The minimal dominant set is a non-empty core-extension

A set of outcomes for a transferable utility game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core. We provide an algorithm to find the minimal dominant set.dynamic solution, absorbing set, core, non-emptiness

Interchange fee rate, merchant discount rate and retail prices in a credit card network: A game-theoretic analysis

We consider two game-theoretic settings to determine the optimal values of an issuer's interchange fee rate, an acquirer's merchant discount rate, and a merchant's retail price in a credit card network. In the first setting, we investigate a two-stage game problem in which the issuer and the acquirer first negotiate the interchange fee rate, and the acquirer and the retailer then determine their merchant discount rate and retail price, respectively. In the second setting, motivated by the recent US bill “H.R. 2695,” we develop a three-player cooperative game in which the issuer, the acquirer, and the merchant form a grand coalition and bargain over the interchange fee rate and the merchant discount rate. Following the cooperative game, the retailer makes its retail pricing decision. We derive both the Shapley value- and the nucleolus-characterized, and globally-optimal unique rates for the grand coalition. Comparing the two game settings, we find that the participation of the merchant in the negotiation process can result in the reduction of both rates. Moreover, the stability of the grand coalition in the cooperative game setting may require that the merchant should delegate the credit card business only to the issuer and the acquirer with sufficiently low operation costs. We also show that the grand coalition is more likely to be stable and the U.S. bill “H.R. 2695” is thus more effective, if the degree of division of labor in the credit card network is higher as the merchant, acquirer, and issuer are more specialized in the retailing, acquiring, and issuing operations, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 201

Interest Groups and Trade Reform in Mexico

Mexico experienced widespread economic reform in the last two decades. From being a protectionist economy with a policy of import substitution, it has turned into an export-oriented open economy. Why was protectionism a stable policy, and how was it overturned by a reform that went against entrenched interests? I apply a game theoretic model of political influence and economic reform to answer these questions using data to calculate the payoffs for the relevant interest groups. In the underlying cooperative game, the core is empty and a protectionist coalition of import-substituting firms and the government was "stable" until the eighties. Adjusting the model's parameters to changes in the government's financing options in the late eighties and early nineties leads to a different and unique outcome. In the predicted outcome a free trade policy is adopted through cooperation between all players.Trade Reform, Mexico, Coalition Formation, Aspirations, Cooperative Games, Interest Groups

Cooperative Games with Bounded Dependency Degree

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.Comment: 10 pages, full version of accepted AAAI-18 pape

Modelling interactive behaviour, and solution concepts

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Modelling interactive behaviour, and solution concepts.

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Finite Bargaining Problems

Bargaining is a process to decide how to divide shared resources between two or more players. And axiomatic bargaining specifies desirable and simple properties the outcome of the bargaining should satisfy and identifies the solution that produces this outcome. This approach was first developed by John Nash in his seminal work(Nash 1950). Since then, numerous studies have been done on bargaining problems with convex feasible set or with non-convex but comprehensive feasible set. There is, however, little work on finite bargaining problems. In this dissertation, we study finite bargaining problems systematically by extending the standard bargaining model to the one consisting of all finite bargaining problems. For our bargaining problems, we first propose the Nash, Maximin, Leximin, Maxiproportionalmin, Lexiproportianlmin solutions, which are the counterparts of those that have been studied extensively in both convex and non-convex but comprehensive problems. We then axiomatically characterize these solutions in our context. We next introduce two new solutions, the maximin-utilitarian solution and the utilitarian-maximin solution, each of which combines the maximin solution and utilitarian solution in different ways. The maximin-utilitarian solution selects the alternatives from the maximin solution that have the greatest sum of individuals’ utilities, and the utilitarian-maximin solution selects the maximin alternatives from the utilitarian solution. These two solutions attempt to combine two important but very different ethical principles to produce compromised solutions to bargaining problems. Finally, we discuss several variants of the egalitarian solution. The egalitarian solution in finite bargaining problems is more complicated than its counterpart in either convex or non-convex but comprehensive bargaining problems. Given its complexity in our context, we start our inquiry by investigating two-person, finite bargaining problems, and then extend some of the analysis to n-person, finite bargaining problems. Our analysis of finite bargaining problems and axiomatic characterizations of the extensions of various standard solutions of convex/non-convex but comprehensive bargaining problems to finite bargaining problems will shed new light on the behavior of these solutions. Our new solutions will expand our understanding of the bargaining theory and distributive justice from a different perspective

A Decade of Experimental Research on Spatial Models of Elections and Committees

The Euclidean representation of political issues and alternative outcomes, and the associated representation of preferences as quasi-concave utility functions is by now a staple of formal models of committees and elections. This theoretical development, moreover, is accompanied by a considerable body of experimental research. We can view that research in two ways: as a test of the basic propositions about equilibria in specific institutional settings, and as an attempt to gain insights into those aspects of political processes that are poorly understood or imperfectly modeled, such as the robustness of theoretical results with respect to procedural details and bargaining environments. This essay reviews that research so that we can gain some sense of its overall import