Non-cooperative Equilibrium Research Articles

Modeling collaborative data service provision around an open source platform under uncertainty with stochastic provision games

This paper uses concepts taken from Cooperative Game Theory to model the incentives to join forces among a group of agents involved in collaborative provision of a mobile app under uncertainty around an open source platform. Demand uncertainty leads the agents to reach a noncooperative equilibrium by offering low quality apps. This can be avoided by introducing a coordination scheme through a common platform that eliminates the effects of lack of information. Coordination is achieved by providing a revenue sharing scheme enforcing the stability of the collaboration but also defined in a “fair” way, depending on the importance of the resources that each provider supplies to the app. To this aim, we introduce the concept of Stochastic Provision Games. This coordination leads both to higher app quality and improved profitability for the participants.

Modeling the initiation and propagation of complex networks of cracks in reinforced concrete plates

The present paper proposes a new finite element formulation for the analysis of RC slabs, accounting for concrete cracking and reinforcement yielding. The proposed formulation, developed within the framework of Lumped Damage Mechanics, considers that all inelastic effects are localized in lines and relates all numerical parameters to the mechanical properties of the slab. The proposed variational approach is presented as a Nash noncooperative equilibrium point. It is verified, numerically, that the proposed FE leads to mesh-independent results. Numerical simulations of some experimental tests are also presented. The results in terms of collapse mechanism, cracking network, and force-deflection curves showed that the model has significant accuracy, even for non-symmetric free clamped and simple supported boundary conditions. It is also shown, through the confrontation with experimental results, that the model correctly characterizes the initiation and development of complex networks of cracks.

Double markups under bilateral vertical contracting

This paper examines price markups at the upstream and downstream levels of a bilateral vertical structure in which firms provide essential inputs to one another and engage in price competition in the downstream market. We show that the ratios of noncooperative equilibrium markups are primarily determined by the price elasticities of demand and the retail pass-through rates and, moreover, that coordination on input prices leads to a collusive equilibrium outcome in the final-product market.

Global shocks, budgets deficits, and international fiscal policy coordination

AbstractA simple two‐country model with trade, fiscal and interest rate externalities is used to study strategic interactions between national policymakers. Optimal fiscal policy internalizes a trade‐off between output stability and fiscal stability. With lump‐sum taxation, the noncooperative equilibrium is inefficient and both countries are better off under coordination. These results also hold if taxation is distortionary and trade generates a fiscal externality as well, regardless of how strong the preference for output stability is. In response to a negative global demand shock, consistent with the disruptions that occurred during the recent pandemic, the optimal policy response is to increase spending by more under cooperation. However, if budget deficits generate a sufficiently strong negative cross‐border externality through higher interest rates, the optimal response calls for lower spending under cooperation.

Protection Without Discrimination

Abstract This paper shows that non-tariff measures may fully respect the non-discrimination principle of the World Trade Organisation and still act as a protectionist device. Non-tariff measures that raise costs of all firms induce some exit, reallocating market shares towards the most efficient firms. The paper analyses when this mechanism generates protectionism. With political economy motives, trade liberalisation increases the use of non-tariff measures in the non-cooperative equilibrium and a trade agreement may be welfare reducing if governments care about the most efficient firms only. Moreover, a Pareto improving agreement may require an income redistribution between countries if firm average productivity differs across countries.

Monetary and macroprudential policy interactions in a model of the euro area

We use the two-country euro area model developed by Quint and Rabanal (2014) to study policymaking in a monetary union. We focus on: 1) a two-policymaker setting where there is strategic interaction between a single monetary authority and an EMU-level macro-prudential authority, and; 2) a three-policymaker setting where there is strategic interaction between a single monetary authority and two regional-level macroprudential authorities. In the former, price stability and financial stability are pursued at the area-wide level, while in the latter each macro-prudential authority adopts region-specific objectives. We compare cooperative and non-cooperative equilibria in simultaneous-move and leadership environments, each obtained assuming discretionary policymaking. In the two-policymaker setting, we find that the gains from either the monetary authority or the macroprudential regulator having a first-mover, or leadership, advantage are somewhat limited, and the most favorable outcome is achieved under cooperation where both policies are formulated and conducted simultaneously. In the three-policymaker setting, we find that delegating macroprudential policy to regional macroprudential regulators plays an important role in achieving regional stability.

Market size asymmetry and strategic environmental policy in a Cournot model

The achievement of Sustainable Development Goals (SDG) related to the environment requires identifying new sources of environmental degradation. This paper analyzes how market size asymmetry affects government decisions on environmental policy in the context of bilateral international trade and imperfect competition. We model an international duopoly with market size asymmetry and product heterogeneity. Each firm produces two different products, one for the domestic and one for the foreign markets, where the firms' production generates local emissions. When planning policies, the government in each country must choose between two options: an emission tax or a production subsidy. The findings of our paper underline the crucial role of market size asymmetry in determining the non-cooperative equilibrium policy in a setting where both firms and governments act strategically. We find that an increase in market size asymmetry between countries encourages governments to shift from emission taxes to production subsidies. Therefore, the environmental policy must consider these aspects to achieve greater effectiveness of regulation in favor of the environment. Actions to mitigate increased pollution should regulate production subsidies and improve the practices of governments and companies.

КОНКУРЕНЦИЯ И СОТРУДНИЧЕСТВО НА РЫНКЕ ТОВАРОВ С НАСЫЩАЕМЫМ СПРОСОМ

The article considers options for achieving market equilibrium in the oligopolistic market of goods with saturated demand. Cooperation and competition of oligopolistic producers are the most important factors influencing the characteristics of the market in question. The article developed a game theoretic model of such a market, and with its help various options for interaction between manufacturers were investigated. It has been established that the main parameters affecting the position of the manufacturer on the market are its production capabilities and the level of technologies used. It has been shown that non-cooperative equilibrium in such a market is possible only if strict antitrust measures are observed. Characteristics of such equilibrium were found. Various options for cooperative behavior of manufacturers have been investigated. With the help of the model proposed in the work, it is shown that on the studied market from a game theoretical point of view it is possible to appear equilibrium states of different nature: equilibrium by Stackelberg and Nash, as well as strong equilibrium. The article identifies the states under which these conditions arise in the market, and identifies the characteristics of these equilibrium states. The possibility of achieving market equilibrium based on threats has been studied separately. It has been established that the ratio of production capabilities of oligopolists who are market participants plays a decisive role in achieving a stable market state.

Collective Action and Intra-group Conflict with Fixed Budgets

ABSTRACT We study collective action under adverse incentives: each member of the group has a given budget (‘use-it-or-lose-it’) that is private information and can be used for contributions to make the group win a prize and for internal fights over this very prize. Even in the face of such rivalry in resource use, the group often succeeds in overcoming the collective action problem in the non-cooperative equilibrium. In one type of equilibrium, all group members jointly contribute; in the other type of equilibrium, volunteers make full standalone contributions. Both types of equilibrium exist for larger and partially overlapping parameter ranges.

Politically influenced counterterrorism policy and welfare efficiency

The paper examines how two targeted countries strategically deploy their counterterror forces when lobbying defense firms influence counterterror provision. For proactive measures, lobbying activities in a single targeted country lessen underprovision, raise overall counterterrorism, and reduce terrorism. Welfare decreases in the lobbied country but increases in the other targeted country owing to enhanced free riding. Lobbying influence on the targeted countries' welfare is tied to terrorists' targeting preferences and how the lobbied government weighs citizens’ welfare. Lobbying in both targeted countries may result in the first-best equilibrium. International policy coordination may lead to less efficient outcomes than the noncooperative equilibrium.

Existence and Stability of Weakly Cooperative Equilibria and Strong Cooperative Equilibria of Multi-Objective Population Games

Motivated by the concept of cooperative equilibria with a single objective, we introduce the concepts of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. We give some examples to explain the difference between the cooperative equilibrium point and noncooperative equilibrium point of multi-objective population games. Under appropriate assumptions, we study the existence and stability of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games.

The Sustainable Supply Chain Network Competition Based on Non-Cooperative Equilibrium under Carbon Emission Permits

Under the background of a circular economy, this paper examines multi-tiered closed-loop supply chain network competition under carbon emission permits and discusses how stringent carbon regulations influence the network performance. We derive the governing equilibrium conditions for carbon-capped mathematical gaming models of each player and provide the equivalent variational inequality formulations, which are then solved by modified projection and contraction algorithms. The numerical examples empower us to investigate the effects of diverse carbon emission regulations (cap-and-trade regulation, mandatory cap policy, and cap-sharing scheme) on enterprises’ decisions. The results reveal that the cap-sharing scheme is effective in coordinating the relationship between system profit and carbon emission abatement, while cap-and-trade regulation loses efficiency compared with the cap-sharing scheme. The government should allocate caps scientifically and encourage enterprises to adopt green production technologies, especially allowing large enterprises to share carbon quotas. This study can also contribute to the enterprises’ decision-making and revenue management under different carbon emissions reduction regulations.

Stationary Markov Nash Equilibria for Nonzero-Sum Constrained ARAT Markov Games

We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff functions and the density function of the transitions of the system, we establish the existence of a constrained stationary Markov Nash equilibrium, that is, the existence of stationary Markov strategies for each of the players yielding an optimal profile within the class of all history-dependent profiles.

A Multi-Agent Motion Prediction and Tracking Method Based on Non-Cooperative Equilibrium

A Multi-Agent Motion Prediction and Tracking method based on non-cooperative equilibrium (MPT-NCE) is proposed according to the fact that some multi-agent intelligent evolution methods, like the MADDPG, lack adaptability facing unfamiliar environments, and are unable to achieve multi-agent motion prediction and tracking, although they own advantages in multi-agent intelligence. Featured by a performance discrimination module using the time difference function together with a random mutation module applying predictive learning, the MPT-NCE is capable of improving the prediction and tracking ability of the agents in the intelligent game confrontation. Two groups of multi-agent prediction and tracking experiments are conducted and the results show that compared with the MADDPG method, in the aspect of prediction ability, the MPT-NCE achieves a prediction rate at more than 90%, which is 23.52% higher and increases the whole evolution efficiency by 16.89%; in the aspect of tracking ability, the MPT-NCE promotes the convergent speed by 11.76% while facilitating the target tracking by 25.85%. The proposed MPT-NCE method shows impressive environmental adaptability and prediction and tracking ability.

Global Lending Conditions and International Coordination of Financial Regulation Policies

Using a model of strategic interactions between two countries, I investigate the gains to international coordination of financial regulation policies, and how these gains depend on global lending conditions. When global lending conditions are determined non-cooperatively, I show that coordinating regulatory policies leads to a Pareto improvement relative to the case of no cooperation. In the non-cooperative equilibrium, one region - the core - determines global lending conditions, leaving the other region - the periphery - in a sub-optimal situation. The periphery then tightens regulatory policy to reduce the cost of sub-optimal lending conditions. Yet, in doing so, it fails to internalise a cross-border externality: tightening regulatory policy in one region limits ex ante borrowing in the other region, which increases the cost of sub-optimal lending conditions for the periphery. The equilibrium with cooperative regulatory policies can then improve on this outcome as both regions take into account the cross-border externality and allow for larger ex ante borrowing, ending in a lower cost of suboptimal lending conditions for the periphery.

Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games

In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

Mobility Choices and Strategic Interactions in a Two-Group Macroeconomic-Epidemiological Model.

We analyze the implications of strategic interactions between two heterogeneous groups (i.e., young and old, men and women) in a macroeconomic–epidemiological framework. The interactions between groups determine the overall prevalence of a communicable disease, which in turn affects the level of economic activity. Individuals may lower their disease exposure by reducing their mobility, but since changing mobility patterns is costly, each group has an incentive to free ride negatively affecting the chances of disease containment at the aggregate level. By focusing on an early epidemic setting, we explicitly characterize the cooperative and noncooperative equilibria, determining how the inefficiency induced by noncooperation (i.e., failure to internalize epidemic externalities) depends both on economic and epidemiological parameters. We show that long-run eradication may be possible even in the absence of coordination, but coordination leads to a faster reduction in the number of infectives in finite time. Moreover, the inefficiency induced by noncooperation increases (decreases) with the factors increasing (decreasing) the pace of the disease spread.

An Interactive Self-Learning Game and Evolutionary Approach Based on Non-Cooperative Equilibrium

Most current studies on multi-agent evolution based on deep learning take a cooperative equilibrium strategy, while interactive self-learning is not always considered. An interactive self-learning game and evolution method based on non-cooperative equilibrium (ISGE-NCE) is proposed to take the benefits of both game theory and interactive learning for multi-agent confrontation evolution. A generative adversarial network (GAN) is designed combining with multi-agent interactive self-learning, and the non-cooperative equilibrium strategy is well adopted within the framework of interactive self-learning, aiming for high evolution efficiency and interest. For assessment, three typical multi-agent confrontation experiments are designed and conducted. The results show that, first, in terms of training speed, the ISGE-NCE produces a training convergence rate of at least 46.3% higher than that of the method without considering interactive self-learning. Second, the evolution rate of the interference and detection agents reaches 60% and 80%, respectively, after training by using our method. In the three different experiment scenarios, compared with the DDPG, our ISGE-NCE method improves the multi-agent evolution effectiveness by 43.4%, 50%, and 20%, respectively, with low training costs. The performances demonstrate the significant superiority of our ISGE-NCE method in swarm intelligence.

Modeling of localization using Nash variational formulations: The extended damage mechanics

It is assumed in this paper that energy dissipation is a two-phase phenomenon. During the pre-localization stage, dissipation is a continuous process. After localization, it is lumped in surfaces of zero volume. To describe this process, it is proposed a new formulation called extended damage mechanics. The new framework incorporates the additional terms of lumped energy dissipation into a weak form of the damage evolution law. The variational formulation allowing for this approach characterizes the solution as a non-cooperative equilibrium point. This concept is also named after its inventor, the mathematician John Forbes Nash, as Nash point. Finally, numerical implementation of the extended damage mechanics is performed to describe the objectivity of the numerical simulations with respect to the finite element meshes in some practical cases of solids and structures.

Allocating positions fairly: Auctions and Shapley value

We study the problem of fairly allocating heterogenous items, priorities, positions, or property rights to participants with equal claims from three perspectives: cooperative, decision theoretic, and non-cooperative. We characterize the Shapley value of the cooperative game and then introduce a class of auctions for non-cooperatively allocating positions. We show that for any auction in this class, each bidder obtains his Shapley value when every bidder follows the auction's unique maxmin perfect bidding strategy. When information is incomplete we characterize the Bayesian equilibrium of these auctions, and show that equilibrium play converges to maxmin perfect play as bidders become infinitely risk averse. The equilibrium allocations thus converges to the Shapley value allocation as bidders become risk averse. Together these results provide both decision theoretic and non-cooperative equilibrium foundations for the Shapley value in the position allocation problem.