center for Mathematical Economics, Bielefeld University) 
Abstract:  In this paper, we propose a definition of Hypothesis Testing Equilibrium (HTE) for general signaling games with nonBayesian players nested by an updating rule according to Hypothesis Testing model characterized by Ortoleva (2012). An HTE may be different from a sequential Nash equilibrium because of the dynamic inconsistency. However, when player 2 only takes zeroprobability message as an unexpected news, an HTE is a refinement of sequential Nash equilibrium and it survives Intuitive Criterion, but not vice versa. We provide existence theorem covering a broad class of signaling games often studied in economics, and the constrained HTE is unique in such signaling games. 
Keywords:  Signaling Games, Hypothesis Testing Equilibrium, Equilibrium Refinement 
Date:  2016–05–30 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:557&r=gth 
By:  Haris Aziz (University of New South Wales, Australia); Jens L. Hougaard (Department of Food and Resource Economics, University of Copenhagen); Juan D. MorenoTernero (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain); Lars P. Osterdal (Department of Business and Economics, University of Southern Denmark) 
Abstract:  We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. We introduce a general approach to compute aggregate gapminimizing assignments, as well as gapegalitarian assignments. The approach relies on an algorithm which is shown to be faster than general purpose algorithms for the assignment problem. We also extend the approach to probabilistic assignments and explore the computational features of existing, as well as new, methods for this setting. 
Keywords:  Random assignment, congested facility, aggregate gap minimization, gapegalitarian assignments, computational speed. 
JEL:  C78 D61 D63 
Date:  2017–03 
URL:  http://d.repec.org/n?u=RePEc:pab:wpaper:17.03&r=gth 
By:  Caterina Calsamiglia (CEMFI and Barcelona GSE); Chao Fu (University of WisconsinMadison); Maia Güell (University of Edinburgh) 
Abstract:  We develop a model of school choices by households under the popular Boston mechanism (BM) and a new method to fully solve household problem that is infeasible to solve via traditional method. We estimate the joint distribution of household preferences and sophistication types using administrative data from Barcelona. Our counterfactual policy analyses show that a change from BM to the student deferred acceptance mechanism would create more losers than winners and decrease the average welfare by 1,020 euros, while a change from BM to the top trading cycles mechanism has the opposite effect and increases the average welfare by 460 euros. 
Keywords:  School choice, Boston, deferred acceptance and top trading cycles. 
JEL:  C78 D63 I24 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2016_1611&r=gth 
By:  Wilhelms, Steven C.; Coatney, Kalyn T.; Chaudhry, Anita M.; Barnes, James N. 
Abstract:  Sustainability of the Mississippi River Valley Alluvial Aquifer (MRVAA) is a growing concern for regulators and farmers alike. Currently, nonbinding and unmonitored regulatory policies have not decelerated the rapid depletion of the MRVAA. As such, the State of Mississippi is facing significant challenges in developing, if necessary, future regulations to maintain water sustainability. The primary goal of this study is to investigate the potential impacts on voluntary water use restrictions and welfare resulting from credible and binding future uselimit regulations. To maintain relevance to MRVAA, we develop a novel commons extraction game accounting for heterogeneously endowed producers in regards to recharge rates and the potential for localized complete depletion. Credibility in the game is established once the majority of producers have ran out of water and are assumed to support regulation. Predictions of the game without regulation, under various strategic assumptions, are subsequently tested in laboratory experiments across various regulatory treatment policies. Treatment policies include: no regulation, limiteduse, and moratorium. Preliminary results indicate, that without the extreme credible threat of moratorium, users do not significantly volunteer to reduce extraction rates. Planned replication of experiments should provide robust insights into future water levels if regulation or volunteering is not instituted. 
Keywords:  natural resource, experimental economics, commons, aquifer, Environmental Economics and Policy, Resource /Energy Economics and Policy, C72, C91, Q25, 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:ags:saea17:252855&r=gth 
By:  Gee, Laura Katherine (Tufts University); Lyu, Xinxin (Tufts University); Urry, Heather (Tufts University) 
Abstract:  The ability to punish freeriders can increase the provision of public goods. However, sometimes the benefit of increased public good provision is outweighed by the costs of punishments. One reason a group may punish to the point that net welfare is reduced is that punishment can express anger about freeriding. If this is the case, then tools that regulate emotions could decrease the use of punishments while keeping welfare high, possibly depending on preexisting levels of aggression. In this lab experiment, we find that adopting an objective attitude (Objective), through a form of emotion regulation called cognitive reappraisal, decreases the use of punishments and makes a statistically insignificant improvement to both net earnings and selfreported emotions compared to a control condition (Natural). Although the interaction between the emotion regulation treatment and level of aggression is not significant, only low aggression types reduce their punishments; the results are of the same direction but statistically insignificant for high aggression types. Overall, our findings suggest that pairing emotion regulation with punishments can decrease the use of punishments without harming monetary and mental welfare. 
Keywords:  public goods, punishment, emotions 
JEL:  C72 C91 C92 D7 H41 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp10499&r=gth 
By:  László Á. Kóczy (Centre for Economic and Regional Studies, Hungarian Academy of Sciences and and Keleti Faculty of Business and Management, Óbuda University); János Kiss Hubert (Centre for Economic and Regional Studies, Hungarian Academy of Sciences) 
Abstract:  The 2016 Nobel Memorial Prize in Economic Sciences was awarded to Oliver Hart and Bengt Holmström for their work on contract theory. Contract theory is a subfield of game theory where the conflict between the owner  the principal  and the CEO  or agent is at the centre of interest. In the following we explain the principalagent model of Holmström with some extensions and then look at the property right aspects of these models based on Hart's work. Although the two researchers are recognised for their theoretical work, in our simple introduction we avoid complex formulae and illustrate the models with examples. 
Keywords:  contract theory, incentives, principalagent problem, Nobel prize, risk, property rights JEL Codes: C72, D82, D86 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:pkk:wpaper:1701&r=gth 