differential games with nonconvexities and positive spillovers abstract this paper deals with differential games characterized by nonconvexities and increasing returns the objective function of the players is convex in the control variables and nonconvex in the state variables we employ the open loop nash equilibrium solution concept this framework enables us to handle games characterized by positive spillovers and strategic complementarities e g capital accumulation differential games with learning by doing where the knowledge available to a firm is given by the knowledge accumulated by the economy as a whole

shipwrecks and treasure hunters we examine dynamic search as a game in which two rivals explore an island for a hidden prize of known value in every period until its discovery the players decide how much of the unsearched area to comb if a player finds the prize alone he wins it and the game ends players have a per period discount factor and costs proportional to the area they search first as a benchmark for efficiency we solve the one player search problem second in the two player setting we show that typically there is inefficient over search a result akin to the tragedy of the commons however for players with intermediate levels of patience there is the possibility of inefficient under search as players incorporate the expected future payoffs in their current search decisions finally with patient players several counterintuitive results can arise for example players might be better off searching a larger island or looking for a less valuable prize

technological expectations and adoption of improved technology abstract attention is focused upon the adoption demand rather than the creation supply of new technology which improves from time to time based on the expected flow of technological progress over which the firm demander has no control it must decide either to adopt the current best available technology or to postpone adoption the distinguishing features of the model are that more than one technological innovation is anticipated and expectations about the likelihood of such innovations are revised as time passes since the last innovation our analysis shows that the firm will adopt the current best practice if its technological lag exceeds a certain threshold moreover as time passes without new technological advances it may become profitable to purchase a technology that has been available even though it was not profitable to do so in the past

trends in female labor force participation in sweden labor force participation of married women increased from 49 1 to 83 5 during the past 2 decades by cross section estimates on micro data of the probability of labor force participation in 1967 1973 and 1980 and by using these estimates for predicting changes in labor force participation we have found that increases in own wage has been by far the most important explanatory factor women s real wages have increased relative to husband s after tax earnings both as an effect of the introduction of compulsory separate taxation in 1971 and as an effect of dramatically decreased sex differentials in pay partly associated with increased female education

racing with uncertainty and strategic interaction between competitors as the race unfolds most of the existing literature examines one or other of these features but not the two combined our aim is to see how the efforts of competitors in a race vary with the intensity of rivalry between them in our principal model whch is of a one dimensional race it is shown that the leader in the race makes greater efforts than the follower and efforts increase as the gap between competitors decreases under certain conditions the same results hold in our second related model which is of a two dimensional race

a closed form solution for a model of precautionary saving this paper analyses life cycle consumption plans and distinguishes between temporal risk aversion and intertemporal substitution the results assume that felicity functions are quadratic and that income follows a linear model with normally distributed errors stochastic dynamic programming then yields closed loop linear decision rules certainty equivalence no longer holds but instead households play a min max strategy against nature one finds a rationale for precautionary saving and a larger sensitivity of changes in consumption to income innovations

innovations and the economics of new technology spreading within and across users gaps and way forward r d subsidies are often considered the main policy tool to stimulate the competitiveness and the innovativeness of firms this is especially true for innovations designed to produce greener products or cleaner and more energy efficient technologies however a consistent literature has now shown that even when a clean or a cost reducing technology is ready available in the market its spreading within intra or across inter households or firms takes several years and in some cases decades therefore it is not only important to generate innovations via investments in r d but it is also important that such innovations are adopted and used by firms this paper briefly illustrates the main theoretical approaches to the analysis of the factors leading to inter firm diffusion and emphasise the existing gap led by the paucity of literature on intra firm diffusion a final section briefly discusses some methodological issues surrounding the diffusion of consumer non durable technologies within and across households and how ad hoc models can be used to test the validity of environmental policies

a patent race in a real options setting investment strategy valuation capm beta and return volatility abstract in this paper we study financial properties of r d intensive firms through a continuous time real options patent race model numerical analysis in this study shows that intense competition drives a firm to invest more aggressively which then pushes up its cost of capital and return volatility while introducing negative return correlation with its competitor furthermore we find that a firm s position in competition has important impacts on its financial properties for instance a firm s cost of capital is a non monotonic function of its relative position in the race in addition the relationship between cash flow uncertainty and investment can be negative when a firm is far ahead or far behind or positive when firms are close in the race

learning under fear of floating in recent years a large fraction of economies overcame the fear of floating we study a model that describes the policy of a central bank uncertain about whether currency depreciations cause output to expand textbook model or contract balance sheet model we conclude that the movement away from fear of floating may not be explained by bayesian or robust policies when the private sector anticipates the central bank s policy and endogenously determines the model central banks may fall in a learning trap an increase in financial volatility provides an escape to such trap that replicates patterns in the data

differential game models in management science abstract this paper reviews a number of differential games applications to management science and operations research problems published with a few exceptions during the last decade the purpose of the article is to provide the reader with an up to date account of the state of the art within this field after having stated in an introduction the general differential games framework as well as some conceptual problems we proceed to review the models which have been divided into the following functional areas investment consumption and employment production inventories and maintenance marketing advertising pricing and rd bargaining natural resources and pollution the survey concludes with some remarks on applicability solvability and directions for future research

preemption in r d races abstract fudenberg gilbert stiglitz and tirole 1983 consider a patent race in which each firm s instantaneous probability of discovering a patentable invention is an increasing function of its cumulative expenditure on rd in particular we show that for intermediate values of it is possible for the follower to spoil the race by forcing the leader to drop out

comparison of indicators of women s labour between turkey and eu member states by employing multidimensional scaling analysis and clustering analysis abstractat present because of social cultural and economic changes women support the economies of their countries by their status as workers in this research we aim at comparing the status of turkey in terms of indicators of women in the labour force with that of eu countries thereby revealing the similarities and differences the variables indicating women in the labour forces of the 28 eu countries and turkey were analysed utilizing multidimensional scaling analysis mdsa and clustering analysis ca according to the mdsa the countries form three different groups in two dimensional space the clusters formed by the ca are congruent with the groups formed according to the mdsa when compared with eu members turkey has very low values particularly in terms of the ratio of working women the ratio of jobless females who are primary or secondary school graduates and the ratio of women who are senior high school graduates

first movers non movers and social gains from subsidising entry in markets for nature based recreational goods abstract the importance of ecosystem services for mankind stresses the issue of identifying different institutional solutions to effectively secure their adequate provision much focus has been on services of the public good type and instruments like payments for environmental services we extend this work to consider the possible social gains from supporting development of new markets for nature based recreational goods which may alleviate negative externalities caused by congestion problems our three main questions are i why is there a lack of market development ii can there be social gains from intervention and supporting the development of such markets and iii if so then how could such intervention be best performed we use a two stage non cooperative bayesian simultaneous move game model and show that in spite of apparent potential first mover advantages in a developing market demand uncertainty and sunk costs may equally well result in widespread presence of non movers on the supplier side we show that social gains can be made from offering a subsidy towards the sunk costs analysing three possible subsidy schemes we show a that fixed costs may make rationing optimal b that sequential rationing does not necessarily dominate strict rationing because c the more subsidies are offered the larger each subsidy must be to induce participation and that d the longer a single agent on the market may keep market information to himself the better a non rationing scheme will perform relative to rationing schemes finally e subsidies for second mover entry may be optimal in some cases

patents imitation and licensing in an asymmetric dynamic r d race abstract rd some may have an advantage in early stages of the r d process while others may have advantages in other stages of the process this paper uses a two firm asymmetric ability multistage r d race model to analyze the effect of patents imitations and licensing arrangements on the speed of innovation firm value and consumers surplus by using numerical analyses to study the mpe of the r d race the paper demonstrates the circumstances under which a weak patent protection regime that facilitates free imitation of any intermediate technology may yield a higher consumers surplus and total surplus than a regime that awards a patent for the final innovation the advantage of imitation may hold even when we allow for voluntary licensing of intermediate technologies

intercountry comparisons of labor force trends and of related developments an overview this paper is a survey of analyses of women s labor force growth in 12 industrialized countries originally presented at a conference in sussex england in june 1983 the main focus of the conference papers and of the current survey is on growth of the labor force of married women in the years 1960 80 trends in fertility wages and family instability also receive attention as related developments married women s labor force growth is observed in all countries except for the ussr after 1970 where labor force rates of women reached the level of men growth rates differ among countries they apparently respond to growth in real wages and to growth in education but response elasticities differ among countries estimates of these elasticities contained in the country papers were helpful in predicting the trends other findings include ubiquitous declines in fertility and growth of divorce in the 1970s both developments are related to long run labor force growth in all countries wages of women were lo

an analysis of cooperative research and development i analyze the effects of cooperative research whereby member firms agree to share the costs andfruits of a research project before they undertake it in this model industrywide agreements tend to have socially beneficial effects when the degree ofproduct market competition is low when there are r d spillovers in the absence of cooperation when a high degree of sharing is technologically feasible and when the agreement concerns basic research rather than development activities i show that a royalty free cross licensing agreement among any number offirms lowers the equilibrium level of innovation even though it increases the efficiency of r d through sharing

optimal monetary policy with an uncertain cost channel the cost channel of monetary transmission describes a supply side effect of interest rates on firms costs previous research has found this effect to vary both over time and across countries moreover the cyclical nature of financial frictions is likely to amplify the cost channel this paper derives optimal monetary policy in the presence of uncertainty about the true size of the cost channel in a min max approach the central bank derives an optimal policy plan to be implemented by a taylor rule it is shown that uncertainty about the cost channel leads to an attenuated interest rate setting behavior in this respect the brainard 1967 principle of cautious policy in the face of uncertainty continues to hold in both a bayesian and a min max framework

the intra firm diffusion of new process technologies the study of intra firm diffusion has largely been neglected and the limited extant literature overwhelmingly relies upon uncertainty reduction via information spreading or epidemic learning as the main driver in this paper an alternative approach is taken whereby the intra firm diffusion of new process technologies reflects the profitability of new technology adoption as proxied by firm characteristics the approach is tested using data relating to the diffusion of computer numerically controlled machine tools within firms in the uk engineering and metalworking sectors the empirical analysis does not reject the hypothesis that profitability considerations are important with a number of firm characteristics being isolated as of special relevance including firm size and the use of complementary technologies and managerial techniques however there is little support for the traditional epidemic effect

innovation timing games a general framework with applications abstract we offer a new algorithm for analyzing innovation timing games its main advantage over the traditional approach is that it applies to problems that had previously been intractable we use the algorithm to examine two classical innovation problems we find that the competition takes the form of a waiting game with a second mover advantage either for any level of r d costs process innovation or for high r d costs product innovation moreover both models predict that the second mover advantage is monotonically increasing in the costs of r d

variable costs and the visible hand the re regulation of electricity supply 1932 37 national transmission grid and rationalize uk electricity generation a constrained cost model estimates the gains from this re regulation of the electricity generating industry the new regime reduced costs by one third radically improving the utilization of capital and boosting the average scale of operations it did so by persuading private and municipal enterprises to accept central direction of the extent and timing of their electricity generation this voluntarism saved on enforcement costs but perhaps one half of the industry cost reduction the ceb actually achieved by 1937 was apparently forgone

dynamic patent races with risky choices this paper investigates equilibrium rd firms compete more vigorously in the later stages of innovation than in the earlier stages and a follower is more likely to choose a riskier innovation path than one requiring on average equivalent effort it provides an explanation of how the expected benefits the cost of r d and interactions between competing firms combine to determine dynamic r d strategies over time

robustly optimal monetary policy in a microfounded new keynesian model we consider optimal monetary stabilization policy in a new keynesian model with explicit microfoundations when the central bank recognizes that private sector expectations need not be precisely model consistent and wishes to choose a policy that will be as good as possible in the case of any beliefs close enough to model consistency we show how to characterize robustly optimal policy without restricting consideration a priori to a particular parametric family of candidate policy rules we show that robustly optimal policy can be implemented through commitment to a target criterion involving only the paths of inflation and a suitably defined output gap but that a concern for robustness requires greater resistance to surprise increases in inflation than would be considered optimal if one could count on the private sector to have rational expectations

insurance policies for monetary policy in the euro area in this paper we aim to design a monetary policy for the euro area that is robust to the high degree of model uncertainty at the start of monetary union and allows for learning about model probabilities using the data that has become available since then to this end we compare and ultimately combine bayesian and worst case analysis using four reference models developed at the ecb and estimated with pre emu synthetic data we start by computing the cost of insurance against model uncertainty that is the relative performance of worst case or minimax policy versus bayesian policy we find that maximum insurance across this range of models can be obtained at moderate costs costs are measured in terms of lower expected performance relative to a bayesian policy with flat priors further scrutiny however highlights three shortcomings of this worst case insurance policy i prior beliefs that would rationalize the minimax policy from a bayesian perspective indicate that such insurance is strongly oriented towards the model with highest baseline losses ii the minimax policy is not as tolerant towards small perturbations of policy parameters as the bayesian policy and iii the minimax policy offers no avenue for incorporating posterior model probabilities derived from data available since monetary union thus we propose preferences for robust policy design that reflect a mixture of the bayesian and minimax approaches these preferences referred to as intermediate ambiguity aversion incorporate model probabilities while still giving extra weight to the worst uncertain outcomes we show how the incoming emu data may then be used to update model probabilities and investigate the implications for policy design

cost reducing r d in oligopoly abstract this paper provides a conjectural variations model to explore competition in cost reducing r d and the nature of the inter firm externalities it is shown that 1 r d investment in a market with price competition becomes optimal if firms expect that changes in their own r d investment are followed by the rival firms 2 the optimal r d subsidies are positive in collusive oligopolies but negative in competitive oligopolies 3 joint r d ventures in oligopoly could reduce total surplus by causing underinvestment and 4 promoting price competition reduces welfare if firms are not collusive in their r d decisions

a stochastic competitive r d race where winner takes all the paper considers a race among multiple firms that compete over the development of a product the first firm to complete the development gains a reward whereas the other firms gain nothing each firm decides how much to invest in developing the product and the time it completes the development is a random variable that depends on the investment level the paper provides a method for explicitly computing a unique nash equilibrium parametrically in the interest rate for a given interest rate the nash equilibrium is determined in time that is linear in the number of firms the structure of the solution yields insights about the behavior of the participants furthermore an explicit expression for a unique globally optimal solution is obtained and compared to the unique nash equilibrium

on the relation between robust and bayesian decision making abstract this paper compares bayesian decision theory with robust decision theory where the decision maker optimizes with respect to the worst state realization for a class of robust decision problems there exists a sequence of bayesian decision problems whose solution converges towards the robust solution it is shown that the limiting bayesian problem displays infinite risk aversion and that decisions are insensitive robust to the precise assignment of prior probabilities this holds independently of whether the preference for robustness is global or restricted to local perturbations around some reference model

strategic learning and entry equilibrium abstract this paper describes the nature of equilibrium for a dynamic game between a monopolist and an entrant who adopts a learning strategy for cost reduction the learning process is characterized as a continuous time poisson process where each success reduces a part of the entrant s cost difference with the incumbent the entrant chooses a stream of expenditure after every success to control the instant probability of the next success the techniques of semi markov decision processes are used to characterize equilibrium learning decisions at every stage distribution of entry times and the effects of subsidies technical progress etc on pre entry and post entry learning strategies

jewish mother goes to work trends in the labor force participation of women in israel 1955 1980 the labor force participation of jewish women in israel increased between 1955 and 1980 accelerating in the 1970s schooling accounts for most of the change the sharpest rise is among mothers ages 25 44 thus differentials in participation by marital status have been sharply narrowed and the life cycle in participation has been transformed the m shaped curve being replaced by an inverted u with delayed labor force entry due to prolonged schooling and more continuous participation throughout the childbearing period the reduced incompatibility between child rearing and market work is associated with part time work and increased reliance on day care services the increased employment of women is concentrated in the service industries mostly public and is accompanied by some decline in the relative wage of highly educated women successive cross section estimates corroborate this picture in general but do not support the notion that over time preschool children interfere less in women s labor supply

model uncertainty and intertemporal tax smoothing in this paper we examine how model uncertainty due to the preference for robustness rb aects optimal taxation and the evolution of debt in the barro tax smoothing model 1979 we rst study how the government spending shocks are absorbed in the short run by varying taxes or through debt under rb furthermore we show that introducing rb improves the model s predictions by generating i the observed relative volatility of the changes in tax rates to government spending ii the observed comovement between government decits and spending and iii more consistent behavior of government budget decits in the us economy finally we show that rb can also improve the model s predictions in the presence of multiple shocks

on the diffusion of new technology a game theoretic approach this paper is an attempt at a rigorous albeit not exceedingly general analysis of the diffusion of new technology in particular consider an industry composed of two firms each using the current best practice technology the firms are assumed to be operating at nash equilibrium output levels generating a market price given demand and profit allocations when a cost reducing innovation is announced each firm must determine when if ever to adopt it based in part upon the discounted cost of implementing the new technology and in part upon the behavior of the rival firm if either firm adopts before the other it can expect to make substantial profits at the expense of the other firm on the other hand the discounted sum of purchase price and adjustment costs may decline with the lengthening of the adjustment period as various quasi fixed factors become more easily variable therefore although waiting costs the firm more in terms of foregone profits it may save money on the cost of purchasing the new technology thus the firm must weigh the costs and benefits of delaying adoption as well as take account of its rival s strategic behavior

developing real option game models by mixing concepts from both game theoretic analysis and real options theory an investment decision in a competitive market can be seen as a game between firms as firms implicitly take into account other firms reactions to their own investment actions we review two decades of real option game models suggesting which critical problems have been solved by considering game theory and which significant problems have not been yet adequately addressed we provide some insights on the plausible empirical applications or shortfalls in applications to date and suggest some promising avenues for future research

gender discrimination and compensating differentials in sweden the determinants of the unexplained component of the male female wage difference in sweden are examined the hypothesis that there is a compensating wage differential associated with undesirable job charcteristics is tested hedonic wage equations are estimated using data collected in the 1981 swedish level of living survey the estimation takes into consideration possible sample selection bias due to the non randomness takes of employment and the potential endogeneity of job choice variables in wage offer equations overall the analysis indicates that compensating wage differentials are not a major determinant of the male female wage difference in sweden

the optimal timing of procurement decisions and patent allocations in a patent race social incentives and private incentives may sometimes coincide and at other times diverge too many researchers remain in the race if the social planner cannot determine what stage the researchers have achieved this informational constraint can result in a socially suboptimal outcome we construct a mechanism in which a planner exploits the researchers private information to determine when and to whom to allocate rights to pursue the final prize this mechanism does not require any payments and therefore will not distort earlier investment incentives it is solvable by the iterative elimination of dominated strategies

patent rights and innovation disclosure this article studies optimal patents with respect to the timing of innovation disclosure in a simple model we identify forces that lead firms to either suboptimally patent too early or too late in equilibrium and we determine conditions so that stronger patents induce earlier or later equilibrium disclosure then by solving an infinite multistage patent game with a more explicit structure we describe innovation growth and derive detailed predictions that can be used for policy experiments as an application we calibrate our multistage game using summary statistics from the seeds breeding industry we find that weaker patent rights may result in welfare gains of 46 relative to the status quo the gains are achieved because weaker patents reduce competition thus leading firms to postpone patenting

equilibrium investment in an industry with moderate investment economies of scale the authors investigate a stationary equilibrium investment sequence in an industry where the costs of investment display initial economies of scale but eventually decreasing returns to scale both the timing and size of new investments are choice variables and they allow the industry structure to be as competitive as one could imagine given the cost conditions the authors argue that competitive private firms will make new investments that are too early and too small their results have implications for the likely performance of industries such as electricity telecommunications gas and water supply after deregulation or privatization copyright 1989 by royal economic society

robust permanent income and pricing i suppose there exists an extremely powerful and if i may so speak malignant being whose whole endeavours are directed toward deceiving me rene descartes meditations ii 1

rationalizability learning and equilibrium in games with strategic complementarities we study a rich class of noncooperative games that includes models of oligopoly competition macroeconomic coordination failures arms races bank runs technology adoption and diffusion r d competition pretrial bargaining coordination in teams and many others for all these games the sets of pure strategy nash equilibria correlated equilibria and rationalizable strategies have identical bounds also for a class of models of dynamic adaptive choice behavior that encompasses both best response dynamics and bayesian learning the players choices lie eventually within the same bounds these bounds are shown to vary monotonically with certain exogenous parameters we study the class of noncooperative supermodular games introduced by topkis 1979 and further analyzed by vives 1985 1989 who also pointed out the importance of these games in industrial economics supermodular games are games in which each player s strategy set is partially ordered the marginal returns to increasing one s strategy rise with increases in the competitors strategies so that the game exhibits strategic complementarity 2 and if a player s strategies are multidimensional marginal returns to any one com ponent of the player s strategy rise with increases in the other components this class turns out to encompass many of the most important economic applications of noncooperative game theory in macroeconomics diamond s 1982 search model and bryant s 1983 1984 rational expectations models can be represented as supermodular games in each of these models more activity by some members of the economy raises the returns to increased levels of activity by others in oligopoly theory some models of bertrand oligopoly with differentiated products qualify as supermodu lar games in these games when a firm s competitors raise their prices the marginal profitability of the firm s own price increase rises a similar structure is present in games of new technology adoption such as those of dybvig and spatt 1983 farrell and saloner 1986 and katz and shapiro 1986 when more users hook into a communication system or more manufacturers adopt an interface standard the marginal return to others of doing the same often rises similarly in some specifications of the bank runs model introduced by diamond and dybvig 1983 when more depositors withdraw their funds from a bank it is more worthwhile for other depositors to do the same in the warrant exercise

firms r d decisions under incomplete information abstract the paper considers a patent race in which firms do not know their relative positions in this setting firms that start in the same position proceed at the highest possible speed and if one firm has an initial advantage it preempts the rival but at the cost of dissipating a significant part of its monopoly rent so the paper shows that incomplete information in a patent race leads to rent dissipation the latter is higher the higher the value of the prize and the lower the cost of r d thus for innovations that provide relatively high profits the time to discovery is shortened but the social losses are likely to be high due to duplication of effort

a dynamic game of r and d patent protection and competitive behavior a theory of dynamic optimal resource allocation to r and d in an n firm industry is developed using differential games this technique represents a synthesis of the analytic methods previously applied to the problem static game theory and optimal control the use of particular functional forms allows the computation and detailed discussion of the nash equilibrium in investment rules this paper addresses the problem of resource allocation to research and development among the important issues that a firm engaging in r and d must evaluate are uncertainty regarding the feasibility and profitability of a particular innovation the possibility of a protracted development period the possibility that a rival firm may innovate first capturing either a patent or a significant share of the new market the possibility that a rival firm may imitate the innovation and appropriate some of the profits in the new market in what follows we will develop a theory of optimal resource allocation to research and development which incorporates the aspects of r and d enumerated above we will use a dynamic game theoretic analysis determining the nash equilibrium strategies for n identical firms the availability of perfect patent protection is shown to accelerate development of the innovation and the effect of increasing rivalry is addressed the impact of increasing rivalry on nash equilibrium investment in r and d depends upon the degree of appropriability of rewards if patent protection is perfect then increasing the number of nash rivals results in increased r and d effort however when imitation is rewarded the opposite may be true finally some notions of competitive and perfectly competitive equilibrium are examined in the context of the model developed below

path shifting of the welfare state electoral competition and the expansion of work family policies in western europe what explains the surprising growth of work family policies in several west european countries much research on the welfare state emphasizes its institutional stickiness and immunity to major change yet over the past two decades governments in germany the netherlands and the united kingdom have introduced important reforms to their welfare regimes enacting paid leave schemes expanded rights to part time work and greater investments in child care a comparison of these countries reveals a similar sequence of political and policy change faced with growing electoral instability and the decline of core constituencies party leaders sought to attract dealigning voter groups such as women this led them to introduce feminizing reforms of their party structures and adopt policies to support mothers employment in all three cases women working within the parties played an important role in hatching or lobbying for these reforms after comparing three countries that moved in a path shifting direction this article engages in a brief traveling exercise examining whether a similar set of dynamics are lacking in two countries austria and italy that have moved more slowly in reforming these policies against the prevailing scholarly literature that emphasizes path dependence and slow moving change this article reveals the continued power of electoral politics in shaping redistributive policies