Non-cooperative Nash Equilibrium Research Articles

Industrialization, environmental externality, and climate mitigation strategies

This study proposes a 12-region global modeling framework that integrates industrialization into climate–economy interactions and applies it to explore national strategic interactions and long-term policy outcomes. In this regard, three policy regimes are considered: a non-cooperative Nash equilibrium and two cooperative regimes that maximize the weighted sum of regional welfare. Negishi weights, ensuring uniform carbon price, and equal weights are applied in cooperative setting. Based on the results, global unmitigated emissions will peak around 2040. Given the future industrialization process, developing countries will make greater mitigation efforts under all regimes, whereas the strategies of developed countries will only be affected under the uniform carbon price regime. In the two cooperative regimes, a clear separation of mitigation efforts is observed between developed and developing countries. Moreover, when accounting for industrialization, the global averaged carbon price should grow faster in the first half-century, followed by a period of slower growth. Sensitivity analysis implies that with the support from developed countries, accelerated industrialization in the developing world can help alleviate its environmental strain.

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.

Trade wars and trade disputes: The role of equity and political support

AbstractRecent theoretical and quantitative analysis of trade wars is grounded in a relatively narrow treatment of optimal tariff theory and noncooperative Nash equilibria. The lynchpin of this approach is the assumption that trade policy makers are rational and have a simple well‐established objective function to optimize. We argue that the preferred specification of this objective function ignores inequality at its peril. We work with a quantitative trade model, introducing a comprehensive tariff‐space grid search new to the literature. This allows us to explicitly check for the presence of multiple Nash outcomes. We show that including income inequality—a primary focus of the earlier literature—as a determinant of social welfare can substantially change noncooperative Nash outcomes. We also show that the optimal tariff of the US falls by half when the social welfare function includes inequality as an objective. Hence, the economic outcomes of actual trade wars may be very different from what recent estimates grounded in optimal tariff theory would suggest.

Economic analysis of the 12th man: Should the fans be paid?

The paper provides a theoretical sports league model to study the pricing of tickets. It considers the trade-off between maximizing match day revenues, through high prices, and maximizing the support of the most demonstrative fans, through low prices. These spectators, the “ultras” contribute to the competitive level of the club along with team-level talent, and therefore indirectly increase the number of victories, hence the revenue from TV rights. We model the role of effusive spectators and show that, in a non-cooperative Nash equilibrium, it may be optimal for the club to subsidize their presence in order to take full advantage of the 12th man effect.

Inventory competition on electronic marketplaces – A competitive newsvendor problem with a unilateral sales commission fee

We present a competitive newsvendor problem with a sales commission paid by one newsvendor to another newsvendor when selling a product. Customer demand is stochastic, and customers individually decide with given probabilities from which newsvendor they want to order or whether they do not want to order at all. These probabilities can vary depending on which newsvendor is out of stock. The problem described arises when marketplace operators offer the same or substitutable products as third-party vendors and therefore directly compete with third-party vendors on their platform. Our research is motivated by practical cases such as the Amazon marketplace, where Amazon is the marketplace operator that sets the sales commission and, simultaneously, directly competes with third-party vendors. Both the marketplace operator and a competing third-party vendor should ideally account for the other party's behavior when deciding their order quantity. We calculate the noncooperative Nash equilibrium and the optimal cooperative order quantities (centralized solution). Additionally, we emphasize analyzing the effect of the sales commission on the optimal order quantities and the gross profits of the two parties.

International cooperation on financial market regulation

At the latest the global financial crisis has raised the awareness of the need for a globally coordinated financial market regulation. Even though the necessity to cooperate is widely acknowledged, cooperation is often limited in practice. This article characterizes the formation of self-enforcing international financial regulation agreements. Our analysis allows to evaluate the desirability and feasibility of cooperative solutions and explains the challenges associated with the process of cooperation. We model the cooperation of national financial regulators in a game-theoretical framework that considers financial stability to be an impure public good. Joint national supervisory effort is supposed to increase aggregate welfare in terms of a more stable financial system both on a global and on a local level by simultaneously generating incentives to free-ride. Our analysis in general indicates the difficulty of reaching a fully cooperative solution. In our basic version of the model we show that partial cooperation of two or three countries is stable and improves the welfare of all countries relative to the non-cooperative Nash equilibrium. Further analyses highlight the role of additional club benefits. When signatory countries of a coalition gain benefits over and above the joint welfare maximization, stable coalitions of any size become feasible.

Pricing Models for the Internet of Things (IoT): Game Perspectives

While large IT companies develop full-stack IoT services with their computing resources, there are many small/medium-sized IoT application/device developers who rely on multiple other service providers for various IoT infrastructure services such as data storage, wireless sensor networks, data analytics, and IoT platforms. While pricing decisions of these IoT services are critical to the sustainable growth of the customer base, there is a paucity of studies on the pricing of a set of services involving multiple service providers. Hence, it is challenging for IoT providers to make informed decisions in regards to the pricing of their IoT devices and services. This paper develops pricing game models involving multiple IoT providers and analyzes both a non-cooperative game and a cooperative game. Nash equilibrium prices for three IoT providers in a non-cooperative game and a cooperative game are derived. The non-cooperative Nash equilibrium price of each provider shows that the Nash equilibrium price consists of the average reservation price of the customers and the provider's cost. While the sum of the providers’ prices affects the IoT customers’ demand, the model shows that in pricing, each provider does not take the other providers’ pricing decisions into account. This paper examines how the cooperative game may generate more profits than the non-cooperative game and applies Shapley solutions for fair and efficient allocation of the payoff of the cooperative game. Contrary to conventional wisdom, consumer welfare and the IoT providers’ profit is not a zero-sum game. The three-provider pricing game model is generalized for any finite number of providers.

COVID Social Distancing and the Poor: An Analysis of the Evidence for England

Abstract Social distancing is a matter of individuals’ choices as well as of regulation. We analyse weekly panel data on such behaviour for English Upper Tier Local Authorities (UTLAs) from March to July 2020, paying attention to the influence of poverty, as measured by free school meals provision. Panel regressions suggest that, although more stringent regulation and slightly lagged local cases of infection increase social distancing, both effects are weaker in UTLAs with higher levels of poverty, in part because of poor housing, and also because shortage of money has forced the poor to keep working. Thus motivated, we develop a two-class (rich/poor) model, in which a Nash non-cooperative equilibrium arises from individual choices in a regulatory regime with penalties for non-compliance. The model yields results in keeping with the empirical findings, indicating the desirability of generous measures to furlough workers in low-paid jobs as a complement to the stringency of general regulation.

Transboundary Emission Under Stochastic Differential Game

In this study we provide a more robust transboundary industrial pollution reduction strategy for global emission collaborations. We consider the dynamics of each country’s quantity of pollution as a Brownian motion with Jumps to capture the systematic jumps caused by surprise effects arising from policy uncertainties within the economy. When the output of each country’s domestic consumption good production is proportional to the level of pollution emissions, we apply optimal control theory to find the Nash noncooperative, cooperative and Stackelberg optimal emission paths. To formulate this problem we allow each country’s discounted stream of net revenues to be maximized via a Stochastic Differential Game (SDG). We then articulate the Nash noncooperative equilibria, cooperative equilibria and Stackelberg equilibria via a feedback control strategy. We show that the outcome of the game depends on the parameters of the game and the type of equilibrium one considers. Furthermore, in this continuous-time differential game paradigm model we show that the feedback Stackelberg equilibrium will not coincide with the feedback Nash noncooperative equilibrium. In this setting, if the first mover advantage of the leader (Player I) disappears then both equilibria coincide.

Improving Public Good Supply and Income Equality: Facing a Trade-Off

It is explored in this paper how – depending on the agents’ preferences – an unequal income distribution may lead to a higher public good supply in a non-cooperative Nash equilibrium than in a cooperative Lindahl equilibrium that arises from a balanced income distribution. The degree of inequality that is needed for producing this result may be moderate what in particular is shown through an example with CES preferences.

Capital accumulation game with quasi-geometric discounting and consumption externalities

This study introduces quasi-geometric discounting into a simple growth model of common capital accumulation that takes consumption externalities into account. We examine how present bias affects economic growth and welfare, and we consider two equilibrium concepts: the non-cooperative Nash equilibrium (NNE) and the cooperative equilibrium (CE). We show that the growth rate in the NNE can be higher than that in the CE if individuals strongly admire the consumption of others regardless of the magnitude of present bias. Contrary to the results in the time-consistent case, we show that, when present bias is incorporated, the welfare level in the NNE can be higher than that in the CE in the initial period. However, in later periods, this relationship can be reversed depending on the difference in the speed of capital accumulation.

A Novel Antagonistic Weapon-Target Assignment Model Considering Uncertainty and its Solution Using Decomposition Co-Evolution Algorithm

The weapon-target assignment (WTA) problem is a crucial decision issue in the process of cooperative aerial warfare (CAW). The decision strategy of fighter teams involved in the CAW is susceptible to the influence of the enemy fire attack and electronic interference, which will lead to both the antagonism and uncertainty of the decision making. In this paper, a novel antagonistic game WTA (AGWTA) model with uncertainty is introduced. The antagonism is described by a non-cooperative zero-sum game model conducted by two fighter teams. Then, a modified sensor data fusion method using belief entropy and similarity of sensor data is presented to manage the uncertainty of AGWTA. According to the characteristics of the AGWTA model, a decomposition co-evolution algorithm (DCEA-AGWTA) is proposed to obtain the non-cooperative Nash equilibrium (NCNE) strategy. The experimental results show that the modified sensor data fusion method contributes to higher reliability of target type identification and the AGWTA model is meaningful in the antagonistic and uncertain situation of CAW. In addition, the DCEA-AGWTA is effective and has a promising ability in finding the closest strategy to the NCNE strategy compared with the other three intelligent evolution-based algorithms.

Noncooperative Dynamic Contribution to a Public Project

We consider a dynamic contribution game in which a group of agents collaborates to complete a public project. The agents exert efforts over time and get rewarded upon completion of the project, once the cumulative effort has reached a pre-specified level. We explicitly derive the cooperative solution and a noncooperative Markov-perfect Nash equilibrium. We characterize the set of socially efficient projects, i.e., projects that cooperative groups find worth completing. Comparing with the Markov-perfect Nash equilibrium, we find that noncooperative groups give up large socially efficient projects. Moreover, they take too much time to complete the projects that they undertake.

Notes on income heterogeneity and number of contributors: Public goods model

AbstractThis paper proves that a large degree of income heterogeneity increases the number of free riders under the noncooperative Nash equilibrium of voluntary contributions to public goods with a Cobb–Douglas utility function. We prove this by investigating an algorithm structure that identifies free riders. We also support this proof by showing the numerical simulation results based on this algorithm.

Lotteries and Lindahl prices in public good provision

AbstractLotteries are traditional instruments for fundraising in general. Morgan has shown that they can also be very effective in the provision of a public good. However, a fair lottery can only enhance provision but never result in the efficient amount. Franke and Leininger show how—by borrowing from optimal contest theory—biased lotteries can provide the efficient amount of the public good. This paper aligns this result with standard public good theory, in particular the classic notion of Lindahl pricing. It shows that biased lotteries can—implicitly—implement Lindahl pricing of the public good in noncooperative Nash equilibrium.

Self-enforcing capital tax coordination

Capital tax competition is known to result in inefficiently low tax rates and an undersupply of public goods. The provision of public goods and with it the welfare of all countries can be enhanced via tax coordination. Based on the standard Zodrow-Mieszkowski-Wilson tax-competition model this paper analyzes the conditions under which tax coordination by a group of countries is self-enforcing. In our analytical framework, there always exists a rather small stable tax coalition. For some subset of the parameter space the grand coalition is stable, even if the total number of countries is large. If the stable coalition is small, it is not very effective in mitigating the inefficiency of the non-cooperative Nash equilibrium. The ineffectiveness is increasing in the total number of countries.

Efficient tax competition under the origin principle

AbstractThis paper studies fiscal competition under the origin principle. It identifies a pattern of consumers' taste heterogeneity under which the first‐best world social optimum arises as a noncooperative Nash equilibrium. Consumers' tastes are characterized by the strength of their preference for home and foreign goods. Nash implementation of the first‐best obtains when in every tax jurisdiction the number of consumers who display a home bias (those consumers who prefer purchasing the home good to shopping abroad at equal prices) equals, for every magnitude of the home bias, the number of consumers who display an “import bias” (those who instead prefer shopping abroad) equal in magnitude.

A cooperative route choice approach via virtual vehicle in IoV

Popular navigation services are used by drivers both to plan out routes and to optimally navigate real time road congestion in internet of vehicles (IoV). However, the navigation system (such as GPS navigation system) and apps (such as Waze) may not be possible for each individual user to avoid traffic without creating congestion on the clearer roads, and it might even be that such a recommendation leads to longer aggregate routes. To solve this dispersion, in this paper, we first apply a concept of virtual vehicle in IoV, which is an image of driver and vehicle. Then, we study a setting of non-atomic routing in a network of m parallel links with symmetry of information. While a virtual vehicle knows the cost function associated with links, they are known to the individual virtual vehicles choosing the link. The virtual vehicles adapt the cooperation approach via strategic concession game, trying to minimize the individual and total travel time. How much benefit of travel time by the virtual vehicles cooperating when vehicles follow the cooperation decisions? We study the concession ratio: the ratio between the concession equilibrium obtained from an individual optimum and the social optimum. We find that cooperation approach can reduce the efficiency loss compared to the non-cooperative Nash equilibrium. In particular, in the case of two links with affine cost functions, the concession ratio is at most 3/2. For general non-decrease cost functions, the concession ratio is at most 2. For the strategic concession game, the concession ratio can approach to 1 which is a significant improvement over the unbounded price of anarchy.

Sustainability of coalitional equilibria within repeated tax competition

This paper analyzes the sustainability of capital tax harmonization agreements in a stylized model where countries have formed coalitions to agree on a common tax rate in order to avoid the inefficient, fully non-cooperative Nash equilibrium. In particular, for a given coalition structure we study to what extent the sustainability of tax agreements is affected by the coalitions that have formed. In our setup, countries are symmetric, but coalitions can be of arbitrary size. We analyze sustainability by means of a repeated game setting employing simple trigger strategies and we allow a sub-coalition to deviate from the coalitional equilibrium. For a given form of punishment we rank the sustainability of different coalition structures. We show that sub-coalitions consisting of singleton regions have the largest incentives to deviate and that the sustainability of cooperation depends on the degree of cooperative behavior ex-ante. Bilateral agreements between pairs of regions turn out to be the form of cooperation that is the easiest to sustain.

Cooperative and Noncooperative Extraction in a Common Pool with Habit Formation

The present paper considers the exploitation of a common-property, nonrenewable resource, by individuals subject to habit formation. We formalize their behavior by means of a utility function, depending on the difference between the individuals’ current consumption and the consumption level which they aspire, the latter being a weighted average of past consumptions in the population. We derive and compare the benchmark cooperative solution and a noncooperative Markov-perfect Nash equilibrium of the differential game. We investigate how the intensity, persistence and initial level of habits shape the cooperative and noncooperative solutions. We prove that habit formation may either mitigate or worsen the tragedy of the commons.