Nash Players Research Articles

Contingent Reasoning and Dynamic Public Goods Provision

Contributions toward public goods often reveal information that is useful to others considering their own contributions. This experiment compares static and dynamic contribution decisions to determine how contingent reasoning differs in dynamic decisions where equilibrium requires understanding how future information can inform about prior events. This identifies partially cursed individuals who can only extract partial information from contingent events, others who are better at extracting information from past rather than future or concurrent events, and Nash players who effectively perform contingent thinking. Contrary to equilibrium, the dynamic provision mechanism does not lead to lower contributions than the static mechanism. (JEL C92, D71, D82, D91, H41)

The Environmental Responsibility of Firms and Insurance Coverage in an Evolutionary Game

Climate change can deeply impact a company’s business performance, therefore insurance is an important tool to mediate such a risk, helping firms to remain on the market. Polluting companies want to maximize profits according to different business strategies and that appeal to their risk attitude. Firms are Nash players in an oligopoly market adopting two production technologies, brown or green. Climate change loss is a function of the firms’ emissions and is considered endogenous in the maximization problem of the players. We study firms’ behavior in choosing their more profitable strategy through a random matching evolutionary context. Analysis of the model reveals that the dynamic system admits at most seven stationary states. The paper focuses on the regime in which all the possible strategies coexist, due to its economic relevance. Moreover, the results of the sensitivity analysis show interesting policies to nudge an ecological transition.

Hybrid evolutionary oligopolies and the dynamics of corporate social responsibility

The diffusion of corporate social responsibility is investigated by employing a hybrid evolutionary game where a firm chooses between being either socially responsible, which implies devoting a fraction of its profit to social projects, or non-socially responsible. Consumers prize socially responsible companies by paying a higher reservation price for their products. The hybrid evolutionary framework is characterized by a quantity dynamics that describes the oligopolistic competition given firms’ belief about the composition of the industry. At regular intervals of time, this belief is endogenously updated by a retrospective comparison on the profits obtained and on the basis of an evolutionary mechanism. Assuming that firms are Nash players, that is at each instant of time they produce the Nash equilibrium-in-belief quantity, the investigation of the model reveals that an industry homogeneously populated by socially responsible firms is a stable equilibrium when the fraction of profits earmarked for socially responsible activities is sufficiently limited. However, the extra marginal profits of a socially responsible firm are reduced when the number of competitors increases, impeding the diffusion of socially responsible companies. In particular, the trade-off between a higher net margin on sales obtained by socially responsible firms and a lower level of production that reduces the profit gap between a socially responsible firm and the rest of the market shows that an increased size of the industry favors mixed oligopolies. Moreover, imposing the hypothesis of neutrality of CSR activities, the model reveals that being socially responsible is an evolutionarily stable strategy for firms and is convenient for customers. Relaxing the hypothesis of Nash players by introducing boundedly rational firms that decide their level of production according to a partial adjustment toward the best reply, the robustness of these results is confirmed.

The tragedy of the commons and socialization: Theory and policy

We revisit the Tragedy of the Commons in a dynamic overlapping generations economy populated of shepherds who decide how many sheep they let graze on a common parcel of land, while relying on different forms of rationality (Nash players and Kantian players). We examine the dynamics of moral behaviors and land congestion when the prevalence of different types evolves over time following a vertical/oblique socialization process à la Bisin and Verdier (2001). We study the impact of a quota and of a tax on the congestion of land, and we show that introducing a quota may, in some cases, reduce the proportion of Kantians, and worsen the Tragedy of the Commons with respect to the laissez-faire. Ignoring the dynamics of moral traits may lead governments to implement policies that make the Tragedy worse than at the laissez-faire, even though such policies would work well for a fixed population composition.

A study of Nash-EGO algorithm for aerodynamic shape design optimizations

In this paper, our newly proposed Nash-EGO algorithm is applied to real large-scale airfoil/wing optimizations. A finite wing is represented by mounting control airfoils parameterized with a set of design variables, which are manipulated to be increased gradually in purpose of enriching the searching space to accommodate possible more optimal solutions. The enriched design territory is technically split into small subsets to be assigned to the players of Nash-EGO. Doing this way, the performance of each efficient global optimization (EGO) player could be expected to keep at a high level due to EGO players now take care of only their own small-scale subsets instead of facing the large-scale problem directly. The algorithm is first applied to a constrained drag minimization of RAE 2822 airfoil with 14 to 54 design variables and two to eight Nash players to investigate the performance of Nash-EGO, particularly for having an understanding of the influences of the numbers of design variables and Nash players. Then, more challenging cases, sectional shape optimizations of DLR-F4 wing with up to 84 design variables, are conducted. The results show that, in comparison with the baselines, up to 47.5% drag reductions can be achieved by Nash-EGO optimizer; meanwhile, the CPU costs are greatly reduced (up to 366.8% speedup) as compared with the counterpart of the traditional EGO. The successful applications presented show the capability of Nash-EGO algorithm for solving real engineering optimizations with large scales.

Evolutionary Stability of Kantian Optimization

In Nash equilibrium, agents are autarchic in their optimization protocol, whereas in Kantian equilibrium, they optimize in an interdependent way. Typically, researchers into the evolution of homo economicus treat preferences as being determined by selective adaptation, but hold fixed the optimization protocol as autarchic. Here, we ask whether natural selection might choose the optimizing protocol to be either autarchic or interdependent. That is, will Kantian players, for whom the stable concept is Kantian equilibrium drive Nash players (for whom the stable concept is Nash equilibrium) to extinction, or otherwise? The answer depends upon whether players can signal their type to others.

Mixed behavior network equilibria and quasi-variational inequalities

In the modeling of competition on networks it is usually assumedthat users either behave following the Wardropian user equilibrium or thesystem optimum concept. Nevertheless, in several equilibriumsituations, for instance in urban traffic flows, intercity freightflows and telecommunication networks, a mixed behavior is observed.This paper presents a time-dependent network-based model shared by twotypes of users: generalized Nash players anduser equilibrium players. Generalized Nash players have a significant impact onthe load of the network, whereas user equilibrium players have a negligibleimpact. Both classes of players choose the paths to send their flows soas to minimize their own costs, but they apply different optimizationcriteria. Players interact via some implicit balance constraintswhich depend on the equilibriumsolution. Thus, the equilibrium distribution is proved to be equivalent to the solutionof a time-dependent quasi-variational inequality problem.Results on existence of solutions are discussed as well as a numerical example.

A Stackelberg-Nash model for new product design

Existing conjoint approaches to optimal new product design have focused on the Nash equilibrium concept to model competitive reactions. Whereas these approaches have treated all competing firms equally as Nash players, one firm may have an advantage over its rivals, e.g., more pre-experience on competitors’ behavior and/or a first-mover advantage. This paper proposes a Stackelberg-Nash (leader-followers) model which can accomodate such information for decision making. The optimal product design problem is formulated from the perspective of a profit-maximizing new entrant (the leader) who wants to launch a brand onto an existing product market and acts with foresight by anticipating price-design reactions of the incumbent firms (the Nash followers). In the absence of closed-form solutions, we use a sequential iterative procedure to compute a Stackelberg-Nash equilibrium and to establish its uniqueness. The new conjoint model is illustrated under several competitive scenarios and price, design and profit implications are compared to a simple Nash equilibrium model. We find that a Stackelberg leader strategy may not only yield a much higher profit for the new entrant than a Nash strategy, but may also lead to strong profit asymmetries between competitors with still higher profits for the incumbent firms. In other words, the incumbent firms may also benefit strongly from a new entrant choosing a Stackelberg leader strategy.

Quasi-Variational Inequality Formulation of the Mixed Equilibrium in Multiclass Routing Games

In the modeling of competition on networks it is usually assumed that users either behave following the Wardrop equilibrium or the Nash equilibrium concept. Nevertheless, in several equilibrium situations, for instance in urban traffic flows, intercity freight flows and telecommunication networks, a mixed behavior is observed. This paper presents a time-dependent network model shared by two types of users: group users (Nash players) and individual users (Wardrop players). A group user has a significant impact on the load of the network, whereas an individual user has a negligible impact. Both classes of users choose the paths to ship their jobs so as to minimize their costs, but they apply different optimization criteria. The source of interaction of users is represented by the travel demand, which is assumed to be elastic with respect to the equilibrium solution. Thus, the equilibrium distribution is proved to be equivalent to the solution of an appropriate time-dependent quasi-variational inequality problem. A result on the existence of solutions is discussed as well as a numerical example.

Efficiency of Atomic Splittable Selfish Routing with Polynomial Cost Functions

Previous works on the inefficiency of selfish routing have focused on the Wardropian traffic equilibria with an infinite number of infinitesimal players, each controlling a negligible fraction of the overall traffic, but only very limited pseudo-approximation results have been obtained for the atomic selfish routing game with a finite number of players. In this note we examine the price of anarchy of selfish routing with atomic Cournot–Nash players, each controlling a strictly positive splittable amount of flow. We obtain an upper bound of the inefficiency of equilibria with polynomial cost functions, and show that the bound is 1 or there is no efficiency loss when there is only one player, and the bound reduces to the result established in the literature when there are an infinite number of infinitesimal players.

Cross-border shopping in a federal economy

The purpose of this paper is to consider an economy that incorporates cross-border shopping and where the different levels of government are concerned with the well-being of their citizens. We assume a federal economy with a central government and two regions with specific characteristics. Two kinds of externalities, horizontal and vertical, arise and we show the possibilities of internalising them. With the governments of symmetric regions behaving as Nash players, they would optimally set their tax rates and replicate the unitary nation optimum. Finally, we show how the central government as a Stackelberg leader can adjust its fiscal instruments so that the tax externalities are also internalised.

Macroeconomic equilibrium with illegal immigration

Illegal immigration (ILM) has been analyzed very little in the context of a macroeconomic framework. This paper introduces immigration of illegal unskilled workers into a simple model of an open economy with heterogeneous labor and, within this context, examines its macroeconomic and welfare consequences. The analysis shows that when skilled native wage setters and the policymakers behave as Nash players, ILM improves the position of the entire native labor force, i.e. both skilled and unskilled workers. Moreover, it reduces the inflationary bias associated with expansionary policies and thus has a positive overall impact on ‘social welfare’ in the economy. This result contrasts with several earlier studies that suggest that illegal immigration causes the position of at least some members of an economy to worsen. It also provides one possible macroeconomic explanation as to why illegal immigrants are currently tolerated in ‘inflation prone’ countries despite the fact that their presence sometimes causes social tensions. On the other hand, when native skilled workers and the policymakers behave cooperatively, ILM may in fact make the entire native workforce worse off. This result suggests that countries with ‘aggressive’ unions in skilled labor markets stand to gain from illegal immigration while countries with ‘soft’ unions may lose. Finally, it is shown that domestic labor market conditions determine the ‘optimum’ degree of government intervention in the illegal migrant labor market.

On Hierarchical Spatial Competition

In this paper we consider a model of spatial electoral competition with two dominant players (incumbents) and one entrant. The incumbents engage in a non-cooperative game against each other and act as Stackelberg leaders with respect to a vote-maximizing entrant. We prove that the equilibrium of this game, called a equilibrium, exists and is unique for an arbitrary single-peaked distribution of voters' ideal points. Moreover, we fully characterize the set of equilibrium strategies and show its equivalence to the set of strategies generated by a perfect-foresight Most of the recently developed models of entry in oligopolistic markets and the theory of political competition deal with the case of dominant firms or parties which face a threat of potential entry. These models possess a number of features on which they may be compared and contrasted. The most important of these features are the ways in which the existing parties or firms compete against each other for votes or profits, and types of expectations the incumbents have about the responses of potential entrants to changes in their decisions. In most of the cases an electoral or oligopolistic competition is represented by some type of a non-cooperative game played by parties or firms. In this paper we also consider a non-cooperative model of electoral race where the established parties (incumbents) compete against each other by offering positions (ideologies) to the population of voters. Given the profile of voters' preferences over the space of ideologies (or, issue space), each of the established parties attempts to maximize its vote share. In making their choices, the incumbents, however, anticipate that a new party (an entrant) will join the electoral race. Consistent with the other parties' objectives, the entrant is assumed to maximize its share of voters while taking the incumbents' choices as given. The resulting non-cooperative game possesses, therefore, a structural hierarchy: the established parties behave as Nash players with respect to each other, whereas acting as Stackelberg leaders with respect to the entrant and correctly anticipating its vote-maximizing response to their choices in the issue space. The main purpose of this paper is to study the properties of the game we described and, in particular, to characterize its equilibrium, which we will call hierarchical equilibrium. Naturally, some assumptions are needed in order to guarantee the existence of the We assume that there are two established parties, the issue space I is the uni-dimensional interval, all voters have symmetric single peaked-peaked preferences over I and the distribution of the voters' ideal points is represented by a quasi-concave continuous density function. Under these rather mild assumptions, we are able to prove the existence and uniqueness of the equilibrium and to completely