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Über dieses Buch

This textbook connects three vibrant areas at the interface between economics and computer science: algorithmic game theory, computational social choice, and fair division. It thus offers an interdisciplinary treatment of collective decision making from an economic and computational perspective. Part I introduces to algorithmic game theory, focusing on both noncooperative and cooperative game theory. Part II introduces to computational social choice, focusing on both preference aggregation (voting) and judgment aggregation. Part III introduces to fair division, focusing on the division of both a single divisible resource ("cake-cutting") and multiple indivisible and unshareable resources ("multiagent resource allocation"). In all these parts, much weight is given to the algorithmic and complexity-theoretic aspects of problems arising in these areas, and the interconnections between the three parts are of central interest.



Chapter 1. Playing, Voting, and Dividing

Playing, voting, and dividing are three everyday activities we all are familiar with. Having their personal chances of winning, their individual preferences, and their private valuations in mind, the players, voters, and dividers follow their individual strategies each. While everyone first and foremost is selfishly interested in his own advantage only, from the interplay of all actors’ individual interests, strategies, and actions there will emerge a collective decision, an outcome of the game with winnings or losings for all players, an elected president ruling over all voters, or a division of the goods among all parties concerned. By the end of the day, there will be winners and losers.
Jörg Rothe

Playing Successfully


Chapter 2. Noncooperative Game Theory

Playing is something profoundly human, and the ability to play is tightly tied to the intelligence of human beings, to their capability of thinking foresightedly and strategically, of choosing a particularly profitable move among all possible moves, of anticipating possible response moves by their adversaries, and thus to their capability of maximizing their own profit. By playing a game we here mean, in general, an interaction under preassigned rules, amongst several players each interested in maximizing their gains and acting strategically to this end. Games are encountered everywhere, be it as a party game, a card game, a computer game, or a game of hazard, be it as an individual or team sport such as chess, foil fencing, soccer, or ice hockey, be it companies organizing their strategies in a market economy, or states and other global players deciding on their geopolitical strategies.
Piotr Faliszewski, Irene Rothe, Jörg Rothe

Chapter 3. Cooperative Game Theory

This chapter provides an introduction to cooperative game theory, which complements noncooperative game theory (Chapter 2). Both of these fields study strategic aspects of cooperation and competition among the players. In noncooperative game theory, players are assumed to choose their actions individually, selfishly seeking to realize their own goals and to maximize their own profit. While this does not mean that players are necessarily adversarial to other players (for example, they may prefer the dove strategy over the hawk strategy in the chicken game), they are not interested in other players’ welfare.
Edith Elkind, Jörg Rothe

Voting and Judging


Chapter 4. Preference Aggregation by Voting

Anna, Belle, and Chris want to spend the afternoon together. They consider to either play miniature golf, or go on a bicycle tour, or go for a swim. However, they cannot come to an agreement, as not all of them have the same preferences.
Dorothea Baumeister, Jörg Rothe

Chapter 5. The Complexity of Manipulative Actions in Single-Peaked Societies

Anna and Belle, who now have become so aware of their role as guides in this book that they can even refer to the book’s content, meet on what will be a very exciting day for them. Let’s listen in on their conversation.
Edith Hemaspaandra, Lane A. Hemaspaandra, Jörg Rothe

Chapter 6. Judgment Aggregation

In Chapters 4 and 5, we were concerned with making collective decisions by voting, i.e., with methods for how to aggregate the voters’ individual preferences so as to determine the winning alternative(s) as a collective consensus. In the present chapter, we turn to the closely related topic of judgment aggregation, i.e., to methods for how to aggregate the individual judgments of a number of judges so as to determine the joint judgment(s) as a collective consensus.
Dorothea Baumeister, Gábor Erdélyi, Jörg Rothe

Fair Division


Chapter 7. Cake-Cutting: Fair Division of Divisible Goods

Everyone knows that whenever there is a party, there is also a variety of tastes. Each to his own, you may say—but what if you are the host? Wishing to keep everyone happy and to avoid arguments amongst the guests, a good host would offer a wide choice of food. But what if there is only a single wedding cake? Well, even a single cake may serve well to account for all the different tastes. There may be several layers of delicious sponge, tasty fresh strawberries, and even loads of cream and chocolate splits. It is easy to see that this cake would offer something for everyone—the fruit lover as well as the chocolate fanatic. The crucial bit, though, is that the host will have to divide the cake such that each guest receives a piece she is satisfied with. Even though this may sound easy at a first glance, it will soon become apparent that this is not necessarily the case. It can actually be quite a challenge to cut a single cake in a way such that everyone is happy with the piece received and does not envy anyone else for their portion.
Claudia Lindner, Jörg Rothe

Chapter 8. Fair Division of Indivisible Goods

Chapters 4, 5, and 6 focused on collective decision making problems (especially, voting) with the default assumption that all agents are concerned with the outcome as a whole, and therefore, all agents are expected to have, and to express, preferences over all alternatives.
Jérôme Lang, Jörg Rothe


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