Compromise values in cooperative game theory

Bargaining;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

Essays on Uncertainty in Public Economics and Cooperative Bargaining

This dissertation consists of two parts. The theme connecting the two parts is the role of uncertainty. The first part focuses on the role of uncertainty in cooperative bargaining and public decision making. I provide an axiomatic characterization of the normalized utilitarian solution to bargaining problems involving uncertainty. In addition to three basic axioms that are common in the bargaining literature, I propose the axiom of weak linearity to characterize the solution. In the second part I study uncertainty in non-cooperative games by designing a principal agent model of public bailouts. The first essay in this part sets up the model and shows that the moral hazard problem, namely the Samaritan\u27s dilemma, exists without an altruistic principal. The second essay in this part builds upon the previous essay and focuses on the informational elements in a bailout game. Mainly, I show the existence of a separating equilibrium, where public bailouts serve as a mechanism to reveal essential information to outsiders and in which the good-type agents can benefit from rejecting a bailout offer

Duality, area-considerations, and the Kalai–Smorodinsky solution

We introduce a new solution concept for 2-person bargaining problems, which can be considered as the dual of the Equal-Area solution (EA) (see Anbarcı and Bigelow (1994)). Hence, we call it the Dual Equal-Area solution (DEA). We show that the point selected by the Kalai–Smorodinsky solution (see Kalai and Smorodinsky (1975)) lies in between those that are selected by EA and DEA. We formulate an axiom–area-based fairness–and offer three characterizations of the Kalai–Smorodinsky solution in which this axiom plays a central role. © 2016 Elsevier B.V

Axiomatic characterizations of the Walras correspondence for generalized economies

Equilibrium Theory;International Trade

Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games

Orthodox game theory is often criticized for its inability to single out intuitively compelling Nash equilibria in non-cooperative games. The theory of virtual bargaining, developed by Misyak and Chater (2014) suggests that players resolve non-cooperative games by making their strategy choices on the basis of what they would agree to play if they could openly bargain. The proposed formal model of bargaining, however, has limited applicability in non-cooperative games due to its reliance on the existence of a unique non-agreement point – a condition that is not satisfied by games with multiple Nash equilibria. In this paper, I propose a model of ordinal hypothetical bargaining, called the Benefit-Equilibration Reasoning, which does not rely on the existence of a unique reference point, and offers a solution to the equilibrium selection problem in a broad class of non-cooperative games. I provide a formal characterization of the solution, and discuss the theoretical predictions of the suggested model in several experimentally relevant games

Cooperative bargaining and coalition formation

In this study, I am working on the relationship between coalition formation and bargaining. More specifically, I use a baseline cooperative bargaining model in which a group of agents with symmetric single peaked preferences form coalitions to bargain with a principle. I use this model to study the e ects of the underlying bargaining process on the structure of the coalition formed by the agents, and to classify the properties that form a grand coalition. Later on, I also introduce an alternative cooperative bargaining model to understand the connection between the bargaining process and coalition formation