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We consider a distributed computing setting wherein a central entity seeks power from computational providers by offering a certain reward in return. The computational providers are classified into long-term stakeholders that invest a constant amount of power over time and players that can strategize on their computational investment. In this paper, we model and analyze a stochastic game in such a distributed computing setting, wherein players arrive and depart over time. While our model is formulated with a focus on volunteer computing, it equally applies to certain other distributed computing applications such as mining in blockchain. We prove that, in Markov perfect equilibrium, only players with cost parameters in a relatively low range which collectively satisfy a certain constraint in a given state, invest. We infer that players need not have knowledge about the system state and other players' parameters, if the total power that is being received by the central entity is communicated to the players as part of the system's protocol. If players are homogeneous and the system consists of a reasonably large number of players, we observe that the total power received by the central entity is proportional to the offered reward and does not vary significantly despite the players' arrivals and departures, thus resulting in a robust and reliable system. We then study by way of simulations and mean field approximation, how the players' utilities are influenced by their arrival and departure rates as well as the system parameters such as the reward's amount and dispensing rate. We observe that the players' expected utilities are maximized when their arrival and departure rates are such that the average number of players present in the system is typically between 1 and 2, since this leads to the system being in the condition of least competition with high probability. Further, their expected utilities increase almost linearly with the offered reward and converge to a constant value with respect to its dispensing rate. We conclude by studying a Stackelberg game, where the central entity decides the amount of reward to offer, and the computational providers decide how much power to invest based on the offered reward. [ABSTRACT FROM AUTHOR]

We study Markov perfect equilibria (MPE) of two-player multi-mode differential games with controlled state dynamics, where one player controls the transition between modes. Different types of MPE are characterized distinguishing between delay equilibria, inducing for some initial conditions mode switches after a positive finite delay, and now or never equilibria, under which, depending on the initial condition, a mode switch occurs immediately or never. These results are applied to analyze the MPE of a game capturing the dynamic interaction between two incumbent firms among which one has to decide when to extend its product range by introducing a new product. The market appeal of the new product can be influenced over time by both firms through costly investments. Under a wide range of market introduction costs a now or never equilibrium coexists with a continuum of delay equilibria, each of them inducing a different time of product introduction. [ABSTRACT FROM AUTHOR]

We study Markov decision processes with Borel state spaces under quasi-hyperbolic discounting. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, we prove the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function. We also show that randomisation can be restricted to two actions in every state of the process. Moreover, we prove that under some conditions, this equilibrium can be replaced by a deterministic one. For models with countable state spaces, we establish the existence of deterministic Markov perfect equilibria. Many examples are given to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting. [ABSTRACT FROM AUTHOR]

This paper analyzes how the transferability of production capacities from an established to a new product influences the incentives of a firm to invest in R&D. A dynamic duopoly model is considered, where initially both firms offer a homogeneous product. The firms invest in production capacities and simultaneously in R&D which determines their innovation rate. The firm that innovates first extends its product line and obtains a patent for the new product that prevents the other firm from catching up. Upon the launch of the new product, the innovator then has the option to transfer part of the capacity for the established product to the production process of the new product. If capacities can be rolled over to the new product, a trade-off can be detected in that this rollover option gives the larger firm more incentive to innovate, whereas the cannibalization effect gives the smaller firm a higher innovation incentive. As a logical consequence we find that the larger firm is expected to innovate first when the capacity transfer does not involve a too high capacity loss. However, if the losses of capacity transfer are considerable, the cannibalization effect starts to dominate and the smaller firm's incentive to innovate is larger. [ABSTRACT FROM AUTHOR]

We study a discrete-time non-stationary decision model in which the preferences of the decision maker change over time and are described by quasi-hyperbolic discounting. A time-consistent optimal solution in this model corresponds with a Markov perfect equilibrium in a stochastic game with uncountable state space played by countably many short-lived players. We show that Markov perfect equilibria may be constructed using a generalized policy iteration algorithm. This method is in part inspired by the fundamental works of Mertens and Parthasarathy (in: Raghavan, Ferguson, Parthasarathy, Vrieze (eds) Stochastic games and related topics, Kluwer Academic Publishers, Dordrecht, 1991; in: Neyman, Sorin (eds) Stochastic games and applications, Academic Publishers, Dordrecht, 2003) devoted to subgame perfect equilibria in standard n-person discounted stochastic games. If the one-period utilities and transition probabilities are independent of time, we obtain on new existence results on stationary Markov perfect equilibria in the models with unbounded from above utilities. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic economic growth model in the form of an intergenerational dynamic game. Both paternalistic and non-paternalistic components are present in the model. Under very general assumptions allowing for unbounded utility functions and weakly continuous transitions, we establish the existence of Markov perfect equilibria that consist of a consumption strategy and an indirect utility function. In the pure paternalistic case, we obtain new results on equilibria. An important point of our contribution is that we make no separability assumptions on the utility functions of generations. [ABSTRACT FROM AUTHOR]

We study the pricing policy optimization problem for cloud providers while considering three properties of the real-world market: 1) providers have only incomplete information about the market; 2) it is in evolution due to the increasing number of users and decreasing marginal cost of providers; 3) it is fully competitive because of providers' and users' revenuedriven nature. As far as we know, there is no existing work investigating the optimal pricing policies under such realistic settings. We first propose a comprehensive model for the real-world cloud market and formulate it as a stochastic game. Then we use the Markov perfect equilibrium (MPE) to describe providers' optimal policies. Next we decompose the problem of computing the MPE into two subtasks: 1) dividing the stochastic game into many normal-formal games and calculating their Nash equilibria, for which we develop an algorithm ensuring to converge, and 2) computing the MPE of the original game, which is efficiently solved by an algorithm combining the Nash equilibria based on a mild assumption. Experimental results show that our algorithms are efficient for computing MPE and the MPE strategy leads to much higher profits for providers compared with existing policies. [ABSTRACT FROM AUTHOR]

Internet services, such as review sites, FAQ sites, online auction sites, online flea markets, and social networking services, are essential to our daily lives. Each Internet service aims to promote information exchange among people who share common interests, activities, or goods. Internet service providers aim to have users of their services actively communicate through their services. Without active interaction, the service falls into disuse. In this study, we consider that an Internet service has a network externality as its main feature, and we model user behavior in the Internet service with network externality (ISNE) as a dynamic game. In particular, we model the diffusion process of users of an ISNE as an infinite-horizon extensive-form game of complete information in which: (1) each user can choose whether or not to use the ISNE in her/his turn and (2) the network effect of the ISNE depends on the history of each player's actions. We then apply Markov perfect equilibrium to analyze how to increase the number of active users. We derive the necessary and sufficient condition under which the state in which every player is an active user is the unique Markov perfect equilibrium outcome. Moreover, we propose an incentive mechanism that enables the number of active users to increase steadily. [ABSTRACT FROM AUTHOR]

We reformulate the quality ladder model of Pakes and McGuire, Rand Journal of Economics, 25(4), 555-589 (1994) as a dynamic stochastic game with random moves in which each period one firm is picked at random to make an investment decision. Contrasting this model to the standard version with simultaneous moves illustrates the computational advantages of random moves. In particular, the quality ladder model with random moves avoids the curse of dimensionality in computing firms' expectations over all possible future states and is therefore orders of magnitude faster to solve than its counterpart with simultaneous moves when there are more than just a few firms. Perhaps unexpectedly, the equilibria of the quality ladder model with random moves are practically indistinguishable from those of the model with simultaneous moves. [ABSTRACT FROM AUTHOR]

The paper examines the issue of international pollution control under a dynamic framework involving heterogeneous countries and a critical threshold. We propose an appealing specification for this type of problem, and its novelty is illustrated by the fact that countries use linear strategies in equilibrium, although their utility and damage functions are highly convex. The stock of pollution under cooperation is always lower. Surprisingly, emissions are always higher in distant periods under the cooperative scenario; and we show through examples that this is a significant finding rather than some marginal effect. It is also shown that the efficient allocation of pollution abatement is driven only by the respective technologies of the countries. Finally, a dynamic transfer scheme allowing to implement the cooperative solution is proposed. [ABSTRACT FROM AUTHOR]

It is well known that the so-called voracity effect can be observed in an economy with a weak property rights system. Voracious behavior is regarded as one of the excess uses of the common assets. In this paper, we seek to examine voracious behavior from a different perspective by introducing a new direction of capital flow: from the private sector to the common sector. A government mandates that all competing interest groups invest their private capital in the common sector to mitigate the effects of excess use of the commons. In this situation, we study how this capital flow affects the voracious behavior of the groups and the growth rate of the economy. The main findings are that, while there is no standard voracity effect, an increase in the contribution of the private sector into the common sector causes more voracious behavior and thus reduces economic growth. This suggests that policies designed to preserve the commons can lead to a harmful effect on the economy. [ABSTRACT FROM AUTHOR]

The literature that conducts numerical analysis of equilibrium in models with hyperbolic (quasi-geometric) discounting reports difficulties in achieving convergence. Surprisingly, numerical methods fail to converge even in a simple, deterministic optimal growth problem that has a well-behaved, smooth closed-form solution. We argue that the reason for nonconvergence is that the generalized Euler equation has a continuum of smooth solutions, each of which is characterized by a different integration constant. We propose two types of restrictions that can rule out the multiplicity: boundary conditions and shape restrictions on equilibrium policy functions. With these additional restrictions, the studied numerical methods deliver a unique smooth solution for both the deterministic and stochastic problems in a wide range of the model's parameters. [ABSTRACT FROM AUTHOR]

Public-private partnerships have seen the daylight in response to the adagio that project responsibilities and risks should be efficiently allocated between the public and the private sector. Nevertheless, the considerable bidding costs inhibit the competition in the market. A trustworthy project agenda, also called a project pipeline, could substantiate the PPP market's attractiveness in the belief that a current success results in a knowledge and cost advantage in future tenders. This paper builds a sequential PPP procurement model and heuristically approximates the Markov perfect equilibrium in which contractors determine how much money they are willing to invest in the bid preparation and which mark-up is appropriate for each project in the pipeline. A pipeline of projects pushes down the mark-ups and the government procurement cost. Nonetheless, according to the experiments, only players with an initial experiential advantage tend to make higher investment efforts so that additional governmental policies, like a fractional reimbursement of the bid preparation efforts, might be required to level the playing field. [ABSTRACT FROM AUTHOR]

We characterize a relatively simple Markov Perfect equilibrium in a continuous-time dynamic model of competition with switching costs. When firms cannot price-discriminate between old and new consumers, the effect of switching costs on prices critically depends on the degree of market share asymmetries: If firms' market shares are sufficiently asymmetric, an increase in switching costs leads to higher prices. However, as market shares become sufficiently symmetric, price competition turns fiercer, and in the long-run, switching costs have a pro-competitive effect. If firms can price-discriminate, an increase in switching costs make all consumers better off regardless of market structure. [ABSTRACT FROM AUTHOR]

We review a class of models in industrial organization theory, in which consumers' foresight takes an important role. As Coase (J Law Econ 15:143-149, ) makes clear, the foresight of consumers may restrain the power of monopolists and oligopolists, especially when the goods are durable and the firms lack the ability to commit to future prices and/or outputs. This important insight clearly has significant implications for antitrust policies. However, the extent to which the powers of firms are curtailed depends on a host of factors which are explored in a number of important contributions. These factors include the length of time between two consecutive offers, the rate of depreciation of the durable goods, the product lines offered by firms producing the durable goods, the nature of network externalities in the primary market and the aftermarkets, the ability of firms to rely on reputational effects, and so on. This paper also reviews issues that are closely related to product durability, such as consumption capital in the case addictive goods, anticipation of future network congestions, and sales of assets such as shares of a firm's subsidiaries, or shares of a majority shareholder who has an influence on managers. [ABSTRACT FROM AUTHOR]

We study partial coalition formation and the strategic timing of membership of an IEA for environmental issues in the Coalitional Bargaining Game (CBG) of Gomes (Econometrica 73:1329-1350, ). We apply the CBG to a specific river sharing problem with two symmetric upstream agents, each at a tributary, and one downstream agent located at the junction of tributaries. We identify five regions in the parameter space of a discount factor and a productivity parameter for water. In one region the grand coalition always forms immediately. In two other regions, immediate formation of the grand coalition and gradual coalition formation both occur with positive probability. In another two regions only gradual coalition formation occurs. In one of these latter regions, a region with discount factors close to one, both upstream agents form a monopoly with positive probability. Formation of the monopoly persists in the limit as the discount factor goes to one. [ABSTRACT FROM AUTHOR]

We study an altruistic growth model with production uncertainty viewed as an intergenerational stochastic game. The existence of stationary Markov perfect equilibria is proved under general assumptions on utility functions for the generations and for non-atomic transition probabilities. This paper answers some issues that arose from the literature in the 1980s decade. [ABSTRACT FROM AUTHOR]

Consumers often incur costs when switching from one product to another. Recently, there has been renewed debate within the literature about whether these switching costs lead to higher prices. We build a theoretical model of dynamic competition and solve it analytically for a wide range of switching costs. We provide a simple condition which determines whether switching costs raise or lower long-run prices. We also show that even if switching costs reduce prices in the long run, they may still increase prices in the short run. Finally, switching costs redistribute surplus across time, and as such are shown to sometimes increase consumer welfare. [ABSTRACT FROM AUTHOR]

Standard economic models of groundwater management impose restrictive assumptions regarding perfect transmissivity (i.e., the aquifer behaves as a bathtub), no external effects of groundwater stocks, observability of individual extraction rates, and/or homogeneous agents. In this article, we derive regulatory mechanisms for inducing the socially optimal extraction path in Markov perfect equilibrium for aquifers in which these assumptions do not hold. In spite of the complexity of the underlying system, we identify an interesting case in which a simple linear mechanism achieves the social optimum. To illustrate potential problems that can arise by erroneously imposing simplifying assumptions, we conduct a simulation based on data from the Indian state of Andhra Pradesh. [ABSTRACT FROM AUTHOR]

International environmental agreements (IEAs) can coordinate abatement of transboundary pollutants. This paper investigates how heterogeneous countries facing a stock pollutant might structure such an agreement. In particular, we examine how an IEA might be implemented with a set of monetary transfers. The focus is on transfers that are time invariant, linear in emissions, and consistent with budget balance. There is a range of such schemes that would induce efficient emissions. We provide a simple and intuitive characterization of these penalties and describe how specific proposals might be chosen in order to facilitate compliance and implementation. Our proposals are illustrated with a simple example. We show that heterogeneity reduces the scope for penalty schemes to jointly satisfy desirable properties. [ABSTRACT FROM AUTHOR]

We investigate the incentives for investments in capacity in a simple strategic dynamic model with random demand growth. We construct non-collusive Markovian equilibria where the firms' decisions depend on the current capacity stock only. The firms maintain small reserve margins and high market prices, and extract large rents. In some equilibria, rationing occurs with positive probability, so the market mechanism does not ensure 'security of supply'. Usually, the price cap reflects the value of lost energy or lost load (VOLL) that consumers place on severely reducing consumption on short notice. Our analysis identifies a minimum price cap, unrelated to the VOLL, that allows the firms to recoup their investment and production costs in equilibrium. However, raising the price cap above this minimum increases market prices and reduces consumer surplus, without affecting the level of investment. [ABSTRACT FROM AUTHOR]

This paper contributes to the understanding of economic strategic behaviors in inter-temporal settings. Comparing the MPE and the OLNE of a widely used class of differential games it is shown: (i) what qualifications on behaviors a markov (dynamic) information structure brings about compared with an open-loop (static) information structure, (ii) what is the reason leading to intensified or reduced competition between the agents in the long run. It depends on whether agents’ interactions are characterized by markov substitutability or markov complementarity, which can be seen as dynamic translations of the ideas of strategic substitutability and strategic complementarity (Bulow et al. 1985, Journal of Political Economy 93:488–511). In addition, an important practical contribution of the paper for modelers is to show that these results can be directly deduced from the payoff structure, with no need to compute equilibria first. [ABSTRACT FROM AUTHOR]

This paper studies how the strength of intellectual property rights (IPRs) affects investments in biological innovations when the value of an innovation is stochastically reduced to zero because of the evolution of pest resistance. We frame the problem as a research and development (R&D) investment game in a duopoly model of sequential innovation. We characterize the incentives to invest in R&D under two competing IPR regimes, which differ in their treatment of the follow-on innovations that become necessary because of pest adaptation. Depending on the magnitude of the R&D cost, ex ante firms might prefer an intellectual property regime with or without a “research exemption” provision. The study of the welfare function that also accounts for benefit spillovers to consumers—which is possible analytically under some parametric conditions, and numerically otherwise—shows that the ranking of the two IPR regimes depends critically on the extent of the R&D cost. [ABSTRACT FROM AUTHOR]

With the continuing growth of the use of the Internet for business purposes, the consequences of a possible cyber attack that could create a large scale outage of long time duration becomes a more and more serious economic issue. In this paper, we construct a game-theoretic model that addresses the economic motivations for investment in added Internet security and makes a case for a possible market failure in the form of underinvestment in the provision of Internet security. This result relies on the fact that the social value derived from consumption (which is at least equal to a fraction of the surplus derived from e-commerce) greatly exceeds the revenue at stake associated with the telecommunications companies’ and ISP’s security levels. If the ratio of social value to revenue at stake to Internet providers continues to grow, the likelihood of underinvestment in security becomes higher and some form of regulation may become necessary. We discuss the difficulties associated with designing and enforcing a regulatory scheme based upon mandatory security standards. [ABSTRACT FROM AUTHOR]

In this paper, we empirically analyze weekly advertising policies of manufacturing firms in consumer goods markets. We assume firms engage in persuasive advertising, thus policies of firms affect the goodwill of a brand. We introduce a demand and a goodwill production function. A simple transformation of the demand function allows us to identify not only the demand parameters but also the parameters of the goodwill production function. We reconstruct the unobserved goodwill levels using these parameters and past advertising levels. We restrict our attention to Markov Perfect Equilibrium (MPE) strategies which are functions of payoff relevant state variables. Without imposing further restrictions on the dynamic competitive environment, we investigate the relationship between observed advertising strategies—which are assumed to be MPE-and payoff relevant state variables by means of several reduced form specifications. The most important determinant of advertising intensity turns out to be goodwill. We demonstrate that controlling for an advertising campaign significantly improves the explanatory power of the model. [ABSTRACT FROM AUTHOR]

This paper develops a model of dynamic advertising competition, and applies it to the problem of optimal advertising scheduling through time. In many industries we observe advertising "pulsing", whereby firms systematically switch advertising on and off at a high-frequency. Hence, we observe periods of zero and nonzero advertising, as opposed to a steady level of positive advertising. Previous research has rationalized pulsing through two features of the sale response function: an S-shaped response to advertising, and long-run effects of current advertising on demand. Despite considerable evidence for advertising carry-over, existing evidence for non-convexities in the shape of the sales-response to advertising has been limited and, often, mixed. We show how both features can be included in a discrete choice based demand system and estimated using a simple partial maximum likelihood estimator. The demand estimates are then taken to the supply side, where we simulate the outcome of a dynamic game using the Markov perfect equilibrium (MPE) concept. Our objective is not to test for the specific game generating observed advertising levels. Rather, we wish to verify whether the use of pulsing (on and off) can be justified as an equilibrium advertising practice. We solve for the equilibrium using numerical dynamic programming methods. The flexibility provided by the numerical solution method allows us to improve on the existing literature, which typically considers only two competitors, and places strong restrictions on the demand models for which the supply side policies can be obtained. We estimate the demand model using data from the Frozen Entree product category. We find evidence for a threshold effect, which is qualitatively similar to the aforementioned S-shaped advertising response. We also show that the threshold is robust to functional form assumptions for the marginal impact of advertising on demand. Our estimates, which are obtained without imposing any supply side restrictions, imply that firms should indeed pulse in equilibrium. Predicted advertising in the MPE is higher, on average, than observed advertising. On average, the optimal advertising policies yield a moderate profit improvement over the profits under observed advertising. [ABSTRACT FROM AUTHOR]