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on Game Theory |
| By: | Hannu Salonen (Department of Economics, University of Turku) |
| Abstract: | Some solution concepts for n -person games admit a recursive definition. In such a recursion, the solution of an n -person game is computed by using the knowledge of how some of the proper subgames of a given game have been solved. While these kind of recursion formulas are of course computational devices, they can also help us to understand the bargaining processes behind various solution concepts. Two recursion formulas leading to the Shapley value are studied in more detail. |
| Keywords: | Shapley value, recursion |
| JEL: | C71 |
| Date: | 2006–03 |
| URL: | http://d.repec.org/n?u=RePEc:utu:wpaper:116&r=gth |
| By: | Dino Gerardi |
| Date: | 2006–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:cla:uclatw:815595000000000006&r=gth |
| By: | Michael Chwe |
| Date: | 2006–04–27 |
| URL: | http://d.repec.org/n?u=RePEc:cla:uclatw:815595000000000004&r=gth |
| By: | Adriana Breccia |
| Abstract: | This paper investigates the uniqueness of subgame perfect (SP) payoffs in a sequential bargaining game. Players are completely informed and the surplus to be allocated follows a geometric Brownian motion. This bargaining problem has not been analysed exhaustively in a stochastic environment. The aim of this paper is to provide a technique to identify the subgame perfect equilibria, i.e. the timing of the agreement and the SP payoffs at which agreement occurs. Even though the main focus is on the uniqueness of the equilibrium, we investigate other features of the equilibrium, such as the Pareto effciency of the outcome and the relation with the Nash axiomatic approach. |
| Date: | 2006–04 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:06/07&r=gth |
| By: | Vincent Merlin (CREM - Centre de Recherche en Economie et Management - http://crem.univ-rennes1.fr/ - [CNRS : UMR6211] - [Université Rennes I][Université de Caen] - []); Matthieu Martin |
| Abstract: | This paper deals with the non-emptiness of the stability set<br /> for any proper voting game. We present an upper bound on<br /> the number of alternatives which guarantees the non<br /> emptiness of this solution concept. We show that this<br /> bound is greater than or equal to the one given by Le Breton<br /> and Salles (1990) for quota games. |
| Keywords: | voting game, core, stability set |
| Date: | 2006–04–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00010172_v1&r=gth |
| By: | Vincent Merlin (CREM - Centre de Recherche en Economie et Management - http://crem.univ-rennes1.fr/ - [CNRS : UMR6211] - [Université Rennes I][Université de Caen] - []); Marc Feix; Dominique Lepelley; Jean Louis Rouet |
| Abstract: | Even, and in fact chiefly, if two or more players in a voting game<br />have on a binary issue independent opinions, they may have<br />interest to form a single voting alliance giving an average gain<br />of influence for all of them. Here, assuming the usual<br />independence of votes, we first study the alliance voting power<br />and obtain new results in the so-called asymptotic limit for which<br />the number of players is large enough and the alliance weight<br />remains a small fraction of the total of the weights. Then, we<br />propose to replace the voting game inside the alliance by a random<br />game which allows new possibilities. The validity of the<br />asymptotic limit and the possibility of new alliances are examined<br />by considering the decision process in the Council of Ministers of<br />the European Union. |
| Keywords: | Voting Power; Alliance |
| Date: | 2006–04–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00010168_v1&r=gth |
| By: | Sergio Currarini (Department of Economics, University Of Venice Cà Foscari) |
| Abstract: | In a recent paper, Demange (2004) has shown that hierarchical organizations can guarantee the existence of stable cooperative outcomes by appropriately allocating the blocking power to a subset of coalitions, the “teams”. This paper extends the analysis of Demange to cooperative problems with spillovers. We show that if blocking coalitions have “pessimistic expectations” on the reaction of outsiders, in all cooperative problems there exists an allocation which is blocked by no team. We also study the case of ”passive expectations”, for which the same result holds in all games with negative spillovers, while stable allocations may fail to exist in games with positive spillovers. In the latter class of games, however, hierarchies are shown to be the most stable organizational forms. |
| Keywords: | Organizational design, networks, group stability, spillovers. |
| JEL: | C7 C71 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:14_06&r=gth |
| By: | Sergio Currarini (Department of Economics, University Of Venice Cà Foscari) |
| Abstract: | How should an organization be designed in order to provide its members with minimal incentives to defect? And how does the optimal design depend on the type of strategic interaction between defectors and remaining organizational members? This paper addresses such issues in a game theoretic model of cooperation, in which an organization is formally represented by a connected network, and where gains from cooperation are given by a partition function. We show that critical structural features of the organization depend in a clear-cut way on the sign of spillovers. In particular, positive spillovers favor the adoption of dispersed and centralized forms, while negative spillovers favor cohesive and horizontal ones. Moreover, if the organizational form determines all the communication possibilities of members, a highly centralized organization - the star - emerges under positive spillovers, whereas two horizontal architectures - the circle and the complete - emerge under negative spillovers. |
| Keywords: | Organizational design, networks, group stability, spillovers. |
| JEL: | C7 C71 D20 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:16_06&r=gth |
| By: | Sergio Currarini (Department of Economics, University Of Venice Cà Foscari); Francesco Feri (Department of Economics, University Of Venice Cà Foscari) |
| Abstract: | We study a simple contracting game with a principal and two agents. Contracts exert an externalities on non contractors. The principal can either contract both agents in a centralized manner, or delegate one agent to contract the other. We show that the choice of the principal depends on the sign of the externality. If this is positive, the principal prefers to delegate as long as the agency costs are not too high; if the externality is negative, the principal prefers to centralize for all sizes of agency costs. |
| Keywords: | Contracts, Externalities, Centralization, Delegation. |
| JEL: | D23 C71 C72 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:15_06&r=gth |
| By: | Duarte Brito (Universidade Nova de Lisboa); João Gata (Autoridade da Concorrência and Universidade de Aveiro and UECE/ISEG-UTL) |
| Abstract: | We compare different notions of stability in three firm merger games. We discuss some of their shortcomings and introduce an alternative notion of stability which overcomes them. The paper concludes with an illustrative example. |
| Keywords: | endogenous mergers, stability, core. |
| JEL: | L13 L41 |
| Date: | 2006–01 |
| URL: | http://d.repec.org/n?u=RePEc:pca:wpaper:10&r=gth |
| By: | Angelov, Nikolay (Department of Economics) |
| Abstract: | We propose a way to model firm mergers using a matching game known as the roommate problem, whereby firms are assumed to make preference rankings of potential merger partners. The position of a firm in another firm's ranking is assumed to be governed by an index, which in turn consists of a deterministic part and of a stochastic one, similar to the latent indices used in standard discrete-choice models. Given all firms' preferences, game-theoretic mechanisms lead to a matching whereby each firm is either self-matched or assigned a merger partner. We derive expressions for the probability of a merger between a specific firm pair, and also a log-likelihood function for estimation using firm-specific data. Using a simulation in a setting with groups of three firms involved in roommate games within each group, the model's finite-sample properties are examined. |
| Keywords: | firm mergers; roommate game; matching markets; discrete response |
| JEL: | C15 C25 C78 G32 |
| Date: | 2006–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:uunewp:2006_010&r=gth |
| By: | Parkash CHANDER (Department of Economics, National University of Singapore); Henry TULKENS (CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium) |
| Abstract: | In essence, any international environmental agreement (IEA) implies cooperation of a form or another. The paper seeks for logical foundations of this. It first deals with how the need for cooperation derives from the public good aspect of the externalities involved, as well as with where the source of cooperation lies in cooperative game theory. In either case, the quest for efficiency is claimed to be at the root of cooperation. Next, cooperation is considered from the point of view of stability. After recalling the two competing concepts of stability in use in the IEA literature, new insights on the nature of the gamma core in general are given as well as of the Chander-Tulkens solution within the gamma core. Free riding is also evaluated in relation with the alternative forms of stability under scrutiny. Finally, it is asked whether with the often mentioned virtue of “self enforcement” any conceptual gain is achieved, different from what is meant by efficiency and stability. A skeptical answer is offered, as a reply to Barrett’s (2003) attempt at giving the notion a specific content. |
| URL: | http://d.repec.org/n?u=RePEc:sca:scaewp:0609&r=gth |
| By: | Vincent Merlin (CREM - Centre de Recherche en Economie et Management - http://crem.univ-rennes1.fr/ - [CNRS : UMR6211] - [Université Rennes I][Université de Caen] - []); Rahhal Lahrach; Jérôme Le Tensorer |
| Abstract: | Since 1992, the international community is trying to arrive at a multilateral agreement on the reduction of emissions for greenhouse gases. A collective decision mechanism was adopted in 1997: An agreement is ratified if and only if it is approved by a coalition gathering more than 55 countries. Moreover, the ratifying industrialized countries - included in the Annex I of the Kyoto Protocol - must represent a total weight corresponding to at least 55% of the total CO2 emissions of the countries of the Annex I, taking the year 1990 as a reference point.<br /><br />One way to study the theoretical power distribution induced by this voting procedure is to compute the Banzhaf index for each country. Firstly, the results of the computation show that the power distribution is largely heterogeneous and benefits to the United-States. Secondly, we analyze the modifications generated by the European coalition scenario in order to prove that the European strategy to act as a single block counterbalanced the US leadership. Finally, we conclude that Japan and Russia benefited from the United States withdrawal in term of a priori decisional power. |
| Keywords: | Power indices, environment, Kyoto Protocol, empirical game theory |
| Date: | 2006–04–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00010171_v1&r=gth |
| By: | Carlo Carraro (Department of Economics, University Of Venice Cà Foscari); Barbara Buchner (Fondazione Eni Enrico Mattei) |
| Abstract: | The present stalemate in climate negotiations between the US and the other Annex I countries has led policy analysts and economists to explore the possible emergence of alternative climate regimes that may be applied after 2012. This paper explores the idea of replacing international cooperation on greenhouse gas emission control with international cooperation on climate-related technological innovation and diffusion. This idea – recently proposed among others by Barrett (2001) and Benedick (2001) – is based on the insight that incentives to free ride are much smaller in the case of technological cooperation than in the case of cooperation on emission control. This paper provides a first applied game theory analysis of a technology-based climate protocol by assessing: (i) the selfenforcingness (namely, the absence of incentives to free ride) of the coalition that would form when countries negotiate on climate-related technological cooperation; (ii) the environmental effectiveness of a technology-based climate protocol. The analysis is carried out by using a model in which endogenous and induced technical change are explicitly modelled. The results of our analysis partly support Barrett’s and Benedick’s conjecture. On the one hand, a self-enforcing agreement is more likely to emerge when countries cooperate on environmental technological innovation and diffusion than when they cooperate on emission abatement. However, technological cooperation – without any commitment to emission control – may not lead to a sufficient abatement of greenhouse gas concentrations. |
| Keywords: | Agreements, Climate, Incentives, Negotiations, Policy |
| JEL: | C72 H23 Q25 Q28 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:12_06&r=gth |
| By: | Carlo Carraro (Department of Economics, University Of Venice Cà Foscari); Barbara Buchner |
| Abstract: | controlling GHG emissions without the involvement of countries such as China, India, the United States, Aust rali a, and possibly other developing countries. This highlights an unambiguous weakness of the Kyoto Protocol, where the aforementioned countries either have no binding emission targets or have decided not to comply with their targets . Therefore, when discussing possible post-Kyoto scenarios, it is crucial to priori tise part icipation incentives for all countries, especially those without explicit or with insufficient abatement targets. This paper offers a bottom-up game-theoretic perspective on participation incentives. Rather than focusing on issue linkage, t ransfers or burden sharing as tools to enhance the incentives to par t icipate in a climate agreement, thi s paper aims at exploring whether a di fferent policy approach could lead more count ries to adopt ef fective climate cont rol policies. This policy approach is explicitly bottom-up, namely i t gives each country the freedom to sign agreements and deals, bilateral ly or multila terally, with other countries, without being constrained by any globa l protocol or convention. This study provides a game-theoretic assessment of this policy approach and then evaluates empirically the possible endogenous emergence of single or multi ple climate coalitions. Welfare and technological consequences of different mul tiple bloc climate regimes will be assessed and their overall environmental effectiveness will be discussed. |
| Keywords: | Agreements, Climate, Incentives, Negotiations, Policy |
| JEL: | C72 H23 Q25 Q28 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:10_06&r=gth |
| By: | Carlo Carraro (Department of Economics, University Of Venice Cà Foscari); Carmen Marchiori (London School of Economics and Fondazione Eni Enrico Mattei); Alessandra Sgobbi (SSAV and Fondazione Eni Enrico Mattei) |
| Abstract: | Bargaining is ubiquitous in real-life. It is a major dimension of political and business activities. It appears at the international level, when governments negotiate on matters ranging from economic issues (such as the removal of trade barriers), to global security (such as fighting against terrorism) to environmental and related issues (e.g. climate change control). What factors determine the outcome of negotiations such as those mentioned above? What strategies can help reach an agreement? How should the parties involved divide the gains from cooperation? With whom will one make alliances? This paper addresses these questions by focusing on a non-cooperative approach to negotiations, which is particularly relevant for the study of international negotiations. By reviewing noncooperative bargaining theory, non-cooperative coalition theory, and the theory of fair division, this paper will try to identify the connection among these different facets of the same problem in an attempt to facilitate the progress towards a unified framework. |
| Keywords: | Negotiation theory, Bragaining, Coalitions, Fairness, Agreements |
| JEL: | C72 C78 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:08_06&r=gth |
| By: | Sudipta Sarangi; Pascal Billand; Christophe Bravard |
| Abstract: | This paper addresses the existence of Nash networks for the one-way flow model of Bala and Goyal (2000) in a number of different settings. First, we provide conditions for he existence of Nash networks in models where costs and values of links are heterogenous and players obtain resources from others only through the directed path between them. We find that costs of establishing links play a vital role in the existence of Nash networks. Next we examine the existence of Nash networks when there are congestion effects in the model. Then, we provide conditions for the existence of Nash networks in a model where a player’s payoff depends on the number of links she has established as well as on the number of links that other players in the population have created. More precisely, we show that convexity and increasing (decreasing) differences allow for the existence of Nash networks. |
| URL: | http://d.repec.org/n?u=RePEc:lsu:lsuwpp:2006-05&r=gth |
| By: | Sergiu Hart; Yishay Mansour |
| Abstract: | We study the question of how long it takes players to reach a Nash equilibrium in "uncoupled" setups, where each player initially knows only his own payoff function. We derive lower bounds on the number of bits that need to be transmitted in order to reach a Nash equilibrium, and thus also on the required number of steps. Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian setting; and (3) reaching a mixed Nash equilibrium. Finally, we show that some very simple and naive procedures lead to similar exponential upper bounds. |
| Date: | 2006–03 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp419&r=gth |
| By: | Harold Houba (Vrije Universiteit Amsterdam); Quan Wen (Vanderbilt University, Nashville, USA) |
| Abstract: | There has been a long debate on equilibrium characterization in the negotiation model when players have different time preferences. We show that players behave quite differently under different time preferences than under common time preferences. Conventional analysis in this literature relies on the key assumption that all continuation payoffs are bounded from above by the bargaining frontier. However, when players have different time preferences, intertemporal trade may lead to continuation payoffs above the bargaining frontier. We provide a thorough study of this problem without imposing the conventional assumption. Our results tie up all the previous findings, and also clarify the controversies that arose in the past. |
| Keywords: | Bargaining; Negotiation; Time Preference; Endogenous Threats |
| JEL: | C72 C73 C78 |
| Date: | 2006–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20060028&r=gth |