As a result of the climate change the situation in Arctic area leads to several important consequences. On the one hand, fossil fuels can be exploited much easier than before. On the other hand, their excavation leads to serious potential threats to fishing by changing natural habitats which in turn creates serious damage to the countries’ economies. Another set of problems arises due to the extension of navigable season for shipping routes. Thus, there are already discussions on how should resources be allocated among countries. In Aleskerov and Victorova (An analysis of potential conflict zones in the Arctic Region, HSE Publishing House, Moscow, 2015) a model was presented analyzing preferences of the countries interested in natural resources and revealing potential conflicts among them. We present several areas allocation models based on different preferences over resources among interested countries. As a result, we constructed several allocations where areas are assigned to countries with respect to the distance or the total interest, or according to the procedure which is counterpart of the Adjusted Winner procedure. We consider this work as an attempt to help decision-making authorities in their complex work on adjusting preferences and conducting negotiations in the Arctic zone. We would like to emphasize that these models can be easily extended to larger number of parameters, to the case when some areas for some reasons should be excluded from consideration, to the case with ‘weighted’ preferences with respect to some parameters. And we strongly believe that such models and evaluations based on them can be helpful for the process of corresponding decision making.
We consider the problem of individual manipulation under incomplete information, when voters do not know a full preference profile. Instead, voters know the result of an opinion poll (the outcome of a poll information function π, e.g. a list of scores or a set of winners). In this case, a voter has an incentive to misrepresent her preferences (π-manipulate) if she knows that she will not become worse off and there is a chance of becoming better off. We consider six voting rules and eight types of poll information functions differing in their informativeness. To compare manipulability, first we calculate the probability that there is a voter which has an incentive to π-manipulate and show that this measure is not illustrative in the case of incomplete information. Then, we suggest considering two other measures: the probability of a successful manipulation and an aggregate stimulus of voters to manipulate, which demonstrate more intuitive behavior. We provide results of computational experiments as well as analytical proofs of some effects observed.
This paper provides an extended analysis of an equilibrium concept for non-cooperative games with boundedly rational players: Nash-2 equilibrium. Players think one step ahead and account for all profitable responses of player-specific subsets of opponents because of both the cognitive limitations on predicting everyone’s reaction and the inability to make deeper and certain predictions. They cautiously reject improvements that might lead to worse profits after some reasonable response. For n-person games we introduce the notion of a reflection network consisting of direct competitors to express the idea of selective farsightedness. For almost every 2-person game with a complete reflection network, we prove the existence of a Nash-2 equilibrium. Nash-2 equilibrium sets are obtained in models of price and quantity competition, and in Tullock’s rent-seeking model with two players. It is shown that such farsighted behavior may provide strategic support for tacit collusion. The analyses of n-person Prisoner’s dilemma and oligopoly models with a star reflection structure demonstrate some possibilities of strategic collusion and a large variety of potentially stable outcomes.
The paper studies group-separable preference profiles. Such a profile is group-separable if for each subset of alternatives there is a partition in two parts such that each voter prefers each alternative in one part to each alternative in the other part. We develop a parenthesization representation of group-separable domain. The precise formula for the number of group-separable preference profiles is obtained. The recursive formula for the number of narcissistic group-separable preference profiles is obtained. Such a profile is narcissistic group-separable if it is group-separable and each alternative is preferred the most by exactly one voter.
Since 9/11, terrorism has become a global issue of the twenty-first century. Terrorist organizations become important actors of world politics as they gain influence on political process and decision-making. Some organizations compete with each other in order to gain more power and influence. We study the distribution of power among terrorist groups using network approach and applying classic and new centrality indices (Short-Range (SRIC) and Long-Range interactions indices (LRIC)). These indices allow to identify terrorist groups with direct and indirect influence on the terrorist network.
Applying new preference diversity axiomatics, a generalization of the Alcalde-Unzu and Vorsatz (Soc Choice Welf 41(4):965–988, 2013) criterion is developed. It is shown that all previously used indices violate this criterion. Two new indices (geometric mean-based and leximax-based) that satisfy a new criterion are developed. Leximax-based orders act as a polarization index and are compared to the polarization index of Can et al. (Math Soc Sci 78:76–79, 2015). New impossibility results are obtained.