Alexei Savvateev

Center for engineering and technology | MIPT · Department of Applied Mathematics

The geometric median of a domain is the point that minimises the average distance from itself to the points of the domain. We will give a gradient system of equations that defines the geometric median of a triangular domain and will prove a simple geometric property of the median. This property states that all three average distances from the media...

We discuss the development of fundamentally new theoretical ideas stated by V. L. Makarov in his article "The calculus of institutions". Some of them have already been implemented for different applied issues. Other ideas have a more debatable nature and require further development and testing on empirical data. In this paper, we pay the main atten...

This paper examines Nash jurisdictional stability in a model with a continuum of agents whose characteristics are distributed over a unidimensional interval. Communal benefits and costs of each individual depend on her identity and the composition of the community which she belongs to. Since the framework is too general to yield an existence of Nas...

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When project...

Consider a finite population located along the real line, which generates a demand for public facilities. The set-up cost of each facility is the same and is given by a positive constant. In addition to contributing towards the facility cost, every user bears transportation cost to the facility location. These are classical prerequisites for the Un...

In this note, we propose a formula for the subdifferential of the maximum functional $m(f) = \max_K f$ on the space of real-valued continuous functions $f$ defined on an arbitrary metric compact $K$. We show that, given $f$, the subdifferential of $m(f)$ always coincides with the set of all probability measures on the arg-maximum (the set of all po...

Consider a population of citizens uniformly spread over the entire plane. The population faces a problem of locating public facilities financed by its users, who face an idiosyncratic private access cost to the facility. We show that, under mild assumptions, an external intervention that covers a tiny portion of the facility cost is sufficient to g...

This paper examines a model of multijurisdiction formation where individuals' characteristics are uniformly distributed over a finite interval. Every jurisdiction locates a public facility and distributes its cost equally among the residents. We consider the notions of Nash and local Nash stability, and examine the existence and characterization of...

We consider a model of the world with several regions that may create a unified entity or be partitioned into several unions (countries). The regions have distinct preferences over policies chosen in the country to which they belong and equally share the cost of public policies. It is known that stable political maps or country partitions, that do...

In this paper we consider a model with multiple jurisdictions where each formed jurisdiction selects a public project from the given uni-dimensional set, equally shares its cost among its members and places the project at the location of its median resident. We examine a cooperative concept of core stability and a non-cooperative notion of Nash sta...

This paper examines the structure and direction of developing Asia’s trade over the past two decades. The impacts on developing Asia of the economic slowdown in 2009–2010 in high-income countries of the Organization for Economic Cooperation and Development (OECD), which includes the European Union (EU), Japan, and United States (US) are projected t...

In this paper, we consider a population represented by a continuum of individuals uniformly distributed over the unit interval that faces a problem of location and financing of public facilities under the equal share rule. We examine three notions of stability of emerging jurisdiction structures (stability under unanimous consent, free mobility and...

In this note we consider a society that partitions itself into disjoint jurisdictions, each choosing a location of its public project and a taxation scheme to finance it. The set of public project is multi-dimensional, and their costs could vary from jurisdiction to jurisdiction. We impose two principles, egalitarianism, that requires the equalizat...

In this note we consider a society that partitions itself into disjoint jurisdictions, each choosing a location of its public project and a taxation scheme to finance it. The set of public project is multi-dimensional, and their costs could vary from jurisdiction to jurisdiction. We impose two principles, egalitarianism, that requires the equalizat...

This paper examines a model of multi-jurisdictional formation where individuals' characteristics are uniformly distributed over the finite interval. Every jurisdiction chooses a location of a public good and equally shares the cost of production among its residents. We consider two notions of stability: Nash stability and its refinement — local sta...

We consider a finite society with of individuals distributed along the real line. The individuals form jurisdictions to consume public projects, equally share their costs and, in addition, bear a transportation cost to the location of the project. We examine a core and Nash notions of stable jurisdiction structures and show that in hedonic games bo...

We calculate the equilibrium fraction of cooperators in a population in which payoffs accrue from playing a single-shot prisoner’s dilemma game. Individuals who are hardwired as cooperators or defectors are randomly matched into pairs, and cooperators are able to perfectly find out the type of a partner to a game by incurring a recognition cost. We...

The paper analyses preferences of private owners over the degree of property rights protection. It is shown that inequality in resource ownership and/or relative inefficiency of production technologies could make wealthier agents favour less than full protection of property rights. If such agents control the choice of a property rights regime, full...

Cheating is a serious problem in many countries. The cheater gets higher marks than deserved, thus reducing the efficiency of a country’s educational system. In this study, the authors did not ask if and how often the student had cheated, but rather what the student’s opinion was about a cheating situation. They investigated whether attitudes d...

We consider the model of jurisdiction formation of Alesina and Spolaore (1997) and Le Breton and Weber (2003). In each jurisdiction, the cost of providing the public good is divided equally among residents and the level of provision is selected through major- ity voting. This coalition formation game is hedonic since once a group of individuals has...

We consider a jurisdiction formation problem on the plane uniformly populated by a continuum of agents. This could be interpreted either as a real two-dimensional space where these agents live, or alternatively as a space of pairs of the two parameters of a public good on which the agents may have horizontally dierentiated preferences. In the latte...

Abstract The paper introduces and analyses a certain class of implementa- tion contracts for the Principal with heterogeneous agents, which are called multistep strategies. These contracts tie the agents’ choices to- gether in a manner that results in a strong equilibrium to be the out- come of the agents’ strategic interaction. Implementation cont...

We consider a jurisdiction formation problem on the plane uniformly populated by a continuum of agents. This could be interpreted either as a real two-dimensional space where these agents live, or alternatively as a space of pairs of two parameters of a public good on which the agents may have horizontally dierentiated preferences, in which case an...

The paper presents sucient conditions for group strategy-proofness in mechanism design and multi-agency problems. These conditions are Spence-Mirrlees single crossing property on the agents' preferences profiles and order semi-invariance and payo complementarity of proposed incentive schemes. Applications include serial cost sharing of non-convex p...