
on Game Theory 
By:  Douglas Davis (Virginia Commonwealth University); Asen Ivanov (Queen Mary University of London); Oleg Korenok (Virginia Commonwealth University) 
Abstract:  We introduce a novel approach to studying behavior in repeated games  one that is based on the psychology of play. Our approach is based on the following six "aspects" of a player's behavior: round1 cooperation, lenience, forgiveness, loyalty, leadership, and following. Using a laboratory experiment, we explore how aspects are correlated between each other in a given repeated game, how they are correlated with behavior at various histories in a given repeated game, and how each aspect is correlated across different repeated games. We also investigate whether two players' aspects from a given repeated game tend to predict the frequency of the cooperatecooperate outcome if these two players are matched to play either the same kind of repeated game or an altogether different repeated game. An important feature of our study is that it addresses the question of crossgame prediction. 
Keywords:  Repeated games, Prisoner's dilemma, Experiment, Cooperation 
JEL:  C92 D03 D70 
Date:  2014–10 
URL:  http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp727&r=gth 
By:  JeanFrançois Caulier (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  Most allocation rules for network games presented in the literature assume that the network structure is fixed. We put explicit emphasis on the construction of networks and examine the dynamic formation of networks whose evolution across time periods is stochastic. Timeseries of networks are studied that describe processes of network formation where links may appear or disappear at any period. Moreover, convergence to an efficient network is not necessarily prescribed. Transitions from one network to another are random and yield a Markov chain. We propose the linkbased allocation rule for such dynamic random network formation processes and provide its axiomatic characterization. By considering a monotone game and a particular (natural) network formation process we recover the linkbased flexible network allocation rule of Jackson. 
Keywords:  Dynamic networks; network game; linkbased allocation rule; Markov chain; characterization 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00881125&r=gth 
By:  Ulrich Faigle (Universität zu Köln  Mathematisches Institut); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  The classical Shapley value is the average marginal contribution of a player, taken over all possible ways to form the grand coalition $N$ when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general coalition formation model where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is only slightly weaker than the original one but allows a much more transparent proof. Moreover, the logical independence of the axioms is exhibited. 
Keywords:  Coalitional game; coalition formation process; Shapley value 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00976923&r=gth 
By:  B. Evci 
Abstract:  Gale and Shapley (1962) proposed that there is a similar game to the marriage problem called "the roommate problem". And, they showed that unlike the marriage problem, the roommate problem may have unstable solutions. In other words, the stability theorem fails for the roommate problem. In this paper, we propose a new mechanism for the roommate problem. The mechanism is successful in determining the reason of instability in our game scenario. And, we show that our mechanism implements the full set of stable matchings in the existence of stability, and it ends up with Pareto Optimal matching in the instance of instability. 
JEL:  C78 D71 D78 
Date:  2014–11 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp975&r=gth 
By:  Ulrich Faigle (Universität zu Köln  Mathematisches Institut); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  The Shapley value is defined as the average marginal contribution of a player, taken over all possible ways to form the grand coalition N when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general model of coalition formation where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is weaker than the one in the original paper but allows a much more transparent correctness proof. Moreover, the logical independence of the axioms is proved. 
Keywords:  Coalitional game; coalition formation process; Shapley value 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00841259&r=gth 
By:  Sylvain Béal (CRESE, Université de FrancheComté); Eric Rémila (Université de SaintEtienne, CNRS UMR 5824 GATE Lyon SaintEtienne); Philippe Solal (Université de SaintEtienne, CNRS UMR 5824 GATE Lyon SaintEtienne) 
Abstract:  We provide a new and concise characterization of the Banzhaf value on the (linear) space of all TUgames on a fixed player set by means of two transparent axioms. The first one is the wellknown Dummy player axiom. The second axiom, called Strong transfer invariance, indicates that a player's payoff is invariant to a transfer of worth between two coalitions he or she belongs to. To prove this result we derive directsum decompositions of the space of all TUgames. We show that, for each player, the space of all TUgames is the direct sum of the subspace of TUgames where this player is dummy and the subspace spanned by the TUgames used to construct the transfers of worth. This decomposition method has several advantages listed as concluding remarks. 
Keywords:  Banzhaf value, Dummy player axiom, Directsum decomposition, Strong Transfer invariance 
JEL:  C71 
Date:  2014–11 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:201405&r=gth 
By:  Herings P.J.J.; Mauleon A.; Vannetelbosch V. (GSBE) 
Abstract:  We provide a tractable concept that can be used to study the influence of the degree of farsightedness on network stability. A set of networks GK is a levelK farsightedly stable set if three conditions are satisfied. First, external deviations should be deterred. Second, from any network outside of GK there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in GK. Third, there is no proper subset of GK satisfying the first two conditions.We show that a levelK farsightedly stable set always exists and we provide a sufficient condition for the uniqueness of a levelK farsightedly stable set. There is a unique level1 farsightedly stable set G1 consisting of all networks that belong to closed cycles. LevelK farsighted stability leads to a refinement of G1 for generic allocation rules. We then provide easy to verify conditions for a set to be levelK farsightedly stable and we consider the relationship between levelK farsighted stability and efficiency of networks. We show the tractability of the concept by applying it to a model of criminal networks. 
Keywords:  Sociology of Economics; Game Theory and Bargaining Theory: General; Production and Organizations: General; 
JEL:  A14 C70 D20 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2014030&r=gth 
By:  Gallier, Carlo; Kesternich, Martin; Sturm, Bodo 
Abstract:  In this experiment, we endogenize the choice of which contribution scheme is implemented in a public goods game. We investigate three rulebased contribution schemes. In a first step, players agree on a common group provision level using the principle of the smallest common denominator. Subsequently, this group investment is allocated according to a specific rule to individual minimum contributions. The game is implemented either as a Single or a MultiPhase Game. In the SinglePhase Game, the contribution schemes are exogenously implemented. In the MultiPhase Game, we let subjects vote on the rulebased contribution schemes. If a scheme obtains a sufficient majority it is implemented. In case no sufficient majority is reached, subjects have to make their contributions to the public good using the voluntary contribution mechanism (VCM). Our results suggest that the endogenous choice of a contribution scheme has an impact on the level of contributions. In case of a rulebased contribution scheme which equalizes payoffs, contributions are higher if subjects choose the scheme than in case the scheme is implemented exogenously. In contrast, contributions are higher if the VCM is implemented exogenously than in case a sufficient majority cannot be obtained and, therefore, subjects have to play the VCM. 
Keywords:  public goods,endogenous institutions,minimum contribution rules,cooperation 
JEL:  C72 C92 H41 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:zbw:zewdip:14056&r=gth 
By:  Nadia Mâagli (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, Università Ca' Foscari Venezia  Calle Larga Foscari); Marco Licalzi (Università Ca' Foscari Venezia  Department of Management) 
Abstract:  Two agents endowed with different individual conceptual spaces are engaged in a dialectic process to reach a common understanding. We model the process as a simple noncooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zerosum structure. When the disagreement is widespread, the zerosum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually agree to associate a region with the same concept end up rebranding it as a different concept. Finally, we document a conversers' dilemma: such equilibrium outcome is Paretodominated by a cooperative solution that avoids retraction. 
Keywords:  Cognitive maps; language differences; semantic bargaining; organisational codes; mental models 
Date:  2014–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01025079&r=gth 
By:  Philippe Bich (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Rida Laraki (Ecole Polytechnique [Palaiseau]  Ecole Polytechnique, IMJ  Institut de Mathématiques de Jussieu  CNRS : UMR7586  Université Pierre et Marie Curie (UPMC)  Paris VI  Université Paris VII  Paris Diderot) 
Abstract:  This paper studies the existence of some known equilibrium solution concepts in a large class of economic models with discontinuous payo functions. The issue is well understood for Nash equilibria, thanks to Reny's betterreply security condition [34], and its recent improvements [3, 25, 35, 36]. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of an approximate equilibrium and of a sharing rule solution in pure and mixed strategies (Simon and Zame [38]). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that in any general equilibrium model with discontinuous preferences, there is a sharing rule solution. 
Keywords:  Discontinuous games, betterreply security, sharing rules, approximate equilibrium, Reny equilibrium, strategic approximation, auctions, timing games, exchange economy 
Date:  2014–10–06 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01071678&r=gth 
By:  Sven Fischer (Max Planck Institute of Economics, Jena, and Max Planck Institute for Research on Collective Goods, Bonn); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); Todd R. Kaplan (University of Exeter, and University of Haifa); Ro'i Zultan (Ben Gurion University of the Negev) 
Abstract:  We study first and secondprice private value auctions with sequential bidding where second movers may discover the first movers bids. There is a unique equilibrium in the firstprice auction and multiple equilibria in the secondprice auction. Consequently, comparative statics across price rules are equivocal. We experimentally find that in the firstprice auction, leaks benefit second movers but harm first movers and sellers. Low to medium probabilities of leak eliminate the usual revenue dominance of firstprice over secondprice auctions. With a high probability of a leak, secondprice auctions generate higher revenue. 
Keywords:  auctions, espionage, collusion, laboratory experiments 
JEL:  C72 C91 D44 
Date:  2014–11–11 
URL:  http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2014027&r=gth 
By:  Ahmet Ozkardas (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  We consider a noncooperative price bargaining model between a monopolistic producer and a monopsonic consumer. The innovative element that our model brings to the existing literature on price negotiation concerns the parties' preferences which are not expressed by constant discount rates, but by sequences of discount factors varying in time. We assume that the sequence of discount rates of a party can be arbitrary, with the only restriction that the infinite series that determines the utility for the given party must be convergent. Under certain parameters, the price negociation model coincides with wage bargaining with the exogenous always strike decision. We determine the unique subgame perfect equilibrium in this model for nodelay strategies independent of the former history of the game. Then we relax the nodelay assumption and determine the highest equilibrium payoff of the seller and the lowest equilibrium payoff of the buyer for the general case. We show that the nodelay equilibrium strategy profiles support these extreme payoffs. 
Keywords:  Price bargaining; alternating offers; varying discount rates; subgame perfect equilibrium 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00881151&r=gth 
By:  Feige, Christian; Ehrhart, KarlMartin; Krämer, Jan 
Abstract:  We introduce a binding unanimous voting rule to a public goods game with an uncertain threshold for the total group contribution. In a laboratory experiment we find that voting generates significantly higher total contributions than making individual voluntary contributions to the public good. Heterogeneity with regard to marginal costs of contribution makes coordination on the threshold value somewhat more di cult when voting, but apparently facilitates coordination when not voting. Homogeneous nonvoting groups instead exhibit a breakdown of contributions commonly observed in linear public goods games, but unusual for a threshold setting. We also notice a preference for payoff symmetry over maximization of expected welfare in heterogeneous voting groups, which to a lesser extent also appears in nonvoting groups. Using a topdown rule, i.e., splitting the voting process into two separate votes on 1) total contribution and 2) individual contributions does not affect these results. 
Keywords:  public good,threshold uncertainty,experimental economics,unanimous voting,committee,heterogeneity 
JEL:  C92 D71 H41 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:zbw:kitwps:60&r=gth 
By:  Manuel Foerster (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, CORE  Center of Operation Research and Econometrics [Louvain]  Université Catholique de Louvain (UCL)  Belgique); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  We study a stochastic model of influence where agents have "yes" or "no" inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modeled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averages are only used to some extent. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like "most" or "at least a few". 
Keywords:  Influence; Anonymity; Ordered weighted averaging operator; Convergence; Consensus; Fuzzy linguistic quantifier 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00913235&r=gth 
By:  Carvalho, JoséRaimundo (Universidade Federal do Ceará); Magnac, Thierry (University of Toulouse I); Xiong, Qizhou (Toulouse School of Economics) 
Abstract:  We evaluate a simple allocation mechanism of students to majors at college entry that was commonly used in universities in Brazil in the 1990s and 2000s. Students first chose a single major and then took exams that select them in or out of the chosen major. The literature analyzing student placement, points out that this decentralized mechanism is not stable and is not strategyproof. This means that some pairs of major & students can be made better off and that students tend to disguise their preferences using such a mechanism. We build up a model of performance and school choices in which expectations are carefully specified and we estimate it using crosssection data reporting choices between two medical schools and grade performances at the entry exams. Given those estimates, we evaluate changes in selection and students' expected utilities when other mechanisms are implemented. Results highlight the importance of strategic motives and redistributive effects of changes of the allocation mechanisms. 
Keywords:  education, twosided matching, school allocation mechanism, policy evaluation 
JEL:  I21 
Date:  2014–10 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp8550&r=gth 
By:  Normann, HansTheo; Rösch, Jürgen; Schultz, Luis Manuel 
Abstract:  We explore whether lawful cooperation in buyer groups facilitates collusion in the product market. Buyer groups purchase inputs more economically. In a repeated game, abandoning the buyer group altogether or excluding single firms constitute credible threats. Hence, in theory, buyer groups facilitate collusion. We run several experimental treatments using threefirm Cournot markets to test these predictions and other effects like how buyer groups affect outcomes when group members can communicate. The experimental results show that buyer groups lead to lower outputs when groups can exclude single firms. Communication is often abused for explicit agreements and this strongly reduces competition. 
Keywords:  buyer groups,cartels,collusion,communication,experiments,repeated games 
JEL:  C7 C9 L4 L41 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:zbw:dicedp:74r&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 present a theory of targeted search, where people with a finite information processing capacity search for a match. Our theory explicitly accounts for both the quantity and the quality of matches. It delivers a unique equilibrium that resides in between the random matching and the directed search outcomes. The equilibrium that emerges from this middle ground is inefficient relative to the constrained Pareto allocation. Our theory encompasses the outcomes of the random matching and the directed search literature as limiting cases. 
Keywords:  Matching; assignment; search; efficiency; information 
JEL:  C78 D83 E24 J64 
Date:  2013–08–23 
URL:  http://d.repec.org/n?u=RePEc:fip:fedlwp:2014035&r=gth 
By:  Georg, CoPierre 
Abstract:  When banks choose similar investment strategies, the financial system becomes vulnerable to common shocks. Banks decide about their investment strategy exante based on a private belief about the state of the world and a social belief formed from observing the actions of peers. When the social belief is strong and the financial network is fragmented, banks follow their peers and their investment strategies synchronize. This effect is stronger for less informative private signals. For endogenously formed interbank networks, however, less informative signals lead to higher network density and less synchronization. It is shown that the former effect dominates the latter. 
Keywords:  social learning,endogenous financial networks,multiagent simulations,systemic risk 
JEL:  G21 C73 D53 D85 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:zbw:bubdps:232014&r=gth 
By:  Gächter, Simon (University of Nottingham); Mengel, Friederike (University of Essex); Tsakas, Elias (Maastricht University); Vostroknutov, Alexander (Maastricht University) 
Abstract:  In a novel experimental design we study public good games with dynamic interdependencies. Each agent's income at the end of a period serves as her endowment in the following period. In this setting growth and inequality arise endogenously allowing us to address new questions regarding their interplay and effect on cooperation levels. In stark contrast to standard public good experiments, we find that contributions are increasing over time even in the absence of punishment possibilities. Inequality and group income are positively correlated for poor groups, but negatively correlated for rich groups. There is very strong path dependence: inequality in early periods is strongly negatively correlated with group income in later periods. These results give new insights into why people cooperate and should make us rethink previous results from the literature on repeated public good games regarding the decay of cooperation in the absence of punishment. 
Keywords:  public goods, inequality, growth 
JEL:  C92 H41 D63 
Date:  2014–09 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp8504&r=gth 