Logic for Automated Mechanism Design and Analysis

Computational social choice is a new interdisciplinary research area at the intersection of social choice theory and computer science that studies computational aspects of social choice mechanisms as well as applications of social choice ideas in the design and analysis of computing systems. Research on computational social choice now encompasses a variety of topics, including the algorithmic aspects of voting rules, computational barriers to strategic behaviour, collective decision-making in multi-agent systems, preference elicitation and communication issues in voting, fair division, computational aspects of weighted voting games, collective decision-making in combinatorial domains, logic-based formalisms for social choice problems, belief and judgement aggregation, and social software. The aim of this special issue is to build on the spectacular success of two workshops on computational social choice (COMSOC’06, Amsterdam and COMSOC’08, Liverpool), and provide a forum for reseachers in the area to present their ideas on a variety of topics. This special issue is composed of nine research articles and a short note that span a fairly wide range of issues, including voting, mechanism design, judgment aggregation, and fairness, and a similarly wide range of techniques, such as logic, experiments, and computational complexity. The paper by Agotnes, van der Hoek and Wooldridge defines a new modal logic for representing and reasoning about preference and judgment aggregation. The authors show that their logic can be used to express a variety of concepts and results from the social choice domain, including majority voting, the discursive paradox, Arrow’s theorem and Condorcet’s paradox. Baharad, Goldberger, Koppel and Nitzan propose a maximum likelihood estimation-based approach for aggregating voters’ opinions over several issues. They argue that their method is vastly superior to simple majority voting, and use both analytical and empirical evaluation to support their argument. Balan, Richards and Luke deal with the problem of selecting a sequence of actions when the actions have multiple beneficiaries. Their goal is to select the actions according to a lexicographic fairness criterion. The explore the complexity of this problem for both finite and infinite sequences of actions and present both algorithms and intractability results for this problem. The paper by Caminada and Pigozzi applies argumentation theory to judgment aggregation, and proposes aggregation operators satisfying not only the usual property of collective rationality, but another highly desirable property,

<p>One important issue in mechanism design theory is to model agents’ behaviors under uncertainty. The classical approach assumes that agents hold commonly known probability assessments towards uncertainty, which has been challenged by economists in many fields. My thesis adopts alternative methods to model agents’ behaviors. The new findings contribute to understanding how the mechanism designer can benefit from agents’ uncertainty aversion and how she should respond to the lack of information on agents’ probability assessments.</p> <p>Chapter 1 of this thesis allows the mechanism designer to introduce ambiguity to the mechanism. Instead of informing agents of the precise payment rule that she commits to, the mechanism designer can tell agents multiple payment rules that she may have committed to. The multiple payment rules are called ambiguous transfers. As agents do not know which rule is chosen by the designer, they are assumed to make decisions based on the worst-case scenario. Under this assumption, this chapter characterizes when the mechanism designer can obtain the first-best outcomes by introducing ambiguous transfers. Compared to the standard approach where the payment rule is unambiguous, first-best mechanism design becomes possible under a broader information structure. Hence, there are cases when the mechanism designer can benefit from introducing ambiguity.</p> <p>Chapter 2 assumes that the mechanism designer does not know agents’ probability assessments about others’ private information. The mechanisms designed to implement the social choice function thus should not depend on the probability assessments, which are called robust mechanisms. Different from the existing robust mechanism design literature where agents are always assumed to act non-cooperatively, this chapter allows them to communicate and form coalitions. This chapter provides necessary and almost sufficient conditions for robustly implementing a social choice function as an equilibrium that is immune to all coalitional deviations. As there are social choice functions that are only implementable with coalitional structures, this chapter provides insights on when agents should be allowed to communicate. As an extension, when the mechanism designer has no information on which coalitions can be formed, this chapter also provides conditions for robust implementation under all coalition patterns.</p> <p>Chapter 3 assumes that agents are not probabilistic about others’ private information. Instead, when they hold ambiguous assessments about others’ information, they make decisions based on the worst-case belief. This chapter provides necessary and almost sufficient conditions on when a social choice goal is implementable under such a behavioral assumption. As there are social choice goals that are only implementable under ambiguous assessments, this chapter provides insights on what information structure is desirable to the mechanism designer.</p>

The global economy is understood as an economy of information, knowledge, creativity, networks and services. The creation of value in the economy is involved in the economic, social and cognitive mechanisms. The economic mechanism emphasizes the processes of cooperation and production, the social mechanism, in turn, communication and marketing techniques, the cognitive mechanism is based on human imagination and interpretation. Under the cognitive mechanism is meant creativity, the ability to bring new motive, ideas. Cognitive mechanisms are in value creation process complementary to economic and social mechanisms and they are capable of producing value separately. One of the approaches to measuring creativity is to define and analyse creative industries. The creative industries are industries in which “combine and overlap the fields of art, culture, business and technology. They create a cycle of creation, production and distribution, using their intellectual capital as primary capital [1]. The contribution of the creative industry lies in its cross-sectoral dimension with minimal territorial constraints. The article will focus on the definition of creative industries and the analysis of creative industries in the Slovakia. The method used was the analysis of trends in the form of percentage year-on-year change. The creative industry is the sensitive on the state and development of the economy in Slovakia.

Intertwined coordination mechanisms in interorganizational relationships with dominated suppliers

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.

Algorithmic mechanism design considers distributed settings where the participants, termed agents, cannot be assumed to follow the protocol but rather their own interests. The protocol can be regarded as an algorithm augmented with a suitable payment rule and the desired condition is termed truthfulness, meaning that it is never convenient for an agent to report false information.Motivated by the applications, we extend the usual one-parameter and multi-parameter settings by considering agents with private capacities: each agent can misreport her cost for “executing” a single unit of work and the maximum amount of work that each agent can actually execute (i.e., the capacity of the agent). We show that truthfulness in this setting is equivalent to a simple condition on the underlying algorithm. By applying this result to various problems considered in the literature (e.g., makespan minimization on related machines) we show that only some of the existing approaches to the case “without capacities” can be adapted to the case with private capacities. This poses new interesting algorithmic challenges.

Much of the existing work in peer to peer networking assumes that users will follow prescribed protocols without deviation. This assumption ignores the user’s ability to modify the behavior of an algorithm for self-interested reasons. We advocate a different model in which peer to peer users are expected to be rational and self-interested. This model is found in the emergent fields of Algorithmic Mechanism Design (AMD) and Distributed Algorithmic Mechanism Design (DAMD), both of which introduce game-theoretic ideas into a computational system. We, as designers, must create systems (peer to peer search, routing, distributed auctions, resource allocation, etc.) that allow nodes to behave rationally while still achieving good overall system outcomes. This paper has three goals. The first is to convince the reader that rationality is a real issue in peer to peer networks. The second is to introduce mechanism design as a tool that can be used when designing networks with rational nodes. The third is to describe three open problems that are relevant in the peer to peer setting but are unsolved in existing AMD/DAMD work. In particular, we consider problems that arise when a networking infrastructure contains rational agents.KeywordsMechanism DesignNode TypeCombinatorial AuctionRational NodeFaulty NodeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Differential Neural Activation for Updating Rule versus Stimulus Information in Working Memory

We consider a social choice problem where individual rationality is required. The status quo belongs to the outcome space, and the selected alternative must be weakly better than the status quo for everybody. If the mechanism designer has no knowledge of the alternatives, we obtain a negative result: any individually rational (IR) and strategy-proof (SP) mechanism can choose at most one alternative (besides the status quo), regardless of the preferences. To overcome this negative result, we consider a domain where the alternatives have a known structure, i.e., an agent is indifferent between the status quo and a subset of the outcomes. This set is exogenously given and public information. This assumption is natural if the social choice involves the participation of agents. For example, consider a group of people organizing a trip where participation is voluntary. We can assume each agent is indifferent between the trip plans in which she does not participate and the status quo (i.e., no trip). In this setting, we obtain more positive results: we develop a class of mechanisms called Approve and Choose mechanisms, which are IR and SP, and can choose multiple alternatives as well as the status quo.

In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions.

Mechanism Design has been developed as a significant tool to model and analyze markets, economies, and societies in the real-world. On the Internet, however, we face some unexpected problems such as false-name manipulations, and traditional mechanism design does not work sufficiently. In this thesis, we will develop mechanism design into a more applicable theory for computer sciences and economics on the Internet. Specifically, we characterize social choice mechanisms that are robust against false-name manipulations.

Suppose a "democratic" society must decide between several options, but the members of society do not unanimously agree on the desirability of the different options. Each member has his or her own ranking, and the goal is to transform this set of preference orders into a single preference order for society as a whole. The top-ranked outcomes according to that social order is what one calls a social choice rule. Ideally a social choice rule should have various desirable features, such as being nondictatorial (the social choice rule does not simply select one person's ranking and ignore the others) and monotonic (if one individual promotes an option on his or her ranking, the societal ranking of this option should not go down). In 1972 Kenneth Arrow won the Nobel Prize in economics for his work on social choice theory, in particular his "impossibility theorem." This theorem states that if society consists of at least two people and there are at least three options to rank, then it is impossible to design a social choice rule that simultaneously satisfies a particular set of desirable features including those mentioned above. In spite of this, choices must be made and a variety of social choice rules have been designed for combining individual preferences into a collective agreement, each having certain limitations. But even once we decide on a particular rule, implementing it in the real world can be a challenge. Consider a multipass voting system---for example, the American system of primary elections followed by the general election between winners of the primary. Just this spring the state of Washington overhauled its primary system to require voters to choose one party's ballot before they can vote, rather than putting candidates of all political parties on the same ballot and letting voters pick and choose among them for each office. The fear with the old system was that voters would misrepresent their own desires in the primary election, in hopes of getting a more easily defeated opposition candidate on the general electionballot. On the other hand, independent-minded voters (of which there are many in Washington state) criticize the new system for not allowing them to express their true preferences for each office. Even when members of society do not intentionally misrepresent their own preferences, decision makers in the real world must always work with incomplete information about the state of the world and people's priorities. The goal of implementation theory is to study the extent to which it is possible to implement a desired social choice rule under various assumptions on the preferences and behavior of members of society. In the following paper, Roberto Serrano, of the Economics Department at Brown University, presents a survey of implementation theory and mathematical results obtained using game theory. The theory is illustrated with a number of interesting examples covering everything from voting and public decision making to King Solomon's dilemma. For more on the subject of voting, please note that this issue contains a related paper in the Problems and Techniques section, "Single Transferable Votes with Tax Cuts," by Eivind Stensholt.

Minimality is usually a desired property of social laws. From the perspective of game theory, minimality closely relates to the concept of maximum social welfare and synthesizing a minimal social law can be modeled as an efficient mechanism design problem. We are required not only to find out the efficient social laws for the objective, but also to formulate the right payment for the agents to induce incentive compatibility and individual rationality. We firstly design a mechanism for this setting based on vcg mechanisms, prove that it satisfies all the required formal properties but suffers from overpayment and false-name manipulation. To solve this problem, we then propose a core-selecting mechanism which is proved to be false-name proof and requires less payment.

Arrow’s celebrated general possibility theorem essentially shows that certain value judgments which we might find fair to incorporate in a social choice mechanism are logically inconsistent. Since the Pareto condition (which simply says that given two alternative social states, a and b, if every individual strictly prefers a to b, then they collectively also strictly prefer a to b), is ethically a compelling normative condition especially in the framework where social choice is based only on the individual’s utility information, one must look at the remaining criteria, i.e., independence of irrelevant alternatives (what Blair and Pollak in the previous chapter called pairwise determination) and transitive rationality. It is now well established that in the absence of the condition of independence of irrelevant alternatives an aggregation procedure is vulnerable to the strategic manipulation, that is, an individual by misrevealing his true or sincere preferences can influence the social outcome in his own advantage. Hence, the relaxation of the transitive rationality requirement becomes the central aspect of the social choice literature.

Choosing social laws for multi-agent systems: Minimality and simplicity