Game theory

game theory

07261 Abstracts Collection -- Fair Division

From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 % generate automatically ``Fair Division\u27\u27 % generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Bankruptcy and Insolvency: An Exploration of Relevant Theories

The essence of the law on bankruptcy is to collect the debt of an entity and distribute such asset among the contending claimholders. It is, also meant to resolve the broad issues of business failure in the context of the imminent or indeed the actual collapse of the indebted entity. The objective of the study is to explore relevant theories guiding the procedure of distribution or entitlement in bankruptcy among a group of agents. The study employed exploratory research method via an extended literature review, to investigate the underlying principles guiding the allocation of a given amount of a perfectly divisible good among a group of agents. The results of this extended literature review indicate that the procedure of distribution or entitlement in bankruptcy is supported by five of the theories reviewed while only value based theory posits the absence of any cogent solution to the financial distress of the debtor. The knowledge of theories is not enough for business survival, the ability to predict the possible occurrence of business failures is necessary. Market based models including the stock market option valuation approach perform better than the earlier models which rely heavily on historical accounting figures. Keywords: Bankruptcy, Bankruptcy Theories, Exploratory Research, Genetic Programming Model JEL Classifications: G33, KII, K1

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

Ex-ante estate division under strong Pareto efficiency

The bankruptcy problem is to divide a homogeneous divisible good (the “estate”) between claimants, when the sum of the claims exceeds the value of the estate. When the problem is looked at from an ex-ante point of view (i.e. before the size of the estate is revealed), it is possible to formulate a notion of Pareto efficiency that is stronger than when the more common ex-post perspective is taken. Under the assumption of common beliefs, the strong notion of efficiency leads, in combination with the requirement that all claims should be fulfilled when the value of the estate is equal to the sum of the claims, to a uniquely defined division rule when utility functions for all agents are given. The resulting rule can be represented in the form of a parametric function. For the case in which all agents are equipped with the same utility function, the class of parametric functions that can be obtained in this way is characterized. In particular, it is shown that two well-known division rules for the bankruptcy problem, namely Constrained Equal Losses and Proportional Division, can be rationalized under strong Pareto efficiency by constant absolute risk aversion and constant relative risk aversion respectively.</p

Decision analysis in competitive and cooperative environments

This thesis contains three chapters in which we axiomatically analyze individual and collective decision problems in competitive and cooperative environments. In Chapter 1, we give a general introduction. In Chapter 2, we propose a theory of revealed preferences that allows both the status-quo bias and indecisiveness between any two alternatives. We extend a standard choice problem by adding a status-quo alternative and we incorporate standard choice theory as a special case. We characterize choice rules that satisfy two rationality requirements, status-quo bias, and strong SQ-irrelevance. In Chapter 3, we analyze bargaining situations where the agents' payoffs fromdisagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash. On our extended domain, we analyze the implications of two central properties which, on the Nash domain, are known to be incompatible: strong monotonicity and scale invariance. We characterize bargaining rules that satisfy strong monotonicity, scale invariance, weak Pareto optimality, and continuity. In Chapter 4, we analyze markets in which the price of a traded commodity is fixed at a level where the supply and the demand are possibly unequal. The agents have single peaked preferences on their consumption and production choices. For such markets, we analyze the implications of population changes as formalized by consistency and population monotonicity properties. We characterize trade rules that satisfy Pareto optimality, no-envy, and consistency as well as population monotonicity together with Pareto optimality, no-envy, and strategy-proofness