Non-cooperative Equilibrium Research Articles

The role of nonzero conjectural variation in pollution abatement and output in the design of emission taxes

AbstractThe presence of nonzero conjectural variations in pollution abatement and output make emission taxes less effective with respect to reducing emissions. This has implications for the characterization of the optimal emission tax, particularly in an international context where there are large asymmetries in pollution intensities. A higher degree of collusion in output between polluting firms results in higher emissions taxes in the non-cooperative equilibrium. In contrast, a higher degree of collusion in abatement between polluting firms results in lower emissions taxes in the non-cooperative equilibrium. These results rely on the presence of nonzero conjectural variations and large asymmetries in pollution intensities across countries. The analysis is relevant to the design of international environmental policy, including cases where countries face increasing global competition and damages from rising global emissions.

On Sellers' Collusion in E-Commerce Marketplaces

Motivated by a recent competition policy debate on retailers' collusion in online marketplaces, this paper studies a simple model to shed light on the competitive and welfare effects of this conduct. I find that, when retailers sell their products through a monopolistic e-commerce platform, consumers are not necessarily harmed by their collusive behaviour. Specifically, if the platform adopts the agency model and is vertically integrated (i.e., sells a private label in competition with third-party sellers), a cartel between third-party sellers induces it to charge them lower fees and to set a lower price for its private label. As a consequence, when products are sufficiently homogeneous, also the cartel members charge lower prices compared to the non-cooperative equilibrium, and collusion benefits consumers and increases total welfare. Notably, these results hold even though the platform has all the bargaining power vis-a-vis (competing or colluding) third-party sellers, and they collude explicitly.

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.

Who starts the trade war? A theory of export controls and quid pro quo

AbstractChina has been accused of its quid pro quo policy which requires multinational firms to transfer technologies in return for market access. What is less well‐known is that developed countries have imposed export controls on a large variety of high‐tech products to China. We develop a simple two‐country model to understand the motives and consequences of these nontraditional trade and FDI policies. Under certain regularity conditions, we show that the coexistence of export controls and quid pro quo is the unique Nash equilibrium in this game. Comparing to the world without policy interventions, both countries are worse off in the noncooperative equilibrium. Therefore, both countries can benefit from international cooperation on knowledge sharing.

Application of game theory non-cooperative equilibrium method in construction project management informationization

Based on the comprehensive application and bibliometrical analysis of the non-cooperative equilibrium theory of game theory, this paper takes the construction project group as the research background, analyzes the obstacles to the application of management informatization in the construction project, and conducts a pair game study on the application of management informatization by single or group subjects. Aims to provide a valuable reference for the application of management information in construction projects, in line with the policy orientation, and has a certain practical significance. On the basis of combing the relevant literature on the application of management information in the field of construction industry and game analysis, this paper first analyzes the appeal, current situation and obstacles of the application of management information in construction projects. The game results show that there are specific management inspirations for different subjects: the designer should change the way of thinking, control the cost of management information application, and carry out in-depth communication with other subjects on building information to ensure consistency; Contractors need to improve their own ability to apply management information, but also to coordinate and control the relative importance of the three objectives, so that efforts can be more easily converted into positive results.

Collective Action and Intra-group Conflict with Fixed Budgets

We study collective action under adverse incentives: each member of the group has a given budget ('use-it-or-lose-it') that is his private information and that can be used for contributions to make the group win a prize and for internal fights about this very prize. Even in the face of such rivalry in resource use, the group often succeeds to overcome the collective action problem in non-cooperative equilibrium. One type of equilibrium has group members who both contribute, the other type has volunteers who make full stand-alone contributions. Both types of equilibrium exist for larger and partially overlapping parameter ranges.

Ambiguity and long-run cooperation in strategic games

Abstract We study the effects of ambiguity on long-run cooperation in infinitely repeated strategic games. Using a simple parametric model of ambiguity, we study conditions for sustaining cooperative equilibria in the long-run. We apply our framework to the prisoner’s dilemma and duopoly models. We find that (i) ambiguity may affect the game’s structure eventually making the noncooperative equilibrium ex ante preferred; (ii) higher levels of ambiguity make long-run cooperation less likely since it makes punishment schemes less effective; and (iii) large levels of ambiguity may preclude the possibility of mutually beneficial long-run agreements, even when cooperation is beneficial from an ex ante perspective.

Devil take the hindmost: Deflecting attacks to other defenders

We study the indirect strategic interactions between several defenders and between several attackers if each attacker chooses one defender to attack and the force of the attack. If the target choice is based on observations about chosen defence efforts, this choice behavior incentivizes the individual defenders and the defenders compete against each other to not being among the weakest targets. If defence effort is unobservable, this competition between defenders is absent. We also compare the fully non-cooperative equilibria with the outcome if the defenders cooperate and study possible non-cooperative contributions to collective defence.

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.

Expected Worth for 2 2 Matrix Games with Variable Grid Sizes

We offer a detailed examination of a broad class of 2 × 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.

Taxing congestion of the space commons

Satellites launched by independent spacefaring agencies and firms create space congestion and collision risk. Taking as benchmark the cost of a marginal reduction of the congestion rate, we discuss tax mechanisms financing a debris removal effort. We compare the non-cooperative equilibrium traffic when there is a tax on each new launch to recover cleanup costs, with the welfare optimal traffic under a centralized tax. We find that under the latter it is twice as easy to recover cleanup costs and increase traffic than under the former. We also show that a linear tax is twice as effective as a quadratic one.

The Best and Worst of All Possible Worlds: Some Crude Evaluations

The 2 x 2 matrix game plays a central role in the teaching and exposition of game theory. It is also the source of much experimentation and research in political science, social psychology, biology and other disciplines. This brief paper is addressed to answering one intuitively simple question without going into the many subtle qualifications that are there. How efficient is the non-cooperative equilibrium? This is part of a series of several papers that address many of the qualifications concerning the uses of the 2 x 2 matrix games.

Trade Wars, Currency Wars

For most of the post WWII period, until recently, trade protectionism followed a downward trend, and was formulated in multilateral or bilateral agreements between countries. Recently however, there hasbeen a sharp shift towards unilateral, discretionary trade policy focused on short term macroeconomic objectives, and as a consequence, the use of trade policy has become entangled with that of monetary policy. This paper explores the consequences of this shift within a standard DSGE open economy macroeconomic model. We find that a discretionary non-cooperative approach to trade policy can significantly worsen macroeconomic conditions. Moreover, the stance of monetary policy has major implications for the degree of protection in a non-cooperative equilibrium. In particular, cooperative determination of monetary policy implies an increase in both equilibrium tariffs and inflation, and a significant fall in welfare. By contrast, when the exchange rate is pegged by one country, equilibrium rates of protection are generally lower, but in this case, there are multiple asymmetric equilibria in tariff rates which benefit one country relative to another. We also explore the determination of non-cooperative tariffs in a situation where monetary policy is constrained by the zero lower bound on nominal interest rates. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Decentralized Supply Chains under Random Price-Dependent Demand: Noncooperative Equilibria vs. Coordination with Cost-Sharing Contracts

It is common for a supplier to sell products to multiple retailers. In this paper, we investigate the equilibrium behavior of a decentralized supply chain with multiple retailers facing a random price-dependent demand in the additive form. Here, we consider two kinds of demand functions: the distribution of the demand depends only on the retailer’s own retail price (noncompeting retailers) and not only on his own retail price but also on that of the other retailers (competing retailers). We present appropriate wholesale price, buy-back, and lost-sales cost-sharing contracts to coordinate the total supply chain, so that when all the retailers adopt their equilibrium response, the supply chain system coordination is also achieved. Furthermore, the coalition formation among retailers is also analyzed. We find that with buy-back and lost-sales cost-sharing contracts and linear price-dependent demand function, retailers always prefer being in the grand coalition to forming any other coalition.

A New Approach to Coalition Analysis Within the Graph Model

Within the framework of the graph model for conflict resolution, the concept of coalition improvement is generalized, resulting in new definitions of Nash, general metarational, symmetric metarational, and sequential stability applicable to coalitions. To illustrate how these generalized stability definitions can be applied to a real conflict, they are used to analyze an offshore oil exploration dispute that occurred in the South China Sea in 2014. The novel approach reveals which coalitions can upset a noncooperative equilibrium or support new cooperative equilibria, and which decision makers can benefit from joining a coalition.

Unintended consequences: The snowball effect of energy communities

In 2019, the European Commission finalized a legal framework for “Citizens” and “Renewable Energy Communities”, paving the way for their deployment. While the benefits of such communities have been discussed, there is increasing concern that inadequate grid tariffs may lead to excess adoption of such business models. Furthermore, snowball effects may be observed following the effects these communities have on grid tariffs. We show that restraining the study to a simple financial analysis is far from satisfactory. Therefore, we use the framework of cooperative game theory to take account of the ability of communities to share gains between members. The interaction between energy communities and the distribution system operator then results in a non-cooperative equilibrium. We provide mathematical formulations and intuitions of such effects, and carry out realistic numerical applications where communities can invest jointly in solar panels and batteries. We show that such a snowball effect may be observed, but its magnitude and its welfare effects will depend on the grid tariff structure that is implemented, leading to possible over-investments in photo-voltaic panels. In particular, we find that setting a fixed grid tariff strongly mitigates such over-investments.

The value of cooperation in interregional transmission planning: A noncooperative equilibrium model approach

Optimization methods for regional transmission planning overlook boundaries between transmission planning entities and do not account for their lack of coordination. The practical result of those boundaries is inefficient plans because one planning region may disregard the costs and benefits that its network changes impose on other regions. We develop a bi-level EPEC (Equilibrium Problem with Equilibrium Constraints) model that represents a game among multiple noncooperative transmission planners in the upper level together with consumers and generators for the entire region in the lower level. We find that the equilibrium transmission plans from such a framework can differ significantly from those from a cooperative framework and have fewer net benefits. Importantly, we find that cooperation among transmission planners leads to increased competition among generators from adjoining regions, which in turn leads to more efficient generator investments. We prove that the system-wide benefit from cooperation among transmission planners is always positive. We then calculate the value of this cooperation for a small test case with two transmission planners, while also identifying the market parties who gain — and those who lose — from this cooperation.

Trade Wars, Currency Wars

For most of the post WWII period, until recently, trade protectionism followed a downward trend, and was formulated in multilateral or bilateral agreements between countries. Recently however, there hasbeen a sharp shift towards unilateral, discretionary trade policy focused on short term macroeconomic objectives, and as a consequence, the use of trade policy has become entangled with that of monetary policy. This paper explores the consequences of this shift within a standard DSGE open economy macroeconomic model. We find that a discretionary non-cooperative approach to trade policy can significantly worsen macroeconomic conditions. Moreover, the stance of monetary policy has major implications for the degree of protection in a non-cooperative equilibrium. In particular, cooperative determination of monetary policy implies an increase in both equilibrium tariffs and inflation, and a significant fall in welfare. By contrast, when the exchange rate is pegged by one country, equilibrium rates of protection are generally lower, but in this case, there are multiple asymmetric equilibria in tariff rates which benefit one country relative to another. We also explore the determination of non-cooperative tariffs in a situation where monetary policy is constrained by the zero lower bound on nominal interest rates. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This a (This abstract was borrowed from another version of this item.)

The role of research in common pool problems

Significant amounts of public spending are allocated towards research on climate change, but considerable uncertainties remain. We analyze the strategic role of information acquisition and the determinants of investments in information in a common pool game. In the first stage, countries can acquire a signal about their own environmental damages caused by total emissions. Because signals are public, there are information spillovers between countries. In the second stage, the countries decide how much pollution to emit. We show that there can be an inefficiently high amount of investments in information in the non-cooperative equilibrium compared to the cooperative solution if the countries are risk averse and the expected emissions are sufficiently large. In addition, we analyze what happens if the countries cooperate in one of the stages but not in the other. We show numerically that if the emissions are decided non-cooperatively, countries might agree not to acquire any information at all. But if the emissions levels are decided cooperatively, investments in the non-cooperative equilibrium are always too low.

Bargaining over collusion: the threat of supply function versus Cournot competition under demand uncertainty and cost asymmetry

In this paper, we study bargaining over collusion profits in a duopolistic industry with cost asymmetry and demand uncertainty. We consider disagreement payoffs obtained from the non-cooperative equilibrium of either the quantity competition or the supply function competition, and bargaining solutions splitting the gains from agreement either equally or proportionally. We find that each duopolist has always incentive to join a collusive agreement, and the more efficient firm (the less efficient firm) in the cartel always obtains a higher agreement payoff when the disagreement payoff is obtained from the equilibrium of supply function competition (quantity competition).