Cooperative games with overlapping coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

Loss aversion in an agent-based asset pricing model

A well-defined agent-based asset pricing model able to match the widely observed properties of financial time series is valuable for testing the implications of various biases associated with investors' behaviour. Extending one of the most successful models in capturing traders behaviour, we present a new behavioural agent-based asset pricing model. Specifically, we introduce a well-known behavioural bias in the model, loss aversion, and evaluate its implications. First, measuring how close the simulated time series are to its empirical counterparts, we show that the model with loss aversion better matches and explains the properties of real-world financial data, compared with the base model without the behavioural bias. Secondly, we assess the impact of different levels of loss aversion not only on the agents' switching mechanisms, but also on the properties of the time series generated by the model. We demonstrate how for different levels of the loss aversion parameter, the biased agents tend to be driven out of the market at different points in time. Since even the simplest strategies have been shown to survive the competition in an agent-based setting, we can link our findings with the behavioural finance literature, which states that investors' systematic biases lead to unexpected market behaviour, instabilities and systematic errors. Finally, we provide an in-depth analysis of the simulated time series and show the resulting dynamics replicate a rich set of the stylized facts including: absence of autocorrelation, heavy tails, volatility clustering and conditional heavy tails of returns, long memory of absolute returns, as well as volume–volatility relations, gain–loss asymmetry, power-law behaviour and long memory of volume

Trembling hand equilibria of plurality voting

Trembling hand (TH) equilibria were introduced by Selten in 1975. Intuitively, these are Nash equilibria that remain stable when players assume that there is a small probability that other players will choose off-equilibrium strategies. This concept is useful for equilibrium refinement, i.e., selecting the most plausible Nash equilibria when the set of all Nash equilibria can be very large, as is the case, for instance, for Plurality voting with strategic voters. In this paper, we analyze TH equilibria of Plurality voting. We provide an efficient algorithm for computing a TH best response and establish many useful properties of TH equilibria in Plurality voting games. On the negative side, we provide an example of a Plurality voting game with no TH equilibria, and show that it is NP-hard to check whether a given Plurality voting game admits a TH equilibrium where a specific candidate is among the election winners

Strategic voting with incomplete information

Classical results in social choice theory on the susceptibility of voting rules to strategic manipulation make the assumption that the manipulator has complete information regarding the preferences of the other voters. In reality, however, voters only have incomplete information, which limits their ability to manipulate. We explore how these limitations affect both the manipulability of voting rules and the dynamics of systems in which voters may repeatedly update their own vote in reaction to the moves made by others. We focus on the Plurality, Veto, k-approval, Borda, Copeland, and Maximin voting rules, and consider several types of information that are natural in the context of these rules, namely information on the current front-runner, on the scores obtained by each alternative, and on the majority graph induced by the individual preferences

An asset pricing model with loss aversion and its stylized facts

A well-defined agent-based model able to match the widely observed properties of financial assets is valuable for testing the implications of various empirically observed heuristics associated with investors behaviour. In this paper, we extend one of the most successful models in capturing the observed behaviour of traders, and present a new behavioural asset pricing model with heterogeneous agents. Specifically, we introduce a new be- havioural bias in the model, loss aversion, and show that it causes a major difference in the agents interactions. As we demonstrate, the resulting dynamics achieve one of the major objectives of the field, replicating a rich set of the stylized facts of financial data. In particular, for the first time our model enables us to match the following empirically observed properties: conditional heavy tails of returns, gains/loss asymmetry, volume power-law and long memory and volume-volatility relations

Administrative regulation of minimizing the causes of corruption in the social sphere

The problems of the progressive development of our society are dictated by the shortcomings of the legal, organizational anti-corruption, especially in the social sphere. This article is aimed at developing proposals to minimize the causes of corruption in the social sphere. The article notes that corruption, along with other reasons, entails negative consequences in the form of inefficient use of budget expenditures, which, according to the law, should have been aimed at solving important social issues, but they are not being addressed. Formed in the modern period, the decentralized nature of the management of the social sphere does not allow building a clear system of administrative opposition to the causes that determine corruption in the social sphere. Based on this, we believe that we should take a different approach to the development of administrative regulation of the fight against corruption in the social sphere, but for this it is necessary to know the causes and conditions that determine corruption in the social sphere, as well as the needs of the law enforcement practice to combat this phenomenon. The article reveals the possibilities of administrative means of combating corruption, as well as identifying and eliminating the causes and conditions that determine the level of corruption in the social sphere using legal and organizational means. Also, the essence of the legal and organizational support of the fight against corruption is revealed in the work, the types of organizational and legal means involved in the mechanism of ensuring the social function of the state are determined. This article was financially supported by the Ministry of Education and Science of the Russian Federation under the program to increase competitiveness of the Peoples' Friendship University of Russia (RUDN University) among the world's leading research and educational centers for 2016-2020

Multiwinner candidacy games

In strategic candidacy games, both voters and candidates have preferences over the set of possible election outcomes, and candidates may strategically withdraw from the election in order to manipulate the result in their favor. In this work, we extend the candidacy game model to the setting of multiwinner elections, where the goal is to select a fixed-size committee of candidates, rather than a single winner. We examine the existence and properties of Nash equilibria in the resulting class of games, under various voting rules and voter preference structures

Iterative voting and acyclic games

Multi-agent decision problems, in which independent agents have to agree on a joint plan of action or allocation of resources, are central to artificial intelligence. In such situations, agents' individual preferences over available alternatives may vary, and they may try to reconcile these differences by voting. We consider scenarios where voters cannot coordinate their actions, but are allowed to change their vote after observing the current outcome, as is often the case both in offline committees and in online voting. Specifically, we are interested in identifying conditions under which such iterative voting processes are guaranteed to converge to a Nash equilibrium state—that is, under which this process is acyclic. We classify convergence results based on the underlying assumptions about the agent scheduler (the order in which the agents take their actions) and the action scheduler (the actions available to the agents at each step). By so doing, we position iterative voting models within the general framework of acyclic games and game forms. In more detail, our main technical results provide a complete picture of conditions for acyclicity in several variations of Plurality voting. In particular, we show that (a) under the traditional lexicographic tie-breaking, the game converges from any state and for any order of agents, under a weak restriction on voters' actions; and that (b) Plurality with randomized tie-breaking is not guaranteed to converge under arbitrary agent schedulers, but there is always some path of better replies from any initial state of the game to a Nash equilibrium. We thus show a first separation between order-free acyclicity and weak acyclicity of game forms, thereby settling an open question from [Kukushkin 2011]. In addition, we refute another conjecture of Kukushkin regarding strongly acyclic voting rules, by proving the existence of strongly acyclic separable game forms

Doodle poll games

In Doodle polls, each voter approves a subset of the available alternatives according to his preferences. While such polls can be captured by the standard models of Approval voting, Zou et al. [18] analyse real-life Doodle poll data and conclude that poll participants' behaviour seems to be affected by considerations other than their intrinsic preferences over the alternatives. To capture this phenomenon, they propose a model of social voting, where voters approve their top alternatives as well as additional 'safe' choices so as to appear cooperative. The predictions of this model turn out to be consistent with the real-life data. However, Zou et al. do not attempt to rationalise the voters' behaviour in the context of social voting: They explicitly describe the voters' strategies rather than explain how these strategies arise from voters' preferences. In this paper, we complement the work of Zou et al. by putting forward a model in which the behaviour described by Zou et al. arises as an equilibrium strategy. In our model, a voter derives a bonus from approving each additional alternative, up to a certain cap. We show that trembling hand perfect Nash equilibria of our model behave consistently with the model of Zou et al. Importantly, placing a cap on the total bonus is an essential component of our model: in the absence of the cap, all Nash equilibria are very far from the behaviour observed in Doodle polls