Cooperative n-person Prisoner's Dilemma on a Network

In the paper n-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the in uence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.

Non-Zero Sum Network Games with Pairwise Interactions

In the paper non-zero sum games on networks with pairwise interactions are investigated. The first stage is network formation stage, where players chose their preferable set of neighbours. In all following stages simultaneous non-zero sum game appears between connected players in network. As cooperative solutions the Shapley value and τ -value are considered. Due to a construction of characteristic function both formulas are simpli ed. It is proved, that the coeffcient λ in τ -value is independent from network form and number of players or neighbours and is equal to 1/2 . Also it is proved that in this type of games on complete network the Shapley value and τ -value are coincide.

Computing the Price of Anarchy in Processor Load Balancing Game with Linear Delays

This paper considers a generalization of the processor load balancing game also known as KP-model. A linear delay of a processor may depend on not only its load but on loads of other processors. Players choose processors of different speeds to run their jobs striving to minimize job's delay, i.e., the job completion time on a chosen processor. The social cost is the maximum delay over all processors. We propose a computing algorithm of the exact PoA value which can be applied to estimate the POA visually if its exact analytical expression is not obtained yet or it is rather complicated to figure out its formula.

Computation Problems for Envy Stable Solutions of Allocation Problems with Public Resources

We consider generalizations of TU games with restricted cooperation in partition function form and propose their interpretation as allocation problems with several public resources. Either all resources are goods or all resources are bads. Each resource is distributed between points of its set and permissible coalitions are subsets of the union of these sets. Each permissible coalition estimates each allocation of resources by its gain/loss function, that depends only on the restriction of the allocation on that coalition. A solution concept of "fair" allocation (envy stable solution) was proposed by the author in (Naumova, 2019). This solution is a simplification of the generalized kernel of cooperative games and it generalizes the equal sacrifice solution for claim problems. An allocation belongs to this solution if there do not exist special objections at this allocation between permissible coalitions. For several classes of such problems we describe methods for computation selectors of envy stable solutions.

A Survey on Two Viruses Extensions of Epidemic Model with Continuous and Impulse Control

The current study represents a survey on several modifications of compartment epidemic models with continuous and impulse control policies. The main contribution of the survey is the modification of the classical Susceptible Infected Recovered (SIR) model with the assumption that two types of viruses are circulating in the population at the same time. Moreover, we also take into consideration the network structure of the initial population in two-virus SIIR models and estimate the e ectiveness of protection measures over complex networks. In each model, the optimal control problem has been formalized to minimize the costs of the virus spreading and find optimal continuous and impulse antivirus controllers. All theoretical results are corroborated by a large number of numerical simulations.

Dynamic Shapley Value in the Game with Perishable Goods

The paper investigates two-stage stochastic minimum spanning tree games with perishable goods. The cooperative behaviour of the players is defined. At each stage, all players jointly take action to construct a network with a cost matrix. At the second stage, a particular player may leave the game, and the probability of this leaving depends on the cooperative behaviour of all players at the first stage. At each stage game, the total cost of the spanning tree is calculated to include the sum of the costs of the contained edges and the cost of the loss of perishable goods expended on that edge of the spanning tree. The characteristic functions in the game are considered, and the dynamic Shapley values are modified. The time consistency of the dynamic Shapley values is studied.

Information Collecting and Dissemination in the Network of Taxpayers: Bayesian Approach

The current research is based on the assumption that the result of tax inspections is not only collection of taxes and fines. The information about audited taxpayers is also collected and helps to renew a priori knowledge of each agent's evasion propensity and obtain new a posteriori estimate of this propensity. In the beginning of the following tax period the fiscal authority can correct auditing strategy using updated information on every taxpayer. Each inspection is considered as a repeated game, in which the choice of agents to audit is associated with their revealed tendency to evade. Taxpayers also renew the information on the number of inspected neighbors using their social connections, represented by networks of various con gurations, and estimate the probability of auditing before the next tax period. Thus, the application of the Bayesian approach to the process of collecting and disseminating information in the network of taxpayers allows to optimize the audit scheme, reducing unnecessary expenses of tax authority and eventually increasing net tax revenue. To illustrate the application of the approach described above to the indicated problem, numerical simulation and scenario analysis were carried out.

Nash Bargaining Solution as Negotiation Concept for Resource Allocation Problem with Groves-Ledyard Mechanism

Motivated by research works on Zeuthen-Hicks bargaining, which leads to the Nash bargaining solution, we analyze experimental data of resource allocation gaming with Groves-Ledyard mechanism. The games were designed in the form of negotiation to allow players to reach consensus. Behavior models based on best response, constant behavior, and Nash bargaining solution are defined. Analysis conducted over decisions made by participants shows that a significant share of all decisions leads to an increase of the Nash bargaining value. It is even higher than the share of decisions that are in agreement with the best-response concept. Consensusended games show light attraction to the Nash bargaining solution, it's less than we obtained in games with the mechanism of Yang-Hajek from another class of so-called proportional allocation mechanisms. We discuss differences of consensus-ended games from timeout-ended games, what decisions lead to the situations with the Nash bargaining value increasing and differences between balanced mechanism Groves-Ledyard and unbalanced mechanism Yang-Hajek.

On the Existence and Determining Stationary Nash Equilibria for Switching Controller Stochastic Games

In this paper we consider the problem of the existence and determining stationary Nash equilibria for switching controller stochastic games with discounted and average payoffs. The set of states and the set of actions in the considered games are assumed to be finite. For a switching controller stochastic game with discounted payoffs we show that all stationary equilibria can be found by using an auxiliary continuous noncooperative static game in normal form in which the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players. Based on this we propose an approach for determining the optimal stationary strategies of the players. In the case of average payoffs for a switching controller stochastic game we also formulate an auxiliary noncooperative static game in normal form with quasi-monotonic payoffs and show that such a game possesses a Nash equilibrium if the corresponding switching controller stochastic game has a stationary Nash equilibrium.

Economic Capital Allocation for Corporate Borrowers Credit Risk Coverage

Both the estimation of economic capital for bank's credit risk coverage, and the allocation of economic capital by sources in order to determine the contribution of individual elements to total credit risk play an important role in the area of risk management of a bank. The estimation of a bank's economic capital for credit risk coverage serves as a starting point in the management of a bank's credit risk, while the allocation of economic capital to cover credit risk among individual elements allows to answer the question of how individual elements contribute to the total credit risk of a bank, which makes it possible to take certain decisions on credit risk management based on the obtained results of allocation. Nowadays, there are various theoretical methods and approaches to solve this nontrivial issue. The authors of the article attempted to implement them in practice, to estimate economic capital for credit risk coverage of a commercial bank and to allocate it among elements. This problem was solved applying the Euler allocation method and kernel regression.