Последовательные труэли: равновесие с выживанием сильнейшего

A sequential truel is a generalisation of duel. This type of games is known because of the «survival of the weakest» paradox, where weakest player have the highest probability of survival. We analyse a typical variation of this model, in which players are allowed to shoot in the air. We show that there exists a SPE-equilibrium, where the strongest player, against the paradox statement, has the highest probability of survival

Achieving stability in heterogeneous societies: multi-jurisdictional structures, and redistribution policies

Consider a “linear world” populated by several agents. These agents’ locations are identified with optimal variety of a horizontally differentiated local public good. Agents are to be partitioned into several communities (hereafter, groups), and each group chooses a variety of public good to be produced and consumed by members of that group via the majority voting procedure. It is shown that a stable partition may fail to exist, where stability means that no potential group would like to secede and form a new community. At the same time, compensation schemes are proposed which guarantee the existence of a stable partition. Small societies are studied in detail, as well as certain special types of distributions of agents’ locations.Russia, stability, partitions, redistribution, core of a cooperative game

Strong equilibrium implementation for a principal with heterogeneous agents

The author models the interaction between the “Center”, represented by inspectors, and free riders in local trains (“hares” in the Russian slang). In order to characterize the optimal deterring strategy of the Center, one must look into the nature the interaction among parties in this game. After accomplishing this task, the author considers a more general class of phenomena that are intimately related to the one just described. Such phenomena will be analyzed in the framework of a “Center-offenders” model (a special case of the “Crime and Punishment” problem). The appropriate solution concept may be called a “natural Stackelberg solution”.

Stability and fairness in models with a multiple membership

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 projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus