Non-cooperative Nash Equilibrium Research Articles

Modeling Misbehavior in Cooperative Diversity: A Dynamic Game Approach

Cooperative diversity protocols are designed with the assumption that terminals always help each other in a socially efficient manner. This assumption may not be valid in commercial wireless networks where terminals may misbehave for selfish or malicious intentions. The presence of misbehaving terminals creates a social-dilemma where terminals exhibit uncertainty about the cooperative behavior of other terminals in the network. Cooperation in social-dilemma is characterized by a suboptimal Nash equilibrium where wireless terminals opt out of cooperation. Hence, without establishing a mechanism to detect and mitigate effects of misbehavior, it is difficult to maintain a socially optimal cooperation. In this paper, we first examine effects of misbehavior assuming static game model and show that cooperation under existing cooperative protocols is characterized by a noncooperative Nash equilibrium. Using evolutionary game dynamics we show that a small number of mutants can successfully invade a population of cooperators, which indicates that misbehavior is an evolutionary stable strategy (ESS). Our main goal is to design a mechanism that would enable wireless terminals to select reliable partners in the presence of uncertainty. To this end, we formulate cooperative diversity as a dynamic game with incomplete information. We show that the proposed dynamic game formulation satisfied the conditions for the existence of perfect Bayesian equilibrium.

Optimal Income Taxation, Outsourcing and Policy Cooperation in a Dynamic Economy

This paper concerns optimal income taxation in a two-country OLG economy, where each country is characterized by asymmetric information between the government and the private sector, and where one of the countries outsources part of its production to the other. In the country whose firms outsource production abroad, the government will respond to outsourcing by implementing a more progressive labor income tax structure and higher marginal capital income tax rates than it would have done in the absence of outsourcing. The tax policy response by the government in the country that receives foreign production capacity is, in general, ambiguous and depends on a tradeoff between wage-equality and factor income from abroad. By using the noncooperative Nash equilibrium as a reference case, we also consider tax policy cooperation leading to higher welfare.

Spatial patterns of biodiversity conservation in a multiregional general equilibrium model

Migration dynamics and local biodiversity are interrelated in a way that is likely to affect patterns of regional specialisation. We assess this relationship with a New Economic Geography model that has been extended with biodiversity. Biodiversity is heterogeneous, and responds to habitat availability. The results indicate that a symmetric pattern of regional specialisation is more likely, and that additional equilibria may emerge as the marginal utility of biodiversity increases. In the policy analysis we focus on the case where the overall social optimum is symmetric and show that it can be supported as a non-cooperative Nash equilibrium. However, multiple Nash equilibria may exist.

Non-Atomic Games for Multi-User Systems

In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the matched filter, the MMSE filter and the optimum filter. The goal of this paper is to extend previous work, and to derive simple expressions for the non-cooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of non-atomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.

Importer and Producer Petroleum Taxation: A Geo-Political Model

We derive non-cooperative Nash equilibrium (NE) importer and exporter petroleum excise taxes given full within-group tax coordination, but no coordination between groups, assuming that importers do not produce and exporters do not consume petroleum, and petroleum consumption causes a global externality. The aggregate NE tax is found to consist of an externality component and an optimal tariff component, and exceeds the standard Pigou tax. The environmental component in isolation is however less than the Pigou tax. With Stackelberg tax setting, the leader's tax is higher than in the Ne, and the follower's tax lower, and the overall tax higher. We show that importers prefer to set a tax instead of an import quota, since exporters' optimal response to a quota is a higher tax. An optimal cap-and-trade scheme will thus fare worse than an optimal tax scheme for importers, and will imply greater petroleum consumption and carbon emissions. When exporters behave as a cartel satisfying demand at a fixed export price, exporters' optimal tax is higher, while importers tax rule is Pigouvian. Exporters then gain at the expense of importers.

Revenue Sharing and Owner Profits in Professional Team Sports

In the sports economics literature, little attention has been paid to the impact of revenue sharing on club owners' profits. In particular, it is unclear how the profits of the large-budget clubs are affected. In this article, the relationship between one specific revenue-sharing arrangement and owner profits is investigated for clubs in a profit-maximization league using two different models. In a Walrasian equilibrium model, revenue sharing will lower profits, whatever the value of the share parameter, if the profits of a large-budget club are higher than the average club budget in the league. In a noncooperative Nash equilibrium model, the impact turns out to be theoretically indeterminate.

Reply: "Professional Team Sports Are Only a Game: The Walrasian Fixed-Supply Conjecture Model, Contest-Nash Equilibrium, and the Invariance Principle"

Szymanski (2004) explained that at a noncooperative Nash equilibrium for talent choice in a team sports league, revenue sharing will lead to a less-balanced distribution of talent (assuming teams have asymmetric revenue-generating potential). This proposition contradicts the well-known invariance principle. Eckard suggests that these results rest on assumptions about the elasticity of talent supply. This reply explains that this is not the case and that revenue sharing leads to a reduction in competitive balance, whether the supply of talent is elastic or not.

Strategic Labeling and Trade of GMOs

The emergence of agricultural biotechnology and the subsequent introduction of genetically modified organisms (GMOs) into the food system have been among the most controversial issues surrounding the increasingly scrutinized agri-food system. They have received considerable attention in the economics literature with the main focus being on the optimal regulatory response to products of biotechnology. This paper builds on the literature on the regulation of products of biotechnology by placing the analysis of labeling decisions in a multi-country context. Specifically, the objective of this study is to examine the effect of the strategic interdependence between countries on their regulatory responses to products of biotechnology. The paper analyzes the strategic effects of national regulatory decisions on labeling of GM products and identifies the determinants of the non-cooperative Nash equilibrium labeling regimes in a small number of producing countries that supply the world market of an agricultural product. Analytical results show that the Nash equilibrium configuration of labeling regimes in countries that have adopted the GM technology depends on (i) the distribution of consumer preferences and the level of consumer aversion to GM products; (ii) the size of the segregation and labeling costs in these countries; (iii) the relative productive efficiency and the cost effectiveness of the GM technology; (iv) the market power of the life science companies; and (v) the strength of intellectual property rights in these countries.

Competitive Multi-period Pricing for Perishable Products: A Robust Optimization Approach

We study a multi-period oligopolistic market for a single perishable product with fixed inventory. Our goal is to address the competitive aspect of the problem together with demand uncertainty using ideas from robust optimization and variational inequalities. The demand function for each seller has some associated uncertainty and we assume that the sellers would like to adopt a policy that is robust to adverse uncertain circumstances. We believe this is the first paper that uses robust optimization for dynamic pricing under competition. In particular, starting with a given fixed inventory, each seller competes over a multi-period time horizon in the market by setting prices and protection levels for each period at the beginning of the time horizon. Any unsold inventory at the end of the horizon is worthless. The sellers do not have the option of periodically reviewing and replenishing their inventory. We study non-cooperative Nash equilibrium policies for sellers under such a model. This kind of a setup can be used to model pricing of air fares, hotel reservations, bandwidth in communication networks, etc. In this paper we demonstrate our results through some numerical examples.

Choosing the size of the public sector under rent seeking from state coffers

This paper incorporates rent seeking from state coffers into a general equilibrium model of economic growth and endogenous policy. Self-interested individuals try to extract, for personal benefit, part of tax revenues that could be used to finance public investment. We solve for a non-cooperative Nash equilibrium in individual agents' behavior. The determinants of rent seeking in general equilibrium are identified and we consider the efficient size of public sector given the rent-seeking activity. Cross-country data from 108 rich and developing countries provide support for our predictions.

OPEN-LOOP AND CLOSED-LOOP MODELS OF DYNAMIC OLIGOPOLY IN THE CRUISE LINE INDUSTRY

In this paper, the competition of dynamic oligopoly in the cruise line industry is modeled as an N-person nonzero-sum noncooperative dynamic game where a finite number of cruise lines compete to maximize their profits over a fixed planning horizon. The noncooperative Nash equilibrium capacity investment strategies of cruise lines are theoretically analyzed under the open-loop and closed-loop information structures. The optimality conditions for open-loop and closed-loop Nash equilibrium solutions are derived using a Pontryagin-type maximum principle and given economic interpretations so as to demonstrate the differences between the open-loop and closed-loop Nash equilibrium solutions. The dynamic oligopolistic competition of three cruise lines in a hypothetical setting is numerically analyzed by using the iterative algorithms for open-loop and closed-loop models. Numerical results provide a number of important managerial guidelines for cruise capacity investment decisions. The paper concludes with a discussion on future research directions.

A dynamic game model of strategic capacity investment in the cruise line industry

In this paper, the cruise line industry is characterized as an oligopoly where a finite number of cruise lines compete to maximize their profits over a fixed planning horizon. The oligopolistic competition is modeled as a N-person nonzero-sum noncooperative dynamic game. The noncooperative Nash equilibrium capacity investment strategies of cruise lines are theoretically analyzed under the open-loop information structure. The necessary conditions for an open-loop Nash equilibrium solution are derived using a Pontryagin-type maximum principle and the sufficient conditions are also established. The economic interpretation of the optimality conditions is given so as to demonstrate the difference between the static and dynamic oligopoly problems. The dynamic oligopolistic competition of three cruise lines in a hypothetical setting is also numerically analyzed by using the iterative algorithm. Numerical results provide a number of important managerial guidelines for cruise capacity investment decisions. The paper concludes with a discussion on future research directions.

Unemployment, welfare and optimal monetary policy: convergence probability

Using a rigorous convergence probability, this note shows why mathematic models are inconsistent with empirical evidence. Using a dynamic quadratic cointegration, a new theory of the concave utility shows that below the optimum, the volatility has a positive impact upon output. Beyond the optimum, the volatility of policy has a negative impact upon output and a positive impact upon the unemployment rate. In this new methodology, our equilibrium targets minimize inflation bias and fiscal bias. First, we compute the equilibrium and optimal policy, then reduce the heteroschedasticity, and finally estimate the convergence probability. Our surprising solution is individually rational and feasible while the budget is balanced over business cycles. For the problem of n＞1 governments or agents, an agent estimates and proposes the maximum non-zero equilibrium which is most acceptable to all participants and outperforms the Nash noncooperative equilibrium. This solves the games and scientific problems unrelated to games as n→∞, regardless of whether the proposal is accepted voluntarily or not.

Welfare Effects of Tax Policy in Open Economies: Stabilization and Cooperation

This paper studies an international tax policy design problem by employing a two-country dynamic general equilibrium model with incomplete asset markets. We investigate the possibility of welfareimproving active tax policies, in particular capital and labor income tax, under the non-cooperative Nash equilibrium and the cooperative equilibrium. Unlike the conventional wisdom regarding stabilization policies, optimal tax policies in our economy are procyclical. Relative to the non-cooperative setting, international tax policy cooperation requires more active tax policies (about two times) and generates large extra welfare gains (by about a third).

Strategic Interactions Between Fiscal and Monetary Policies in a Monetary Union

This paper develops a dynamic game model to study strategic interactions between policy-makers in a monetary union. In this union, governments of the participating countries pursue national goals when deciding on fiscal policies, whereas the common central bank's monetary policy aims at union-wide objective variables. For a symmetric demand shock, we derive solutions of the dynamic game between the governments and the central bank. The different solution concepts for this dynamic game can be interpreted as models of a conflict between national and supra-national institutions (non-cooperative Nash equilibrium) on the one hand and of coordinated policy-making (cooperative Pareto solutions) on the other.

The effects of information on producer and consumer incentives to undertake food safety efforts: A theoretical model and policy implications

AbstractFood safety presents a double moral hazard problem. This author develops a model of food safety where consumers and producers undertake unobservable preventive measures to reduce the probability of a food‐borne illness. Losses from a food‐borne illness are shared by consumers and producers according to the existing tort law. We characterize the optimal solution and show that this risk‐sharing arrangement and imperfect information create an incentive problem where suboptimal levels of precautions by producers and consumers are attained in a noncooperative Nash equilibrium solution. We conduct comparative static analysis to trace out the effects of changes in the size of losses, the degree of orientation of the legal system, and government regulation of information provision on precautions undertaken by consumers and producers. [EconLit citations: L150, Q180.] © 2003 Wiley Periodicals, Inc. Agribusiness 19: 29–42, 2003.

Optimum Tariffs and Retaliation Revisited: How Country Size Matters

In his seminal work on retaliation, Johnson (Review of Economic Studies, 21, 1953-1954) showed that a country will win a bilateral tariff war if its relative monopoly/monopsony power in world trade is sufficiently large. However, it is unclear from Johnson's analysis and from subsequent research on the subject how this power is determined in general economic environments. An important goal of this paper is to address this issue. With the help of a neoclassical trade model in which country size is at centre stage, it is shown that a sufficient condition for a country to prefer a non-cooperative Nash equilibrium (retaliation) over free trade is that its relative size be sufficiently large. The paper also refines the structure of the general trade model and generates additional characterization results on the importance of country size for best-response functions, retaliatory tariffs, and welfare.

The revival of regional trade arrangements: a GE evaluation of the impact on small countries

In this paper we analyse the implications of various potential regional trade arrangements on the globe for small, medium, and large countries using a general equilibrium multi-region model of world trade. We show that the effects of regional trade arrangements on member and non-member countries are different for different equilibrium concept and the nature of agreements. In a traditional competitive equilibrium framework the welfare effects are small and non-member nations lose marginally due to a trade diversion. In a non-cooperative Nash equilibrium framework small non-member nations are worse affected. Since the larger regions can bring the terms of trade in their favor by retaliation, and hence could gain from retaliation, the growth of regional trade arrangements is a great cause of concern for the smaller regions. This concern becomes stronger if these trade arrangements are customs unions (CU). This makes small and medium size nations seeking trading arrangement with larger nations as a safe heaven strategy.

COLLUSION IN PROCUREMENT AUCTIONS: AN EXPERIMENTAL EXAMINATION

Experimental methods are used to examine the existence and detectability of collusion in environments that exhibit critical parallels to procurement auctions. We find that given the opportunity sellers often raise prices considerably. Moreover, noncollusive Nash equilibrium predictions are insufficient to dismiss “suspicious” behavior as innocuous: in an environment where identical prices are predicted in a noncollusive Nash equilibrium, common prices are observed only when sellers communicate. In a second environment designed to parallel construction procurement contracting, market rotations are observed both with and without collusion, but collusion can often be detected from the pattern of losing bids.

Diversity and ingenuity in voluntary collective action

The standard theory of collective action predicts that voluntary provision will result in undersupply of public goods. In practice, we observe provision at various levels, some high, and there is often no evidence of an acute undersupply problem. The outcomes derived by the standard theory envisage the set of strategies of each member of society as the feasible levels of an individuals own contributions. Allowing each player to employ matching functions as strategies allows every feasible point to be implemented as a non-cooperative Nash equilibrium in the new game. The creative design of such matching mechanisms is open to infinite variation and resourcefulness, and can account for the observed diversity in voluntary public good supply.