### Article

## Fairness and efficiency in strategy-proof object allocation mechanisms

I consider the problem of allocating *N* indivisible objects among *N* agents according to their preferences when transfers are absent and an outside option may exist. I study the tradeoff between fairness and efficiency in the class of *strategy-proof* mechanisms. The main finding is that for *strategy-proof* mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) *ex-post efficiency* and *envy-freeness*, (2) *ordinal efficiency* and *weak envy-freeness,* and (3) *ordinal efficiency* and *equal division lower bound*. Result 1 is the first impossibility result for this setting that uses *ex-post efficiency *; results 2 and 3 are more practical than similar results in the literature. In addition, for N=3, I give two characterizations of the celebrated random serial dictatorship mechanism: it is the unique *strategy-proof*, *ex-post efficient* mechanism that (4) provides agents that have the same ordinal preferences with assignments not dominated by each other (*weak envy-freeness among equals*), or (5) provides agents that have the same cardinal preferences with assignments of equal expected utility (*symmetry*). These results strengthen the characterization by Bogomolnaia and Moulin (2001); result 5 implies the impossibility result by Zhou (1990).

The coalitional manipulability of voting rules for special case of coalition formation is studied by computer experiment. For the considered case, the coalition, upon manipulation, consists of agents with the same alternative on the first place in their orderings. Not necessary all agents of the manipulating coalition should report insincere preferences, i.e. manipulating agents can join others by adjusting the preferences. This makes the coalition formation more flexible, inducing the increase of the Nitzan-Kelly manipulability index by different value for different voting rules. Calculations are made for 3 alternatives for knows aggregation procedures.

We consider the problem of manipulability of social choice rules in the impartial anonymous and neutral culture model (IANC) and provide a new theoretical study of the IANC model, which allows us to analytically derive the difference between the Nitzan-Kelly index in the Impartial Culture (IC) and IANC models. We show in which cases this difference is almost zero, and in which the Nitzan-Kelly index for IANC is the same as for IC. However, in some cases this difference is large enough to cause changes in the relative manipulability of social choice rules. We provide an example of such cases.

The coalitional manipulability of 13 majoritarian aggregation schemes (voting rules) is studied by computational experiments. We consider a special case of coalition formation in which all agents of manipulating coalition report the same first-ranked alternative upon manipulation, i.e. a group of agents misrepresents their preferences and they agree that the same alternative will be on the first place of their insincere preferences. We find out that in most cases one of the least manipulable rules in this framework is Minimal Dominant Set, which was not among the least manipulable rules in the case of individual manipulation.

The problem of the manipulability of known social choice rules in the case of multiple choice is considered. Several concepts of expanded preferences (preferences over the sets of alternatives) are elaborated. As a result of this analysis ordinal and nonordinal methods of preferences expanding are defined. The notions of the degree of manipulability are extended to the case under study. Using the results of theoretical investigation, 22 known social choice rules are studied via computational experiments to reveal their degree of manipulability.

I argue that Friedrich von Hayek anticipated some major results in the theory of mechanism design. © 2015, Springer Science+Business Media New York.

Analysis of problems of utilization of oil associated gas is given. Method for optimal distribution of expenses to laying of gas pi peline, taking into account a financing from oil companies and possible participation of government, is proposed. A multi-criteria model for selection of optimal alternative of utilization of oil associated gas is given. Software is made implementing the developed algorithms.

Aleskerov et al. [1] and [2] estimated the degree of manipulability for the case of multi-valued choice (without using any tie-breaking rule) and for Impartial Culture (IC). In our paper, we address the similar question for the multi-valued choice and for Impartial Anonymous Culture (IAC). We use Nitzan-Kelly's (NK) index to estimate the degree of manipulability, which is calculated as the share of all manipulable voting situations, and calculate indices for 3 alternatives and up to 10000 voters. We have found that for the case of 3 alternatives Nanson's procedure shows the best results. Hare's procedure shows close, but a bit higher results. The worst aggregation procedure in terms of manipulability is Plurality rule. Additionally, it turned out that NK indices for IAC are smaller than NK indices for IC.

Smoking is a problem, bringing signifi cant social and economic costs to Russiansociety. However, ratifi cation of the World health organization Framework conventionon tobacco control makes it possible to improve Russian legislation accordingto the international standards. So, I describe some measures that should be taken bythe Russian authorities in the nearest future, and I examine their effi ciency. By studyingthe international evidence I analyze the impact of the smoke-free areas, advertisementand sponsorship bans, tax increases, etc. on the prevalence of smoking, cigaretteconsumption and some other indicators. I also investigate the obstacles confrontingthe Russian authorities when they introduce new policy measures and the public attitudetowards these measures. I conclude that there is a number of easy-to-implementanti-smoking activities that need no fi nancial resources but only a political will.

One of the most important indicators of company's success is the increase of its value. The article investigates traditional methods of company's value assessment and the evidence that the application of these methods is incorrect in the new stage of economy. So it is necessary to create a new method of valuation based on the new main sources of company's success that is its intellectual capital.