Anarchy, state, and utopia

http://rcer.econ.rochester.edu/RCERPAPERS/rcer_578.pdf

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update

Lecture audiences and students were asked to respond to virtual decision and game situations at gametheory.tau.ac.il. Several thousand observations were collected and the response time for each answer was recorded. There were significant differences in response time across responses. It is suggested that choices made instinctively, that is, on the basis of an emotional response, require less response time than choices that require the use of cognitive reasoning.

/pdf/instinctive-and-cognitive-reasoning-a-study-of-response-50i40s4xfw.pdf

Instinctive and Cognitive Reasoning: A Study of Response Times

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

/pdf/handbook-of-computational-social-choice-12i1xbv1b8.pdf

Handbook of Computational Social Choice

The theory of cooperative games provides a rich mathematical framework with which to understand the interactions between self-interested agents in settings where they can benefit from cooperation, and where binding agreements between agents can be made. Our aim in this talk is to describe the issues that arise when we consider cooperative game theory through a computational lens. We begin by introducing basic concepts from cooperative game theory, and in particular the key solution concepts: the core and the Shapley value. We then introduce the key issues that arise if one is to consider the cooperative games in a computational setting: in particular, the issue of representing games, and the computational complexity of cooperative solution concepts.

/pdf/computational-aspects-of-cooperative-game-theory-22sw4t9fz8.pdf

Computational Aspects of Cooperative Game Theory

Cooperative Games with Crisp Coalitions.- Preliminaries.- Cores and Related Solution Concepts.- The Shapley Value, the ?-value, and the Average Lexicographic Value.- Egalitarianism-based Solution Concepts.- Classes of Cooperative Crisp Games.- Cooperative Games with Fuzzy Coalitions.- Preliminaries.- Solution Concepts for Fuzzy Games.- Convex Fuzzy Games.- Fuzzy Clan Games.- Multi-Choice Games.- Preliminaries.- Solution Concepts for Multi-Choice Games.- Classes of Multi-Choice Games.

Models in Cooperative Game Theory

We present a taxonomy of myopic stability concepts for hedonic games in terms of deviations, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and provide sufficient conditions for the existence of contractually Nash stable and weak individually stable coalition structures on the class of separable games.

A taxonomy of myopic stability concepts for hedonic games

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. It turns out that the first domain restriction guarantees non-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic games. Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an element of the weak core under enemies aversion is NP-hard. We examine also the relationship between our domain restrictions and some sufficient conditions for non-emptiness of the core already known in the literature.

Simple priorities and core stability in hedonic games

In this paper interval bankruptcy games arising from bankruptcy situations with interval claims are introduced. For this class of cooperative games two (marginal-based) Shapley-like values are considered and the relation between them is studied.

Shapley-like values for interval bankruptcy games

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. We characterize internally stable coalitions on the proposed domains and show how these characterizations can be used for generating a strict core element in the first case and a core element in the second case. Moreover, we prove that an element of the strict core under friends appreciation can be found in polynomial time, while finding an element of the core under enemies aversion is NP-hard.

https://www.econstor.eu/bitstream/10419/117928/1/NDL2004-051.pdf

Dinko Dimitrov

Papers

Models in Cooperative Game Theory

A taxonomy of myopic stability concepts for hedonic games

Simple priorities and core stability in hedonic games

Shapley-like values for interval bankruptcy games

Simple priorities and core stability in hedonic games