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on Game Theory |
| By: | René van den Brink (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Valeri Vasil'ev (Sobolev Institute of Mathematics, Russia) |
| Abstract: | Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems, such as river games, queueing games and auction games, the game is totally positive (i.e., all dividends are nonnegative), and there is some hierarchical ordering of the players. In this paper we introduce the 'Restricted Core' for such 'games with ordered players' which is based on the distribution of 'dividends' taking into account the hierarchical ordering of the players. For totally positive games this solution is always contained in the 'Core', and contains the well-known 'Shapley value' (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions). For special orderings it equals the Core, respectively Shapley value. We provide an axiomatization and apply this solution to river games. |
| Keywords: | Totally positive TU-game, Harsanyi dividends, Core, Shapley value, Harsanyi set, Selectope, Digraph, River game |
| JEL: | C71 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20090038&r=gth |
| By: | Arantza Estévez-Fernández (VU University Amsterdam); Peter Borm (Tilburg University, the Netherlands); M. Gloria Fiestras-Janeiro (Universidade de Vigo, Spain) |
| Abstract: | In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalitional merge convex and ordinal convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the NTU-adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games. |
| Keywords: | NTU-bankruptcy problem, NTU-bankruptcy game, Coalitional merge convexity, Ordinal convexity, Compromise stability, Core cover, Adjusted proportional rule |
| JEL: | C71 |
| Date: | 2014–03–04 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140030&r=gth |
| By: | René van den Brink (VU University Amsterdam); Chris Dietz (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam, the Netherlands); Genjiu Xu (Northwestern Polytechnical University, Xi'an, Shaanxi, P.R. China) |
| Abstract: | There is an extensive literature that studies situations of restricted cooperation in cooperative games. Myerson (1979) introduced communication graph games, where players can only cooperate if they are connected in an undirected graph representing the communication possibilities. The Myerson value is obtained by taking the Shapley value of the corresponding restricted game. For cycle-free connected graphs, Demange (2004) introduced for each player the corresponding hierarchical outcome, being the marginal contribution vector for a particular permutation of the player set induced by the graph. Gilles, Owen and van den Brink (1992) introduced games with a (hierarchical) permission structure modeled by a directed graph on the set of players. In the conjunctive (disjunctive) approach, a coalition is said to be feasible, if for every player in the coalition also all (at least one of) its predecessors (if any) belong(s) to the coalition. The conjunctive (disjunctive) permission value is obtained by taking the Shapley value of the associated conjunctive (disjunctive) restricted game. The two approaches coincide when the permission structure is a rooted tree. In this paper we consider games with a hierarchical permission structure given by a rooted tree and modify the Myerson value to a value for such games. We also consider for these games the hierarchical outcome with respect to the root of the tree (top player), along with a new solution that assigns all payoff to the unique top player in the hierarchy. Then comparable characterizations are given of these three solutions and the (conjunctive) permission value. |
| Keywords: | Cooperative TU-game, rooted tree, Myerson value, hierarchical outcome, permission value, axiomatization |
| JEL: | C71 |
| Date: | 2015–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150021&r=gth |
| By: | Estela Sánchez-Rodríguez (Vigo University, Spain); Peter Borm (CentER, University of Tilburg, the Netherlands); Arantza Estévez-Fernández (VU University Amsterdam); M. Gloria Fiestras-Janeiro (Vigo University, Spain); Manuel A. Mosquera (Vigo University, Spain) |
| Abstract: | This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the k-core cover as an extension of the core cover. The k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set N coincides with the ⌊|N |/2⌋-core cover. Furthermore, full characteriz ations of games for which a k-core cover is nonempty and for which a k-core cover coincides with the core are provided. |
| Keywords: | Core, core cover, k-core cover, k-compromise admissibility, k-compromise stability, assignment games |
| JEL: | C71 |
| Date: | 2013–10–24 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130177&r=gth |
| By: | Encarnación Algaba (Escuela Técnica Superior de Ingenierá, Sevilla, Spain); Rene van den Brink (VU University Amsterdam); Chris Dietz (VU University Amsterdam) |
| Abstract: | Agents participating in different kind of organizations, usually take different positions in some relational structure. The aim of this paper is to introduce a new framework taking into account both communication and hierachical features derived from this participation. In fact, this new set or network structure unifies and generalizes well-known models from the literature, such as communication networks and hierarchies. We introduce and analyze accessible union stable systems where union stability reflects the communication network and accessibility describes the hierarchy. Particular cases of these new structures are the sets of connected coalitions in a communication graph, antimatroids (and therefore also sets of feasible coalitions in permission structures) and augmenting systems which have numerous applications in the literature. We give special attention to th e class of cycle-free accessible union stable systems. We also consider cooperative games with restricted cooperation where the set of feasible coalitions is an accessible union stable system, and provide an axiomatization of an extension of the Shapley value to this class of games. |
| Keywords: | union stable system, accessibility, cooperative TU-game, Shapley value |
| JEL: | C71 |
| Date: | 2013–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130207&r=gth |
| By: | Encarnacion Algaba (University of Seville, Spain); René van den Brink (VU University Amsterdam, the Netherlands); Chris Dietz (VU University Amsterdam, the Netherlands) |
| Abstract: | In the literature, there exist several models where a cooperative TU-game is enriched with a hierarchical structure on the player set that is represented by a digraph. We consider games under precedence constraints introduced by Faigle and Kern (1992) who also introduce a generalization of the Shapley value for such games. They characterized this solution by efficiency, linearity, the null player property and hierarchical strength which states that in unanimity games the payoffs are allocated among the players in the unanimity coalition proportional to their hierarchical strength in the corresponding coalition. The hierarchical strength of a player in a coalition in an acyclic digraph is the number of admissible permutations (those in which successors in the digraph enter before predecessors) where this player is the last of that coalition to enter. We introduce and axiomatize a new solution for games under precedence constraints, called hierarchical solution. Unlike the precedence Shapley value, this new solution satisfies the desirable axiom of irrelevant player independence meaning that payoffs assigned to relevant players are not affected by the presence of irrelevant players. This hierarchical solution is defined in a similar spirit as the precedence Shapley value but is a precedence power solution, and thus allocates the dividend of a coalition proportionally to a power measure for acyclic digraphs, specifically proportionally to the hierarchical measure. We give an axiomatization of this measure and extend it to regular set systems. Finally, we consider the normalized hierarchical measure on the subclasses of forests and sink. |
| Keywords: | Cooperative TU-game, acyclic digraph, hierarchical strength, irrelevant player, power measure, regular set system, rooted and sink trees |
| JEL: | C71 |
| Date: | 2015–01–16 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150007&r=gth |
| By: | Luís Carvalho |
| Abstract: | The best known equilibrium strategies of multiplayer bargaining dene that the agreement is established at the rst moment. In this paper two new subgame perfect Nash equilibria strategies are proposed, one in which the agreement moment is delayed for T > 1 periods and one other in which the bargaining proposals proceed endlessly. |
| Keywords: | Multiplayer Bargaining |
| JEL: | C72 C78 |
| Date: | 2015–04–20 |
| URL: | http://d.repec.org/n?u=RePEc:isc:iscwp2:bruwp1503&r=gth |
| By: | Maurice Koster (University of Amsterdam); Sascha Kurz (University of Bayreuth, Germany); Ines Lindner (VU University Amsterdam); Stefan Napel (University of Bayreuth, Germany) |
| Abstract: | We introduce the prediction value (PV) as a measure of players’ informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player i’s prediction value equals the difference between the conditional expectations of v(S) when i cooperates or not. We characterize the prediction value as a special member of the class of (extended) values which satisfy anonymity, linearity and a consistency property. Every n-player binomial semivalue coincides with the PV for a particular family of probability distributions over coalitions. The PV can thus be regarded as a power index in specific cases. Conversely, some semivalues – including the Banzhaf but not the Shapley value – can be interpreted in terms of informational importance. |
| Keywords: | influence, voting games, cooperative games, Banzhaf value, Shapley value |
| JEL: | C71 D71 D72 |
| Date: | 2013–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130188&r=gth |
| By: | Oddvar M. Kaarbøe (University of Bergen); Alexander F. Tieman (Vrije Universiteit Amsterdam) |
| Abstract: | We apply the stochastic evolutionary approach of equilibrium selection tomacroeconomic models in which a complementarity at the macro level ispresent. These models often exhibit multiple Pareto-ranked Nash equilibria,and the best response-correspondence of an individual increases with ameasure of the aggregate state of the economy. Our main theoretical resultshows how the equilibrium that is singled out by the evolutionary dynamicsis directly related to the underlying externality that creates themultiplicity problem in the underlying macroeconomic stage game. We alsoprovide clarifying examples from the macroeconomic literature. |
| JEL: | C63 C72 C73 E19 L16 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:19990096&r=gth |
| By: | Boris van Leeuwen (University of Amsterdam); Theo Offerman (University of Amsterdam); Arthur Schram (University of Amsterdam) |
| Abstract: | We investigate contributions to the provision of public goods on a network when efficient provision requires the formation of a star network. We provide a theoretical analysis and study behavior in a controlled laboratory experiment. In a 2x2 design, we examine the effects of group size and the presence of (social) benefits for incoming links. We find that social benefits are highly important. They facilitate convergence to equilibrium networks and enhance the stability and efficiency of the outcome. Moreover, in large groups social benefits encourage the formation of superstars: star networks in which the core contributes more than expected in the stage-game equilibrium. We show that this result is predicted by a repeated game equilibrium. |
| Keywords: | Network formation, networked public goods, peer production, social benefits, open source software |
| JEL: | C91 D85 H41 |
| Date: | 2013–08–08 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130112&r=gth |
| By: | Emiliya Lazarova (University of East Anglia, United Kingdom); Peter Borm (Tilburg University, the Netherlands); Arantza Estévez-Fernández (VU University Amsterdam, the Netherlands) |
| Abstract: | In this paper we consider one-to-many matching problems where the preferences of the agents involved are represented by monetary reward functions. We characterize Pareto optimal matchings by means of contractually exchange stability and matchings of maximum total reward by means of compensation exchange stability. To conclude, we show that in going from an initial matching to a matching of maximum total reward, one can always provide a compensation schedule that will be ex-post stable in the sense that there will be no subset of agents who can all by deviation obtain a higher reward. The proof of this result uses the fact that the core of an associated compensation matching game with constraints is nonempty. |
| Keywords: | matching, Pareto optimal matching, contractually exchange stability, compensation stability, compensation schedule |
| JEL: | C78 C71 D60 |
| Date: | 2014–07–08 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140086&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Youngsub Chun (Seoul National University, Korea); Yuan Ju (University of York, United Kingdom) |
| Abstract: | This discussion paper resulted in a publication in the 'Journal of Economic Theory', 2014, 153, 33-45.<P> Complementary to the axiomatic and mechanism design studies on queueing problems, this paper proposes a strategic bargaining approach to resolve queueing conflicts. Given a situation where players with different waiting costs have to form a queue in order to be served, they firstly compete with each other for a specific position in the queue. Then, the winner can decide to take up the position or sell it to the others. In the former case, the rest of the players will proceed to compete for the remaining positions in the same manner; whereas for the latter case the seller can propose a queue with corresponding payments to the others which can be accepted or rejected. Depending on which position players are going to compete for, the subgame perfect equilibrium outcome of the corresponding mechanism coincides with one of the two best known rules for queueing problems, t he maximal and the minimal transfer rules, while an efficient queue is always formed in equilibrium. The analysis discovers a striking relationship between pessimism and optimism in this type of decision making. |
| Keywords: | Queueing problem, minimal transfer rule, maximal transfer rule, Shapley value, bidding mechanism, implementation, Queuing problem |
| JEL: | C71 C72 D60 |
| Date: | 2014–01–28 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140016&r=gth |
| By: | Bezalel Peleg; Peter Sudholter |
| Abstract: | We show that the Aumann-Davis-Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex. |
| Keywords: | NTU game, Convex game, Bargaining set |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp681&r=gth |
| By: | Adrian de Groot Ruiz (Radboud University Nijmegen, the Netherlands); Theo Offerman (Amsterdam School of Economics, University of Amsterdam, the Netherlands); Sander Onderstal (Amsterdam School of Economics, University of Amsterdam, the Netherlands) |
| Abstract: | In the past, many refinements have been proposed to select equilibria in cheap talk games. Usually, these refinements were motivated by a discussion of how rational agents would reason in some particular cheap talk games. In this paper, we propose a new refinement and stability measure that is intended to predict actual behavior in a wide range of cheap talk games. According to our Average Credible Deviation Criterion (ACDC), the stability of an equilibrium is determined by the frequency and size of credible deviations. ACDC organizes the results from several cheap talk experiments in which behavior converged to equilibrium, even in cases where other criteria do not make a prediction. |
| Keywords: | Cheap talk, Neologism proofness, Credible deviation, Refinement, ACDC, Experiment |
| JEL: | C72 C92 D82 D83 |
| Date: | 2015–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150012&r=gth |
| By: | P. Jean-Jacques Herings (Maastricht University, the Netherlands); Harold Houba (VU University Amsterdam, the Netherlands) |
| Abstract: | We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions are necessary for SSPE but insufficient because these equations can be singular. Strategy profiles excluding perpetual disagreement guarantee non-singularity. The necessary and sufficient conditions for existence of stationary best responses additionally require either an equalizing condition or a minimality condition. Quasi SSPE only satisfy the recursive equations and optimality conditions. These always exist and are SSPE if either all equalizing conditions or all minimality conditions hold. |
| Keywords: | Bargaining, existence, one-stage-deviation principle, dynamic programming, recursive equations, Markov Decision Theory |
| JEL: | C72 C73 C78 |
| Date: | 2015–01–22 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150010&r=gth |
| By: | Erik Ansink (VU University Amsterdam); Harold Houba (VU University Amsterdam) |
| Abstract: | We survey the economics of transboundary river water allocation, which emerged in the 1960s and has matured over the last decade due to increasing concerns over water scarcity and pollution. We outline the major approaches and pay specific attention to the strategic aspects of transboundary river water allocation. These strategic aspects are captured by employing game theory to assess the economics of transboundary river water allocation in a simple model of river sharing. This model allows us to show how conflict and cooperation over transboundary water resources may occur. It also allows us to pay specific attention to the efficiency, sustainability, and fairness of solutions to this model. We compare and contrast both cooperative and non-cooperative approaches and we relate their solutions to illustrative examples. |
| Keywords: | River sharing problem, River claims problem, Fairness, Efficiency, Sustainability, Water allocation agreement, Bargaining, Water trade, Sharing rules, Axiomatic approach |
| JEL: | C71 C73 D63 D74 F53 Q25 |
| Date: | 2014–10–06 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140132&r=gth |
| By: | René van den Brink (VU University Amsterdam); Enrique González-Aranguena (Universidad Complutense de Madrid, Spain); Conrado Manuel (Universidad Complutense de Madrid, Spain); Mónica del Pozo (Universidad Carlos III de Madrid, Spain) |
| Abstract: | This discussion paper resulted in a publication in the 'European Journal of Operational Research', 2014, 238, 786-796.<P> Generalized characteristic functions extend characteristic functions of 'classical' TU-games by assigning a real number to every ordered coalition being a permutation of any subset of the player set. Such generalized characteristic functions can be applied when the earnings or costs of cooperation among a set of players depends on the order in which the players enter a coalition. In the literature, the two main solutions for generalized characteristic functions are the one of Nowak and Radzik (1994), shortly called NR-value, and the one introduced by Sanchez and Bergantinos (1997), shortly called SB-value. In this paper, we introduce the axiom of <I> order monotonicity</I> with respect to the order of the players in a unanimity coalition, requiring that players who enter earlier should get not more in the corresponding (ordered) unanimity game than players who enter later. We propose several classes of order monotonic solutions for generalized characteristic functions that contain the NR-value and SB-value as special (extreme) cases. We also provide axiomatizations of these classes. |
| Keywords: | Cooperative TU-game, generalized characteristic function, order monotonicity |
| JEL: | C71 |
| Date: | 2013–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130093&r=gth |
| By: | De Luca, Giacomo; Sekeris, Petros; Spengler, Dominic |
| Abstract: | While folk theorems for dynamic renewable common pool resource games sustain cooperation as an equilibrium, the possibility of reverting to violence to appropriate the resource destroys the incentives to cooperate, because of the expectation of conflict when resources are sufficiently depleted. In this paper, we provide experimental evidence that individuals behave according to the theoretical predictions. For high stocks of resources, when conflict is a highly costly activity, participants cooperate less than in the control group, and they play the non-cooperative action with higher frequency. This comes as a consequence of the (correct) anticipation that, when resources run low, the conflict option is used by a large share of participants. |
| Keywords: | Experiment, Dynamic Game, Cooperation |
| JEL: | C72 C73 C91 D74 |
| Date: | 2015–04–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:63697&r=gth |
| By: | Jia-Ping Huang (VU University Amsterdam); Maurice Koster (University of Amsterdam); Ines Lindner (VU University Amsterdam) |
| Abstract: | The novelty of our model is to combine models of collective action on networks with models of social learning. Agents are connected according to an undirected graph, the social network, and have the choice between two actions: either to adopt a new behavior or technology or stay with the default behavior. The individual believed return depends on how many neighbors an agent has, how many of those neighbors already adopted the new behavior and some agent-specic cost-benefit parameter. There are four main insights of our model: (1) A variety of collective adoption behaviors is determined by the network. (2) Average inclination governs collective adoption behavior. (3) Initial inclinations determine the critical mass of adoption which ensures the new behavior to prevail. (4) Equilibria and dynamic be- havior changes as we change the underlying network and other parameters. Given the complexity of the system we use a standard technique for estimating the solution. |
| Keywords: | Diffusion, Social Networks, Social Learning, Tipping, Technology Adoption |
| JEL: | C72 C73 D83 D85 O33 |
| Date: | 2013–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130208&r=gth |
| By: | Harold Houba (VU University Amsterdam); Erik Ansink (VU University Amsterdam) |
| Abstract: | Many water allocation agreements in transboundary river basins are inherently unstable. Due to stochastic river flow, agreements may be broken in case of drought. The objective of this paper is to analyze whether water allocation agreements can be self-enforcing, or sustainable. We do so using an infinitely-repeated sequential game that we apply to several classes of agreements.To derive our main results we apply the Folk Theorem to the river sharing problem using the equilibrium concepts of subgame-perfect equilibrium and renegotiation-proof equilibrium. We show that, given the upstream-downstream asymmetry, sustainable agreements allow downstream agents to reap the larger share of the benefits of cooperation. |
| Keywords: | river sharing, sustainable agreements, repeated sequential game, Folk Theorem, water allocation, renegotiation-proofness |
| JEL: | C73 D74 F53 Q25 |
| Date: | 2013–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130182&r=gth |
| By: | Daan in 't Veld (University of Amsterdam); Marco van der Leij (University of Amsterdam, and De Nederlandsche Bank, the Netherlands); Cars Hommes (University of Amsterdam, the Netherlands) |
| Abstract: | Recent empirical evidence suggests that financial networks exhibit a core periphery network structure. This paper aims at giving an economic explanation for the emergence of such a structure using network formation theory. Focusing on intermediation benefits, we find that a core periphery network cannot be unilaterally stable when agents are homogeneous. The best-response dynamics converge to a unique unilaterally stable outcome ranging from an empty to denser networks as the costs of linking decrease. A core periphery network structure can form endogenously, however, if we allow for heterogeneity among agents in size. We show that our model can reproduce the observed core periphery structure in the Dutch interbank market for reasonable parameter values. |
| Keywords: | financial networks, core periphery structure, network formation models |
| JEL: | D85 G21 L14 |
| Date: | 2014–07–28 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140098&r=gth |
| By: | Harold Houba (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Yuyu Zeng (VU University Amsterdam) |
| Abstract: | This discussion paper led to a publication in <A href="http://link.springer.com/article/10.1007/s10640-014-9862-0">Environmental and Resource Economics</A> (forthcoming).<P> We study coalition formation and the strategic timing of membership of an IEA for environmental issues in the Coalitional Bargaining Game (CBG) of Gomes 2005, Econometrica). For the general CBG, we derive the necessary and sufficient condition for immediate formation of the grand coalition. We apply the CBG to a river sharing problem with two symmetric upstream agents and one downstream agent. Taking the discount factor and a productivity variable of water as parameters, we identify five regions in the parameter space. First, there is a region in which the grand coalition always forms immediately. Second, there are two regions in which there is for sure gradual coalition formation, in one of these regions there is a positive probability that the upstream agents form a monopoly. Third, there are two regions in which the grand coalition forms immediately with positive probability, but also gradual coalition formation might occur with positive probability. |
| Keywords: | Coalitional Bargaining Game, International Environmental Agreements, River Sharing Problems, Markov Perfect Equilibrium, Efficiency, Monopoly |
| JEL: | C78 Q25 |
| Date: | 2013–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130157&r=gth |
| By: | Elon Kohlberg; Abraham Neyman |
| Abstract: | Building on the work of Nash, Harsanyi, and Shapley, we define a cooperative solution for strategic games that takes account of both the competitive and the cooperative aspects of such games. We prove existence in the general (NTU) case and uniqueness in the TU case. Our main result is an extension of the definition and the existence and uniqueness theorems to stochastic games - discounted or undiscounted. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp679&r=gth |
| By: | Erik Ansink (VU University Amsterdam, the Netherlands); Cees Withagen (VU University Amsterdam, the Netherlands) |
| Abstract: | We augment the standard cartel formation game from non-cooperative coalition theory, often applied in the context of international environmental agreements on climate change, with the possibility that singletons support coalition formation without becoming coalition members themselves. Rather, their support takes the form of a monetary transfer to the coalition, which increases the members' payoffs, and thereby provides an incentive for other singletons to join the coalition. We show that, under mild conditions on the costs and benefits of contributing to the public good (i.e. abatement of CO<SUB>2</SUB> emissions), supporters exist in equilibrium. The existence of supporters increases the size of stable coalitions, increases abatement of CO<SUB>2</SUB> emissions, and increases payoffs to each of four types of agents: members, joiners, free-riders, and supporters. Importantly, this result does not require commitment. |
| Keywords: | Coalition formation; Public goods; Support; Transfers; International Environmental Agreements |
| JEL: | C72 D02 |
| Date: | 2015–01–27 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150015&r=gth |
| By: | Erik Ansink (VU University Amsterdam, the Netherlands); Michael Gengenbach (Wageningen University, the Netherlands); Hans-Peter Weikard (Wageningen University, the Netherlands) |
| Abstract: | We analyse river sharing games in which a set of agents located along a river shares the available water. Using coalition theory, we find that the potential benefits of water trade may not be sufficient to make all agents in the river cooperate and acknowledge property rights as a prerequisite for trade. Specifically, a complete market for river water may not emerge if there are four or more agents along the river. Instead, a partial market may emerge where a subset of agents trades river water while other agents can take some of the river water that passes their territory. |
| Keywords: | river sharing, water trade, market emergence, property rights, coalition stability |
| JEL: | D62 C72 Q25 |
| Date: | 2015–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150001&r=gth |
| By: | Chen, Yi-Chun; Kunimoto, Takashi; Sun, Yifei |
| Abstract: | We say that a social choice rule is implementable with (small) transfers if one can design a mechanism whose set of equilibrium outcomes coincides with that specified by the rule but the mechanism allows for (small) ex post transfers among the players. We then show in private-value environments that any incentive compatible rule is implementable with small transfers. Therefore, our mechanism only needs small ex post transfers to make our implementation results completely free from the multiple equilibrium problem. In addition, our mechanism possesses the unique equilibrium that is robust to higher-order belief perturbations. We also identify a class of interdependent-value environments to which our results can be extended. |
| Keywords: | Full implementation, universal type space, robustness, transfers |
| JEL: | C72 D78 D82 |
| Date: | 2015–03–06 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2015-04&r=gth |
| By: | Sabien Dobbelaere (VU University Amsterdam, the Netherlands, and IZA, Germany); Roland Iwan Luttens (VU University Amsterdam, and Amsterdam University College, the Netherlands) |
| Abstract: | This paper provides an economic foundation for non-binding mediation to stimulate first collective bargaining agreements, as implemented in British Columbia since 1993. We show that the outcome of first-contract mediation is Pareto efficient and proves immune to the insider-outsider problem of underhiring. We also demonstrate that equilibrium wages and profits under mediation coincide with the Owen values of the corresponding cooperative game with the coalitional structure that follows from unionization. |
| Keywords: | BC first-contract model, mediation, collective bargaining, union, non-binding contract |
| JEL: | C71 J51 L20 K12 |
| Date: | 2013–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130096&r=gth |
| By: | Ennio Bilancini; Leonardo Boncinelli |
| Abstract: | In this paper we study the typical dilemma of social coordination between a risk- dominant convention and a payoff-dominant convention. In particular, we consider a model where a population of agents play a coordination game over time, choosing both the action and the network of agents with whom to interact. The main novelty with respect to the existing literature is that: (i) agents come in two distinct types, (ii) the interaction with a di.erent type is costly, and (iii) an agent's type is unobservable prior to interaction. We show that when the cost of interacting with a different type is small with respect to the payo. of coordination, then the payoff-dominant convention is the only stochastically stable convention; instead, when the cost of interacting with a different type is large, the only stochastically stable conventions are those where all agents of one type play the payoff-dominant action and all agents of the other type play the risk-dominant action. |
| Keywords: | coordination, equilibrium selection, stochastic stability, learning, network formation |
| JEL: | C73 D83 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:mod:recent:108&r=gth |
| By: | Andrew F. Daughety (Vanderbilt University); Reinganum F. Reinganum (Vanderbilt University) |
| Abstract: | This Handbook chapter provides a brief review of selected settlement bargaining models in some areas where new work is developing and where additional work is likely to yield yet further important results. This work has focused on what might be thought of as the environment of the settlement negotiation process, where bargaining failure generally results in trial, and our survey will use that perspective to organize the work discussed |
| Keywords: | Settlement, bargaining |
| JEL: | K4 C7 |
| Date: | 2014–07–08 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-14-00005&r=gth |
| By: | Andrew F. Daughety (Vanderbilt University); Jennifer F. Reinganum (Vanderbilt University) |
| Abstract: | This Handbook chapter provides a brief review of selected settlement bargaining models in some areas where new work is developing and where additional work is likely to yield yet further important results. This work has focused on what might be thought of as the environment of the settlement negotiation process, where bargaining failure generally results in trial, and our survey will use that perspective to organize the work discussed |
| Keywords: | Settlement, bargaining |
| JEL: | K4 C7 |
| Date: | 2014–07–09 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-14-00006&r=gth |
| By: | Erik Ansink (VU University Amsterdam); Hans-Peter Weikard (Wageningen University) |
| Abstract: | In a river claims problem, agents are ordered linearly, and they have both an initial water endowment as well as a claim to the total water resource. We provide characterizations of two solutions to this problem, using Composition properties which have particularly relevant interpretations for the river claims problem. Specifically, these properties relate to situations where river flow is uncertain or highly variable, possibly due to climate change impacts. The only solution that satisfies all Composition properties is the 'Harmon rule' induced by the Harmon Doctrine, which says that agents are free to use any water available on their territory, without concern for downstream impacts. The other solution that we assess is the 'No-harm rule', an extreme interpretation of the "no-harm" principle from international water law, which implies that water is allocated with p riority to downstream needs. In addition to characterizing both solutions, we show their relation to priority rules and sequential sharing rules. |
| Keywords: | river claims problem, sharing rule, Harmon Doctrine, composition axioms, water allocation |
| JEL: | D63 C71 Q25 |
| Date: | 2013–12–13 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130199&r=gth |
| By: | Matthias Weber (CREED, University of Amsterdam) |
| Abstract: | There are many situations in which different groups make collective decisions by committee voting, where each group is represented by a single person. Theoretical concepts suggest how the voting systems in such committees should be designed, but these abstract rules can usually not be implemented perfectly. To find voting systems that approximate these rules the so called inverse power problem needs to be solved. I introduce a new method to address this problem in two-tier voting settings using the coefficient of variation. This method can easily be applied to a wide variety of settings and rules. After deriving the new method, I illustrate why it is to be preferred over more traditional methods. |
| Keywords: | inverse power problem, indirect voting power, two-tier voting, Penrose’s Square Root Rule |
| JEL: | D71 D72 |
| Date: | 2014–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140019&r=gth |
| By: | Belik, Ivan (Dept. of Business and Management Science, Norwegian School of Economics); Jörnsten, Kurt (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | In the given research we study a leadership formation of the most influential nodes in networks. Specifically, we analyze the competition between a leader and a follower based on the Stackelberg leadership model. Applying the concept of Shapley value to measure node’s importance, we represent the mechanism of Shapley-based Stackelberg leadership formation in networks. The approach is tested and represented in tabular and graphical formats. |
| Keywords: | Stackelberg competition; Shapley value; leadership; networks analysis |
| JEL: | C00 C60 C61 Z13 |
| Date: | 2015–04–10 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2015_016&r=gth |
| By: | Peter Csoka (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Finance, Corvinus University of Budapest) |
| Abstract: | Let us consider a financially constrained leveraged financial firm having some divisions which have invested into some risky assets. Using coherent measures of risk the sum of the capital requirements of the divisions is larger than the capital requirement of the firm itself, there is some diversification benefit that should be allocated somehow for proper performance evaluation of the divisions. In this paper we use cooperative game theory and simulation to assess the possibility to jointly satisfy three natural fairness requirements for allocating risk capital in illiquid markets: Core Compatibility, Equal Treatment Property and Strong Monotonicity. Core Compatibility can be viewed as the allocated risk to each coalition (subset) of divisions should be at least as much as the risk increment the coalition causes by joining the rest of the divisions. Equal Treatment Property guarantees that if two divisions have the same stand-alone risk and also they contribute the same risk to all the subsets of divisions not containing them, then the same risk capital should be allocated to them. Strong Monotonicity requires that if a division weakly reduces its stand-alone risk and also its risk contribution to all the subsets of the other divisions, then as an incentive its allocated risk capital should not increase. Analyzing the simulation results we conclude that in most of the cases it is not possible to allocate risk in illiquid markets satisfying the three fairness notions at the same time, one has to give up at least one of them. |
| Keywords: | Market Microstructure, Coherent Measures of Risk, Market Liquidity, Funding Liquidity, Portfolio Performance Evaluation, Risk Capital Allocation, Risk Contributions, Totally Balanced Games, Simulation |
| JEL: | C71 G10 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1509&r=gth |
| By: | Marina S. Sandomirskaia (National Research University Higher School of Economics) |
| Abstract: | The paper examines an interaction of boundedly rational firms that are able to calculate their gains after reaction of an opponent to their own deviations from the current strategy. We consider an equilibrium concept that we call a Nash-2 equilibrium. We discuss the problem of existence and possible multiplicity of such equilibria, relation to infinite rationality approach of folk theorem and security considerations of equilibrium in secure strategies. For a number of models (Bertrand with homogeneous and heterogeneous product, Cournot, Tullock competition) the Nash-2 equilibrium sets are obtained and considered as tacit collusion or strong competition in dependence of additional security considerations |
| Keywords: | Nash-2 equilibrium, secure deviation, secure profile, Bertrand model, Cournot duopoly, differentiated product, Tullock contest, tacit collusion, tough competition. |
| JEL: | C72 D03 D43 D70 L13 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:93/ec/2015&r=gth |
| By: | Audrey Hu (University of Amsterdam, the Netherlands); Liang Zou (University of Amsterdam, the Netherlands) |
| Abstract: | We analyze sequential Dutch and Vickrey auctions where risk averse, or risk preferring, bidders may have heterogeneous risk exposures. We derive and characterize a pure strategy equilibrium of both auctions for arbitrary number of identical objects. A sufficient, and to certain extent necessary, condition for this result is that bidders' marginal utilities are log-submodular in income and type. We then show that when bidders are risk averse (preferring), the equilibrium price sequences should be downward (upward) drifting, and in each period the conditional expected revenue is higher (lower) in the Dutch than in the Vickrey sequential auctions. In particular, the "declining price anomaly" is perfectly consistent with nonincreasing absolute risk aversion when bidders have exposures to background risk. |
| Keywords: | sequential auction, background risk, risk preferences, declining prices, log-submodularity |
| JEL: | D44 D82 |
| Date: | 2014–10–20 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140139&r=gth |
| By: | David Csercsik (Momentum Game Theory Research Group, Institute of Economics - Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Pázmány Péter Catholic University) |
| Abstract: | Optimal power flow (OPF) problems are focussing on the question how a power transmission network can be operated in the most economic way. The general aim in such scenarios is to optimize generator scheduling in order to meet consumption re-quirements, transmission constraints and to minimize the overall generation cost and transmission losses. We use a simple lossless DC load flow model for the description of the transmission network, and assume linearly decreasing marginal cost of generators with different parameters for each generator. We consider a scenario in which the generation values regarding the OPF are calculated by a central authority who is aware of the network parameters and production characteristics. Furthermore, we assume that a central mechanism is applied for the determination of generator payoffs in order to cover their generation costs and assign them with some profit. We analyze the situation when generators may provide false information about their production parameters and thus manipulate the OPF computation in order to potentially increase their resulting profit. We consider two central payoff mechanisms and compare their vulnerability for such manipulations and analyze their effect on the total social cost. |
| Keywords: | networks, manipulability, power transmission, optimal power flow |
| JEL: | C71 L14 L94 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1511&r=gth |
| By: | Matthias Weber (CREED, University of Amsterdam) |
| Abstract: | There are many situations in which different groups make collective decisions by committee voting, with each group represented by a single person. A natural question is what voting system such a committee should use. Concepts based on voting power provide guidelines for this choice. The two most prominent concepts require the Banzhaf power index to be proportional to the square root of group size or the Shapley-Shubik power index to be proportional to group size. Instead of studying the choice of voting systems based on such theoretical concepts, in this paper, I ask which systems individuals actually prefer. To answer this question, I design a laboratory experiment in which participants choose voting systems. I find that people behind the veil of ignorance prefer voting systems following the rule of proportional Shapley-Shubik power; in front of the veil subjects pr efer voting systems benefiting their own group. Participants' choices can only partially be explained by utility maximization or other outcome based concepts. |
| Keywords: | assembly voting, EU council, Penrose's Square Root Rule, optimal voting rule |
| JEL: | D71 D72 C91 |
| Date: | 2014–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140042&r=gth |
| By: | Andre Veski (Tallinn University of Technology); Kaire Põder (Tallinn University of Technology) |
| Abstract: | Within the first 20 years of the market economy in Estonia, the public school market has been decentralized in Tallinn. Firstly, we describe how students are allocated to primary schools in a narrative, and secondly, in a formal mechanism design language. We indicate the closest equivalent algorithms from the matching markets design theory and conclude that the current system in Tallinn is a hybrid. The decentralized part of the market namely inter-district exam schools apply autonomous school proposing deferred acceptance; and the centralized part of the market intra-district regular schools apply school random serial dictatorship. Finally using data from Tallinn primary school matching, we show by an empirical evaluation of matching mechanisms. Since the currently the collected data does not reveal the students preference ordering we simulate some potential orderings for comparison. |
| Date: | 2015–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:ttu:tuteco:20&r=gth |
| By: | Harold Houba (VU University Amsterdam, the Netherlands); Kim Hang Pham Do (Massey University, New Zealand); Xueqin Zhu (Wageningen University, the Netherlands) |
| Abstract: | This paper studies the relation between optimal dam capacity and water management under rivalry uses and externalities. We extend the hydropower generation model, based on Haddad (2011), by including the competing use of water resource, non-linear building cost of dam capacity and externalities in a welfare optimization model. We obtain the optimal dam capacity for multi-functional dams such as providing infrastructure for industrial and households water use, conjunctive use of hydropower generation and irrigation; storing water in the wet season for use in the dry season, and mitigating flooding damages. The optimal solution shows that optimal dam capacity is characterized by the marginal benefits of hydropower generation, the marginal costs of flooding damages, and the constraining factors. Moreover, the optimal water management can be achieved by using derived sea sonal prices in a decentralized manner. |
| Keywords: | OR in environment and climate change, river-basin management, dam capacity, welfare optimization, externalities |
| JEL: | C71 C72 D62 |
| Date: | 2014–10–30 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140143&r=gth |
| By: | Harold Houba (VU University Amsterdam); Evgenia Motchenkova (VU University Amsterdam); Quan Wen (University of Chicago, United States) |
| Abstract: | We analyze how leniency affects cartel pricing in an infinitely-repeated oligopoly model where the fine rates are linked to illegal gains and detection probabilities depend on the degree of collusion. A novel aspect of this study is that we focus on the worst possible outcome. We investigate the maximal cartel price, the largest price for which the conditions for sustainability hold. We analyze how the maximal cartel price supported by different cartel strategies adjusts in response to the introduction of (ex-ante and ex-post) leniency programs. We disentangle the effects of traditional antitrust enforcement, leniency, and cartel strategies on the maximal cartel price. Ex-ante leniency cannot reduce the maximal cartel price below the price under antitrust without leniency. On the other hand, for ex-post leniency, improvement is possible and granting full immunity to single-reporting firms achieves the largest reduction in the maximal cartel price. To reduce adverse effects under both leniency programs, fine reductions to multiple-reporting firms should be moderate or absent. Finally, ex-post leniency should provide less generous fine reductions to multiple-reporting firms, which is supported by the current practice in the US and the EU. |
| Keywords: | Cartel, Antitrust, Competition Policy, Leniency Program, Self-reporting, Repeated Game |
| JEL: | L41 K21 C72 |
| Date: | 2014–11–10 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20140146&r=gth |
| By: | Harold Houba (VU University Amsterdam); Evgenia Motchenkova (VU University Amsterdam); Quan Wen (University of Washington, United States) |
| Abstract: | We study antitrust enforcement that channels price-fixing incentives through setting fines and allocating resources to detection activities. Antitrust fines obey four legal principles: punishments should fit the crime, proportionality, bankruptcy considerations, and minimum fines. Bankruptcy considerations limit maximum fines, ensure abnormal cartel profits and impose a challenge for optimal antitrust enforcement. We integrate the mentioned legal principles into an infinitely-repeated oligopoly model. We derive the optimal level of detection activities and the optimal fine schedule that achieves maximal social welfare under these legal principles. The optimal fine schedule remains below the maximum fine and induces collusion on a lower price by making it more attractive than collusion on higher prices. For a range of low cartel prices, the fine is set to the legal minimum. Raising minimum fines will enable the cartel to raise its price and is better avoided. Our analysis and results relate to the marginal deterrence literature. |
| Keywords: | Antitrust enforcement, Antitrust Law, Cartel, Oligopoly, Repeated game |
| JEL: | L4 K21 D43 C73 |
| Date: | 2013–10–25 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20130178&r=gth |