
on Game Theory 
By:  Herings P. JeanJacques; Predtetchinski Arkadi (METEOR) 
Abstract:  This note reexamines the connection between the asymmetric Nash bargaining solution and the equilibria of strategic bargaining games. Several papers in the literature obtain the asymmetric Nash bargaining solution as the unique limit of subgame perfect equilibria in stationary strategies when the breakdown probability approaches zero. This note illustrates by means of two examples that this result depends crucially on the differentiability of the boundary of the set of feasible payoffs. In the first example the game has a unique stationary subgame perfect equilibrium that fails to converge to the asymmetric Nash bargaining solution. In the second example the game has two stationary subgame perfect equilibria that converge to two distinct limits as the breakdown probability vanishes. This example demonstrates that without differentiability of the set of feasible payoffs there is not even asymptotic uniqueness of stationary equilibria in the bargaining model. 
Keywords:  microeconomics ; 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:umamet:2010010&r=gth 
By:  Pedro Calleja; Carles Rafels; Stef Tijs (Universitat de Barcelona) 
Abstract:  We characterize singlevalued solutions of transferable utility cooperative games satisfying core selection and aggregate monotonicity. Fur thermore, we show that these two properties are compatible with individual rationality, the dummy player property and the symmetry property. We nish characterizing singlevalued solutions satisfying these ve properties. 
Keywords:  core, cooperative games, symmetry, individual rationality, dummy player, aggregate monotonicity 
JEL:  C71 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:bar:bedcje:2010237&r=gth 
By:  Bozbay Irem; Dietrich Franz; Peters Hans (METEOR) 
Abstract:  Following Vartiainen (2007) we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome as well as a disagreement outcome: the interpretation is that the latter results if the compromise outcome is not accepted. For this framework we propose and study an extension of the classical KalaiSmorodinsky bargaining solution. We present a characterization with an axiom of Independence ofNonUtopia Information as the main condition. 
Keywords:  mathematical economics; 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:umamet:2010008&r=gth 
By:  GRANDJEAN, Gilles (UniversitŽ catholique de Louvain, CORE, B1348 LouvainlaNeuve, Belgium); MAULEON, Ana (FNRS and UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); VANNETELBOSCH, Vincent (FNRS and UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)) 
Abstract:  Curb sets [Basu and Weibull, Econ. Letters 36 (1991), 141146] are product sets of pure strategies containing all individual bestresponses against beliefs restricted to the recommendations to the remaining players. The concept of minimal curb sets is a settheoretic coarsening of the notion of strict Nash equilibrium. We introduce the concept of minimal strong curb sets which is a settheoretic coarsening of the notion of strong Nash equilibrium. Strong curb sets are product sets of pure strategies such that each player's set of recommended strategies must contain all coalitional bestresponses of each coalition to whatever belief each coalition member may have that is consistent with the recommendations to the other players. Minimal strong curb sets are shown to exist and are compared with other well known solution concepts. We also provide a dynamic learning process leading the players to playing strategies from a minimal strong curb set. 
Keywords:  setvalued solution concept, coalitional bestresponse, strong curb set, learning 
JEL:  C72 
Date:  2009–11–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009066&r=gth 
By:  UNO, Hiroshi (UniversitŽ catholique de Louvain, CORE, B1348 LouvainlaNeuve, Belgium) 
Abstract:  This note shows that every finite game of strategic complementarities is a nested pseudopotential game defined in Uno (2007, Economics Bulletin 3 (17)) if the action set of each player is onedimensional, except possibly for one player 
Keywords:  Strategic complementarities, potential games, existence of a pure strategy Nash equilibrium 
JEL:  C72 
Date:  2009–12–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009080&r=gth 
By:  DEHEZ, Pierre (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)) 
Keywords:  cost allocation, Shapley value, fixed cost 
JEL:  C71 D46 
Date:  2009–05–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009035&r=gth 
By:  Yves Breitmoser (Department of Economics, EUV Frankfurt (Oder), Germany); Jonathan H.W. Tan (Nottingham University Business School, UK; University of East Anglia, School of Economics, Norwich, UK) 
Abstract:  This paper studies the relevance of equilibrium and nonequilibrium explanations of behavior, with respects to equilibrium refinement, as players gain experience. We investigate this experimentally using an incomplete information sequential move game with heterogeneous preferences and multiple perfect equilibria. Only the limit point of quantal response (the limiting logit equilibrium), and alternatively that of levelk reasoning (extensive form rationalizability), restricts beliefs off the equilibrium path. Both concepts converge to the same unique equilibrium, but the predictions differ prior to convergence. We show that with experience of repeated play in relatively constant environments, subjects approach equilibrium via the quantal response learning path. With experience spanning also across relatively novel environments, though, levelk reasoning tends to dominate. 
Keywords:  Incomplete information, equilibrium refinement, logit equilibrium, rationalizability, quantal response, levelk, inequity aversion, experiment. 
JEL:  C72 C91 D62 
Date:  2009–03–17 
URL:  http://d.repec.org/n?u=RePEc:bbr:workpa:9&r=gth 
By:  Lovo, Stefano; Calcagno, Ricardo 
Abstract:  In this paper, the authors introduce a form of preplay communication that we call "preopening". During the preopening, players announce their tentative actions to be played in the underlying game. Announcements are made using a posting system which is subject to stochastic failures. Posted actions are publicly observable and players payo¤s only depend on the opening outcome, i.e. the action pro…le that is posted at the end of the preopening phase. We show that when the posting failures hit players idiosyncratically all equilibria of the preopening game lead to the same opening outcome that corresponds to the most "sensible" pure Nash equilibrium of the underlying game. By contrast preopening does not operate an equilibrium selection when posting failure hits players simultaneously. 
Keywords:  Preopening; equilibrium selection; bargaining; cheap talk 
JEL:  C72 C73 C78 G10 
Date:  2010–02–16 
URL:  http://d.repec.org/n?u=RePEc:ebg:heccah:0927&r=gth 
By:  GANDJEAN, Gilles; MAULEON, Ana (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); VANNETELBOSCH, Vincent (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)) 
Keywords:  farsighted players, stability, efficiency, connections model, buyerseller networks 
JEL:  A14 C70 D20 
Date:  2009–05–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009031&r=gth 
By:  Wang, Yafeng; Graham , Brett 
Abstract:  We propose a dataconstrained generalized maximum entropy (GME) estimator for discrete sequential move games of perfect information which can be easily implemented on optimization software with highlevel interfaces such as GAMS. Unlike most other work on the estimation of complete information games, the method we proposed is data constrained and does not require simulation and normal distribution of random preference shocks. We formulate the GME estimation as a (convex) mixedinteger nonlinear optimization problem (MINLP) which is well developed over the last few years. The model is identified with only weak scale and location normalizations, monte carlo evidence demonstrates that the estimator can perform well in moderately size samples. As an application, we study the social security acceptance decisions in dual career households. 
Keywords:  GameTheoretic Econometric Models; SequentialMove Game; Generalized Maximum Entropy; MixedInteger Nonlinear Programming 
JEL:  C13 C01 
Date:  2009–12–20 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:21331&r=gth 
By:  GERMAIN, Marc; TULKENS, Henry (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); MAGNUS, Alphonse 
Keywords:  stock pollutant, capital accumulation, international environmental agreements, dynamic core solution 
JEL:  Q54 Q58 F42 F53 O21 
Date:  2009–04–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009021&r=gth 
By:  George J. Mailath; Andrew Postlewaite; Larry Samuelson 
Date:  2010–03–17 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:661465000000000011&r=gth 
By:  Joseph Abdou (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  We study the structure of unstable local effectivity functions defined for n players and p alternatives. A stability index based on the notion of cycle is introduced. In the particular case of simple games, the stability index is closely related to the Nakamura Number. In general it may be any integer between 2 and p. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3. 
Keywords:  Stability Index ; Acyclicity ; Strong Nash Equilibrium ; Core ; Solvability ; Consistency ; Simple Game ; Effectivity Function 
Date:  2009–10–09 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00389003_v1&r=gth 
By:  Andersson, Ola (Dept. of Economics, Stockholm School of Economics); Wengström, Erik (Department of Economics, University of Copenhagen) 
Abstract:  This paper extends the concept of weak renegotiationproof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique purestrategy WRP equilibrium without renegotiation costs, which implies marginalcost pricing in every period. Moreover, in comparison to the findings of McCutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion. 
Keywords:  Noncooperative game theory; Weak Renegotiationproofness; Costly Renegotation; Repeated Bertrand games 
JEL:  C72 D43 
Date:  2010–03–22 
URL:  http://d.repec.org/n?u=RePEc:hhs:hastef:0725&r=gth 
By:  Herings P. JeanJacques; Houba Harold (METEOR) 
Abstract:  We analyze the simplest Condorcet cycle with three players and three alternatives within a strategic bargaining model with recognition probabilities and costless delay. Mixed consistent subgame perfect equilibria exist whenever the geometric mean of the agents'' risk coefficients, ratios of utility differences between alternatives, is at most one. Equilibria are generically unique, Pareto efficient, and ensure agreement within finite expected time. Agents propose best or secondbest alternatives. Agents accept best alternatives, may reject secondbest alternatives with positive probability, and reject otherwise. For symmetric recognition probabilities and risk coefficients below one, agreement is immediate and each agent proposes his best alternative. 
Keywords:  public economics ; 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:umamet:2010009&r=gth 
By:  ALCALDEUNZU, Jorge (Department of Applied Economics IV (Mathematics), UPVEHU. Bilbao, Spain); MOLIS, Elena (FacultŽs Universitaires SaintLouis, CEREC, Bruxelles ; UniversitŽ Catholique de Louvain, CORE, LouvainlaNeuve) 
Abstract:  There is a wide range of economic problems involving the exchange of indivisible goods without monetary transfers, starting from the housing market model of the seminal paper of Shapley and Scarf [10] and including other problems like the kidney exchange or the school choice problems. For many of these models, the classical solution is the application of an algorithm/mechanism called Top Trading Cycles, attributed to David Gale, which satisÞes good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, that generalizes the Top Trading Cycles for the general case in which individuals can report indifferences, and preserves all its desirable properties. 
Keywords:  housing market, indifferences, top trading cycles, absorbing sets 
JEL:  C71 C78 D71 D78 
Date:  2009–10–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009062&r=gth 
By:  MARINUCCI, Marco (UniversitŽ catholique de Louvain, CORE, B1348 LouvainlaNeuve, Belgium); VERGOTE, Wouter (FacultŽs universitaires SaintLouis, CEREC, B1000 Bruxelles, Belgium and UniversitŽ catholique de Louvain, CORE, B1348 LouvainlaNeuve, Belgium) 
Abstract:  In a setting of R&D coopetition we study, by using an allpay auction approach, how collaboration affects strategic decisions during a patent contest, and how the latter influences the possible collaboration network structures the firms can hope to form. The all pay auction approach allows us to 1) endogenize both network formation and R&D intensities and 2) take heterogeneous and private valuations for patents into account. We find that, different from previous literature, the complete network is not always the only pairwise stable network, even and especially if the benefits from cooperating are important. Interestingly, the other possible stable networks all have the realistic property that some firms decide not to participate in the contest. Thus, weak cooperation through network formation can serve as a barrier to entry on the market for innovation. We further show that there need not be any network that survives a well known refinement of pairwise stability, strong stability, which imposes networks to be immune to coalitional deviations. 
Keywords:  patent game, networks, R&D cooperation, allpay auction 
JEL:  L14 L24 O32 
Date:  2009–11–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009068&r=gth 
By:  Tomala, Tristan; Renou, Ludovic 
Abstract:  This paper studies a mechanism design model where the players and the designer are nodes in a communication network. The authors characterize the communication networks (directed graphs) for which, in any environment (utilities and beliefs), every incentive compatible social choice function is implementable. They show that any incentive compatible social choice function is implementable on a given communication network, in all environments with either common independent beliefs and private values or a worst outcome, if and only if the network is strongly connected and weakly 2connected. A network is strongly connected if for each player, there exists a directed path to the designer. It is weakly 2connected if each player is either directly connected to the designer or indirectly connected to the designer through two disjoint paths, not necessarily directed. They couple encryption techniques together with appropriate incentives to secure the transmission of each player’s private information to the designer. 
Keywords:  Mechanism design; incentives; Bayesian equilibrium; communication networks; encryption; secure transmission 
JEL:  C72 D82 
Date:  2010–01–05 
URL:  http://d.repec.org/n?u=RePEc:ebg:heccah:0926&r=gth 
By:  GOERTZ, Johanna M.; MANIQUET, Franois (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)) 
Keywords:  efficient information aggregation, scoring rules, Poisson games, approval voting 
JEL:  C72 D72 D81 D82 
Date:  2009–04–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2009026&r=gth 