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Register a new userConversion/Preference Games
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Added by
Pierre Lescanne
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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We introduce the concept of Conversion/Preference Games, or CP games for short. CP games generalize the standard notion of strategic games. First we exemplify the use of CP games. Second we formally introduce and define the CP-games formalism. Then we sketch two `real-life applications, namely a connection between CP games and gene regulation networks, and the use of CP games to formalize implied information in Chinese Wall security. We end with a study of a particular fixed-point construction over CP games and of the resulting existence of equilibria in possibly infinite games.
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Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic People. Despot wants to make the set of possible Peoples behaviors as small as possible, while Tribune wants to make it as large as possible.An MMG is played by two players that alternately write matrices from some predefined finite sets. One wants to maximize the growth rate of the product, and the other to minimize it. We show that in general MMGs are undecidable in quite a strong sense.On the positive side, EGs correspond to a subclass of MMGs, and we prove that such MMGs and EGs are determined, and that the optimal strategies are simple. The complexity of solving such games is in NP&coNP.
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to nearby games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games.
Course assignment is a wide-spread problem in education and beyond. Often students have preferences for bundles of course seats or course schedules over the week, which need to be considered. The problem is a challenging distributed scheduling task requiring decision support. First-Come First-Served (FCFS) is simple and the most widely used assignment rule in practice, but it leads to inefficient outcomes and envy in the allocation. Recent theoretical results suggest alternatives with attractive economic and computational properties. Bundled Probabilistic Serial (BPS) is a randomized mechanism satisfying ordinal efficiency, envy-freeness, and weak strategy-proofness. This mechanism also runs in polynomial time, which is important for the large problem instances in the field. We report empirical results from a first implementation of BPS at the Technical University of Munich, which allows us to provide important empirical metrics such as the size of the resulting matching, the average rank, the profile, and the popularity of the assignments. These metrics were central for the adoption of BPS. In particular, we compare these metrics to Random Serial Dictatorship with bundle bids (BRSD). The BRSD mechanism is used to simulate the wide-spread First-Come First-Served (FCFS) mechanism and it allows us to compare FCFS (BRSD) and BPS. While theoretically appealing, preference elicitation is a major challenge when considering preferences over exponentially many packages. We introduce tools to elicit preferences which reduce the number of parameters a student needs to a manageable set. The approach together with BPS yields a computationally effective tool to solve course assignment problems with thousands of students, and possibly provides an approach for other distributed scheduling tasks in organizations.
One of the natural objectives of the field of the social networks is to predict agents behaviour. To better understand the spread of various products through a social network arXiv:1105.2434 introduced a threshold model, in which the nodes influenced by their neighbours can adopt one out of several alternatives. To analyze the consequences of such product adoption we associate here with each such social network a natural strategic game between the agents. In these games the payoff of each player weakly increases when more players choose his strategy, which is exactly opposite to the congestion games. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining an existence of a Nash equilibrium, also of a special type, is NP-complete. This implies the same result for a more general class of games, namely polymatrix games. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or, more generally, has no source nodes. For these three classes we determine the complexity of an existence of (a special type of) Nash equilibria. We also clarify for these categories of games the status and the complexity of the finite best response property (FBRP) and the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for the property of being a weakly acyclic game. A preliminary version of this paper appeared as [19].
Firms engaged in electronic commerce increasingly rely on machine learning algorithms to drive a wide array of managerial decisions. The goal of this paper is to understand how competition between firms affects their strategic choice of such algorithms. We model the interaction of two firms choosing learning algorithms as a game, and analyze its equilibria in terms of the resolution of the bias-variance tradeoffs faced by the players. We show that competition can lead to strange phenomena---for example, reducing the error incurred by a firms algorithm can be harmful to that firm---and provide conditions under which such phenomena do not occur. We also show that players prefer to incur error due to variance than due to bias. Much of our analysis is theoretical, but we also show that our insights persist empirically in several publicly-available data sets.
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