Robustness of Intermediate Agreements and Bargaining Solutions

Most real-life bargaining is resolved gradually; two parties reach intermediate agreements without knowing the whole range of possibilities. These intermediate agreements serve as disagreement points in subsequent rounds. Cooperative bargaining solutions ignore these dynamics and can therefore yield accurate predictions only if they are robust to its specification. We identify robustness criteria which are satisfied by four of the best-known bargaining solutions, the Nash, Kalai-Smorodinsky, Proportional and Discrete Raiffa solutions. We show that the “robustness of intermediate agreements” plus additional well-known and plausible axioms, provide the first characterization of the Discrete Raiffa solution and novel axiomatizations of the other three solutions. Hence, we provide a unified framework for comparing these solutions’ bargaining theories.Nash’s bargaining problem, robustness, intermediate agreements, the Discrete Raiffa solution, the Nash solution, the Kalai-Smorodinsky solution, Proportional solutions.

Essays in microeconomic theory

My thesis considers various aspects of microeconomic theory and focuses on the different types of uncertainty that players can encounter. Each chapter studies a setting with a different type of uncertainty and draws conclusions about how players are likely to behave in such a situation. The first chapter focuses on games of incomplete information and is joint work with Peter Eccles. We provide conditions to allow modelling situations of asymmetric information in a tractable manner. In addition we show a novel relationship between certain games of asymmetric information and corresponding games of symmetric information. This framework establishes links between certain games separately studied in the literature. The class of games considered is defined by scalable preference relations and a scalable information structure. We show that this framework can be used to solve asymmetric contests and auctions with loss aversion. In the second chapter I move to situations in which information is almost complete. In joint work with Peter Eccles, we consider the robustness of subgame perfect implementation in situations when the preferences of players are almost perfectly known. More precisely we consider a class of information perturbations where in each state of the world players know their own preferences with certainty and receive almost perfectly informative signals about the preferences of other players. We show that implementations using two-stage sequential move mechanisms are always robust under this class of restricted perturbations, while those using more stages are often not. The third chapter deals with a case of complete information and is joint work with Peter Eccles. We introduce the family of weighted Raiffa solutions. An individual solution is characterised by two parameters representing the bargaining weight of each player and the speed at which agreement is reached. First we provide a cooperative foundation for this family of solutions, by appealing to two of the original axioms used by Nash and a simple monotonicity axiom. Using similar axioms we give a new axiomatization for a family of weighted Kalai-Smorodinsky solutions. Secondly we provide a non-cooperative foundation for weighted Raiffa solutions, showing how they can be implemented using simple bargaining models where offers are intermittent or the identity of the proposer is persistent. This shows that weighted Raiffa solutions have cooperative foundations closely related to those of the Kalai-Smorodinksy solution, and non-cooperative foundations closely related to those of the Nash solution. The fourth chapter is closely related to the third chapter and is joint work with Bram Driesen and Peter Eccles. It provides a non-cooperative foundation for asymmetric generalizations of the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Stahl-Rubinstein bargaining model, in which each player's opportunity to make proposals is produced by an independent Poisson process, and a definite deadline ends the negotiations. Under the assumption that future payoffs are not discounted, it is shown that the payoffs realized in the unique subgame perfect equilibrium of this game approach the continuous Raiffa solution as the time horizon tends to infinity. The weights reflecting the asymmetries among the players, correspond with the Poisson arrival rates of their respective proposal processesScalable games: modelling games of incomplete information / Nora Wegner and Peter Eccles. -- Robustness of Subgame Perfect Implementation / Nora Wegner and Peter Eccles. -- Generalised weighted Raiffa Solutions / Nora Wegner and Peter Eccles. -- A non-cooperative foundation for the continuous Raiffa solution / Nora Wegner, Bram Driesen and Peter EcclesPrograma Oficial de Doctorado en EconomíaPresidente: Christopher Wallace; Secretario: Miltiadis Makris; Vocal: Ludovic Reno

Essays in microeconomic theory

My thesis considers various aspects of microeconomic theory and focuses on the different types of uncertainty that players can encounter. Each chapter studies a setting with a different type of uncertainty and draws conclusions about how players are likely to behave in such a situation. The first chapter focuses on games of incomplete information and is joint work with Peter Eccles. We provide conditions to allow modelling situations of asymmetric information in a tractable manner. In addition we show a novel relationship between certain games of asymmetric information and corresponding games of symmetric information. This framework establishes links between certain games separately studied in the literature. The class of games considered is defined by scalable preference relations and a scalable information structure. We show that this framework can be used to solve asymmetric contests and auctions with loss aversion. In the second chapter I move to situations in which information is almost complete. In joint work with Peter Eccles, we consider the robustness of subgame perfect implementation in situations when the preferences of players are almost perfectly known. More precisely we consider a class of information perturbations where in each state of the world players know their own preferences with certainty and receive almost perfectly informative signals about the preferences of other players. We show that implementations using two-stage sequential move mechanisms are always robust under this class of restricted perturbations, while those using more stages are often not. The third chapter deals with a case of complete information and is joint work with Peter Eccles. We introduce the family of weighted Raiffa solutions. An individual solution is characterised by two parameters representing the bargaining weight of each player and the speed at which agreement is reached. First we provide a cooperative foundation for this family of solutions, by appealing to two of the original axioms used by Nash and a simple monotonicity axiom. Using similar axioms we give a new axiomatization for a family of weighted Kalai-Smorodinsky solutions. Secondly we provide a non-cooperative foundation for weighted Raiffa solutions, showing how they can be implemented using simple bargaining models where offers are intermittent or the identity of the proposer is persistent. This shows that weighted Raiffa solutions have cooperative foundations closely related to those of the Kalai-Smorodinksy solution, and non-cooperative foundations closely related to those of the Nash solution. The fourth chapter is closely related to the third chapter and is joint work with Bram Driesen and Peter Eccles. It provides a non-cooperative foundation for asymmetric generalizations of the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Stahl-Rubinstein bargaining model, in which each player's opportunity to make proposals is produced by an independent Poisson process, and a definite deadline ends the negotiations. Under the assumption that future payoffs are not discounted, it is shown that the payoffs realized in the unique subgame perfect equilibrium of this game approach the continuous Raiffa solution as the time horizon tends to infinity. The weights reflecting the asymmetries among the players, correspond with the Poisson arrival rates of their respective proposal processesScalable games: modelling games of incomplete information / Nora Wegner and Peter Eccles. -- Robustness of Subgame Perfect Implementation / Nora Wegner and Peter Eccles. -- Generalised weighted Raiffa Solutions / Nora Wegner and Peter Eccles. -- A non-cooperative foundation for the continuous Raiffa solution / Nora Wegner, Bram Driesen and Peter EcclesPrograma Oficial de Doctorado en EconomíaPresidente: Christopher Wallace; Secretario: Miltiadis Makris; Vocal: Ludovic Reno

Iterated Kalai-Smorodinsky-Nash Compromise

In this paper, we present a new n-person bargaining solution, which we call Iterated Kalai-Smorodinsky-Nash Compromise. We show that this solution is the unique solution satisfying a new axiom called Kalai-Smorodinsky-Nash Decomposability

Iterated Kalai-Smorodinsky-Nash Compromise

In this paper, we present a new n-person bargaining solution, which we call Iterated Kalai-Smorodinsky-Nash Compromise. We show that this solution is the unique solution satisfying a new axiom called Kalai-Smorodinsky-Nash Decomposability

Value Focused Thinking in Developing Aerobatic Aircraft Selection Model for Turkish Air Force

The purpose of this research is to lessen the potential human errors by using decision analysis and cost analysis techniques. This research uses Value- Focused Thinking in conjunction with Multi-Objective Decision Analysis and Cost Analysis. It creates a decision-making model that allows decision makers to interact with analysts by specifying his/her objectives, values and preferences. On the other hand, cost analysis process determines cost effective alternatives. Alternatives are scored using 17 evaluation measures that are identified by interviews with the decision maker and stakeholders. Robustness of the model is tested by sensitivity analysis. Results of sensitivity analysis on current weights indicate that this model has robust results. Nevertheless, sensitivity analysis on cost indicates that many issues may influence the robustness of cost estimates and the best cost effective alternative

An Alternative Characterization for Iterated Kalai-Smorodinsky-Nash Compromise

In this paper, we offer for two-person games an alternative characterization of Iterated Kalai-Smorodinsky-Nash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$-person games. We present an axiom called Gamma-Decomposability, satisfied by any solution that is decomposable with respect to a given reference solution Gamma. We then show that the IKSNC solution is uniquely characterized by Gamma-Decomposability whenever Gamma satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry