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on Game Theory |
| By: | Parkash Chander (National University of Singapore and CORE, Universite Catholique de Louvain); Myrna Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | This paper brings together two of the most important solution concepts of game theory –subgame-perfect Nash equilibrium of a non-cooperative game and the core of a cooperativegame. Our approach rests on two fundamental ideas: (1) Given an extensive game, the formationof a coalition leads to a new game where all the members of the coalition become one player. (2)At the origin of any subgame, the only possible coalitions consist of players who have decision nodes in the subgame. We introduce a concept of subgame perfect cooperative equilibrium, which we label the gamma-core of an extensive game. We provide a necessary and sufficient condition for the existence of the gamma-core of an extensive game of perfect information. As a motivating example, we formulate the problem of global warming as a dynamic game with simultaneous moves and show that if the payoff functions are quadratic, then the gamma-core of the game is nonempty. |
| Keywords: | subgame perfect cooperation, extensive form game, subgame perfection, gamma-core |
| JEL: | C72 |
| Date: | 2010–06 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:1008&r=gth |
| By: | hanjoon michael, jung/j |
| Abstract: | We propose a revised version of the perfect Bayesian equilibrium in general multi-period games with observed actions. In finite games, perfect Bayesian equilibria are weakly consistent and subgame perfect Nash equilibria. In general games that allow a continuum of types and strategies, however, perfect Bayesian equilibria might not satisfy these criteria of rational solution concepts. To solve this problem, we revise the definition of the perfect Bayesian equilibrium by replacing Bayes' rule with a regular conditional probability. We call this revised solution concept a perfect regular equilibrium. Perfect regular equilibria are always weakly consistent and subgame perfect Nash equilibria in general games. In addition, perfect regular equilibria are equivalent to simplified perfect Bayesian equilibria in finite games. Therefore, the perfect regular equilibrium is an extended and simple version of the perfect Bayesian equilibrium in general multi-period games with observed actions. |
| Keywords: | Bayes' rule; general Multi-period game; Perfect Bayesian equilibrium; Perfect regular equilibrium; Regular conditional probability; Solution concept. |
| JEL: | C72 |
| Date: | 2010–10–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:26534&r=gth |
| By: | Francesc Llerena; Marina Nunez; Carles Rafels (Universitat de Barcelona) |
| Keywords: | core, assignment game, lorenz domination, kernel |
| JEL: | C71 C78 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bar:bedcje:2010246&r=gth |
| By: | Béal, Sylvain; Rémila, Eric; Solal, Philippe |
| Abstract: | For any transferable utility game in coalitional form with nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is less than or equal to n(n-1)/2, where n is the cardinality of the player set. This number considerably improves the upper bounds found so far by Koczy (2006) and Yang (2010). Our result relies on an altered version of the procedure proposed by Sengupta and Sengupta (1996). The use of the Davis-Maschler reduced-games is also pointed out. |
| Keywords: | Core; excess function; dominance path; Davis-Maschler reduced-game |
| JEL: | C71 |
| Date: | 2010–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:26578&r=gth |
| By: | Khmelnitskaya, A.; Talman, A.J.J. (Tilburg University, Center for Economic Research) |
| Abstract: | Mathematics Subject Classification 2000: 91A12, 91A43 |
| Keywords: | TU game;cooperation structure;Myerson value;efficiency;deletion link property;stability |
| JEL: | C71 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2010113&r=gth |
| By: | Barbara von Schnurbein |
| Abstract: | Cost allocation problems on networks can be interpreted as cooperative games on a graph structure. In the classical standard tree game, the cost of a service delivered, by a source has to be allocated between homogeneous users at the vertices. But, modern networks have also the capacity to supply different (levels of) services. For example, a cable network that provides diff erent television standards. Users that choose different levels of service can not be treated equally. The extended tree game accounts for such differences between users. Here, players are characterised by their level of demand, consequently the implications on the cost structure of the problem can be considered. We show how an ET-game can be formulated as the sum of unanimity games. This observation enables us to directly calculate the weighted Shapley values and to identify the core of an ET-game. |
| Keywords: | Cooperative game theory; extended tree game; core |
| JEL: | C71 C44 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0212&r=gth |
| By: | Keller, Godfrey; Rady, Sven |
| Abstract: | We study a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process. Its intensity is either high or low, and unknown to the players. We consider Markov perfect equilibria with beliefs as the state variable and show that all such equilibria exhibit an “encouragement effect” relative to the single-agent optimum. There is no equilibrium in which all players use cutoff strategies. Owing to the encouragement effect, asymmetric equilibria in which players take turns playing the risky arm before all experimentation stops Pareto dominate the unique symmetric equilibrium. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce the intensity of experimentation at more optimistic beliefs. This suggests that there is no equilibrium that uniformly maximizes the players' average payoff. |
| JEL: | D83 C73 O32 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ner:oxford:http://economics.ouls.ox.ac.uk/14975/&r=gth |
| By: | Kfir Eliaz; Roberto Serrano |
| Abstract: | Consider the problem of information disclosure for a planner who faces two agents interacting in a state-dependent multi-action prisoners?dilemma. We ?nd conditions under which the planner can make use of his superior information by disclosing some of it to the agents, and conditions under which such information leakage is not possible. Although the problem is entirely symmetric, the planner?s only way to reveal part of the information is based on creating asymmetries between the two agents by giving them di¤erent pieces of information. We also ? nd conditions under which such partially informative equilibria are the planner?s best equilibria. |
| Keywords: | Information Disclosure; Generalized Prisoners Dilemma; Uninformative Equilibria; Partially or Fully Informative Equilibria |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2010-16&r=gth |
| By: | Sunghoon Hong (Department of Economics, Vanderbilt University); Myrna Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | We develop a strategic model of network interdiction in a non-cooperative game of flow. A security agency operates a network with arc capacities. An adversary, endowed with a bounded quantity of bads, chooses a flow that specifies a plan for carrying bads through the network from a base to a target. Simultaneously, the agency chooses a blockage, which specifies a plan for blocking the transport of bads through arcs in the network. However, the blockage of arcs disrupts the operation of the network. The adversary gains and the agency loses from the target damage and the network disruption. The adversary incurs the expense of carrying bads. We characterize the Nash equilibria in terms of the primitives of our model. Our model contributes to the literature of game theory by introducing non-cooperative behavior into a Kalai-Zemel type mode of a (cooperative) game of flow. Our research also advances models and results on network interdiction. |
| Keywords: | Network interdiction, Noncooperative game of flow, Blockage, Nash equilibrium, Kalai- Zemel game of flow |
| JEL: | C72 D85 H56 |
| Date: | 2010–06 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:1010&r=gth |
| By: | Itay Fainmesser |
| Abstract: | Consider a large market with asymmetric information, in which sellers choose whether to cooperate or deviate and ?cheat?their buyers, and buyers decide whether to re-purchase from di¤erent sellers. We model active trade relationships as links in a buyer-seller network and suggest a framework for studying repeated games in such networks. In our framework, buyers and sellers have rich yet incomplete knowledge of the network structure; allowing us to derive meaningful conditions that determine whether a network is consistent with trade and cooperation between every buyer and seller that are connected. We show that three network features reduce the minimal discount factor necessary for sustaining cooperation: moderate competition, sparseness, and segregation. We ? nd that the incentive constraints rule out networks that maximize the volume of trade and that the constrained trade maximizing networks are in between ?old world? segregated and sparse networks, and a ?global market? |
| Keywords: | Buyer-Seller networks; repeated games; moral hazard;asymmetric information; trust; cooperation; institutions |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2010-14&r=gth |
| By: | Erik O. Kimbrough (Department of Economics (AE1), School of Business and Economics, Maastricht University); Roman Sheremeta (Argyros School of Business and Economics, Chapman University) |
| Abstract: | The equilibrium of a two-stage conflict game with side-payments predicts that with binding stage-one offers, proposers make and responders accept side-payments, generating settlements that strongly favor proposers. When side-payments are non-binding, proposers offer nothing and conflicts always arise. Laboratory experiments confirm that binding side-payments reduce conflicts. However, 30% of responders reject binding offers, and offers are more egalitarian than predicted. Surprisingly, non-binding side-payments also improve efficiency, although less than binding. With binding side-payments, 98% of efficiency gains come from avoided conflicts. However, with non-binding side-payments, only 49% of gains come from avoided conflicts and 51% from reduced conflict expenditures. |
| Keywords: | contest, conflict resolution, side payments, experiments |
| JEL: | C72 C91 D72 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:10-23&r=gth |
| By: | Salvador Barberà; Dolors Berga; Bernardo Moreno |
| Abstract: | We define different concepts of group strategy-proofness for social choice functions. We discuss the connections between the defined concepts under different assumptions on their domains of definition. We characterize the social choice functions that satisfy each one of them and whose ranges consist of two alternatives, in terms of two types of basic properties. |
| Keywords: | Social choice functions, Binary ranges, group strategy-proofness, xy-monotonicity, xy-based rules. |
| JEL: | D71 |
| Date: | 2010–04–28 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:853.10&r=gth |
| By: | Christopher Bruce; Jeremy Clark (University of Canterbury) |
| Abstract: | In many bargaining situations a third party is authorized to impose a backstop position on the bargainers. Prominent examples include governments who use collaborative policymaking between stakeholders to set public policy, but also compulsory arbitration in labour negotiations. Axiomatic models of cooperative bargaining, such as the Nash bargain, presume that the status quo allocation will have no effect on the outcome parties reach if it differs from the backstop set by the third party. In contrast, experimental findings have suggested that both equality of outcomes and entitlement (where the status quo establishes a focal point) may affect the agreements bargainers reach, at least under full information. This paper extends the investigation of the effect of equality and entitlement on cooperative bargaining to the case where parties have private, unverifiable information concerning the value of outcomes. We use a two-party, two-attribute experimental design in which subjects take part in unstructured, face-to-face bargaining to jointly select from among approximately 200 potential outcomes. We find that, relative to full information, parties who bargain under private information are almost as likely to reach agreements as those under full information, and that these agreements are still approximately Pareto efficient. Further, the effect of the status quo (rather than backstop) allocation seems amplified under private information, while the effect of equality is dampened, but not eliminated. |
| Keywords: | cooperative bargaining; private information; Nash bargain; egalitarian; entitlement; fairness; focal points |
| JEL: | C92 D74 H44 Q58 |
| Date: | 2010–11–04 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/68&r=gth |
| By: | Ben Zissimos (Department of Economics, Vanderbilt University) |
| Abstract: | This paper shows how distance may be used to coordinate on a unique equilibrium in which trade agreements are regional. Trade agreement formation is modeled as coalition formation. In a standard trade model with no distance between countries a familiar problem of coordination failure occurs, giving rise to multiple equilibria; any one of many possible trade agreements can form. With distance between countries, regional trade agreements generate larger rent-shifting effects than non-regional agreements. Countries use these effects to coordinate on a unique equilibrium. |
| Keywords: | Coalition, coordination, regionalism, preferential trade agreement, trade liberalization |
| JEL: | F02 F13 F15 C72 |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:1002&r=gth |
| By: | Dipjyoti Majumdar (Concordia University); Artyom Shneyerov (Concordia University); Huan Xie (Concordia University) |
| Abstract: | We study a market search equilibrium with aggregate uncertainty, private information and heterogeneus beiefs. Traders initially start out optimistic and then update their beliefs based on their matching experience in the market, using the Bayes rule. It is shown that all separating equilibria converge to perfect competition in the limit as the time between matches tends to 0. We also establish existence of a separating equilibrium. |
| Keywords: | Markets with search frictions, aggregate uncertainty, heterogeneous beliefs, optimism, bargaining, foundations of Walrasian equilibrium |
| JEL: | C73 C78 D83 |
| Date: | 2010–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:crd:wpaper:10004&r=gth |
| By: | Federica Alberti; Edward J. Cartwright |
| Abstract: | We investigate experimentally whether the endowment of potential contributors changes the success rate of providing threshold public goods. We find a U shaped relationship in which the success rate is relatively high when the endowment is either relatively small or large. We also find an inverted U shaped relationship in terms of the variance of contributions. This suggests that people find it hardest to coordinate and provide threshold public goods when endowments are of ‘intermediate’ size. By this we mean that the endowment is small enough that people do need to contribute relatively a lot to fund the good, but is also large enough that no one person is critical in providing the good. Coordinating is difficult in this case because there is an incentive to free ride and the possibility to do so creating a conflict of interest. |
| Keywords: | Public Good; Threshold; Endowment |
| JEL: | C72 H41 |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:ukc:ukcedp:1009&r=gth |