innovation and imitation in a duopoly in a duopoly where one firm has the idea for a non patentable innovation the expected profits from the innovation will not be a monotonic function of the cost of innovating furthermore a costly innovation may be undertaken where an inexpensive one would not have been all other things being equal

the wait and see option in ascending price auctions ascending auctions offer agents the option to wait and see before deciding to drop out we show that in contexts where as time proceeds agents get finer and finer estimates of their valuations incentives to drop out at one s expected valuation are weak it is optimal for agents to wait and see we first illustrate the claim in a private value setting we next analyze an interdependent value setting in which this wait and see option results in an imperfect information aggregation we also analyze the implications for the seller s revenue and show that the ascending format may dominate the second price format independently of the date at which the second price auction is run jel d44 d83

technology acquisition with technological progress effects of expectations rivalry and uncertainty abstract we study the effect of expectations regarding technological progress on a firm s technology adoption decision in a duopoly new generation technologies become available one in each period with successive generations representing better and better performance a game theoretic framework is used involving two identical firms competing in the same market over two periods it is shown that expectations retard adoption of the first period technology it is also shown that an asymmetric equilibrium results in higher social welfare and that more investment does not necessarily mean higher levels of welfare uncertainty is shown to have either no effect or a negative effect on the adoption of the current technology when nash equilibrium holds however when subgame perfect equilibrium holds uncertainty has a more complicated effect and numerical examples show that it may even encourage the adoption of the current technology relative to the deterministic equilibrium

existence of equilibrium in single and double private value auctions we show existence of equilibria in distributional strategies for a wide class of private value auctions including the first general existence result for double auctions the set of equilibria is invariant to the tie breaking rule the model incorporates multiple unit demands all standard pricing rules reserve prices entry costs and stochastic demand and supply valuations can be correlated and asymmetrically distributed for double auctions we show further that at least one equilibrium involves a positive volume of trade the existence proof establishes new connections among existence techniques for discontinuous bayesian games

on minimal ascending auctions with payment discounts the literature on ascending combinatorial auctions yields conflicting insights regarding the possibility to implement the vickrey payoffs for general valuations we introduce the class of minimal ascending auctions a class which allows one to disconnect the final payments from the final bids but which prohibits the raising of the price vector of a provisionally winning bidder we first establish the impossibility of implementing the vickrey payoffs for general valuations second we propose a minimal ascending auction that yields a bidder optimal competitive equilibrium thanks to payment discounts

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

collusion and signaling in auctions with interdependent values abstract the standard approach to collusion in auctions posits an uninformed disinterested third party who prior to the auction designs and implements a collusive mechanism in environments where collusion agreements are likely to be both proposed and executed by the involved parties this approach may neglect information leakages from simply a proposal to collude we consider a model of collusion where one informed bidder proposes to another as in es and schummer 2004 we allow for general interdependent values and affiliated signals in contrast to third party modeling approaches collusion is inefficient from both a social perspective except for the case of pure common values and from the perspective of the ring both bidders are better off than without colluding but the surplus extracted from the seller is distributed asymmetrically between the bidders the potential for information leakage from proposing is bad for low types who reveal that they are weak competitors but is advantageous for high types because they are able to signal their strength we identify a so called briber s curse whereby acceptance of a proposal causes the proposer to downgrade her expected value for the object when there is additional competition in the form of bidders outside of the cartel the briber s curse significantly harms cartel profits and raises seller revenues

the war of attrition in continuous time with complete information this paper provides a complete characterization of the nash equilibrium outcomes for the war of attrition when time is continuous and information is complete it allows for asymmetric payoffs and an arbitrary time horizon in addition to certain asymme tric pure strategy equilibria that always exist the authors establi sh the conditions under which there is also a continuum of mixed strategy equilibria these are most likely to exist when either the horizon is infinite or the game is symmetric copyright 1988 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

english auctions and the stolper samuelson theorem we prove that the english auction with bidders that need not be ex ante identical and may have interdependent valuations has an efficient ex post equilibrium we establish this result for environments where it has not been previously obtained we also prove two versions of the stolper samuelson theorem one for economies with n goods and n factors and one for non square economies similar assumptions and methods underlie these seemingly unrelated results

potential competition in preemption games we consider a preemption game with two potential competitors who come into play at some random secret times the presence of a competitor is revealed to a player only when the former moves which terminates the game we show that all perfect bayesian equilibria give rise to the same distribution of players moving times moreover there exists a unique perfect bayesian equilibrium in which each player s behavior from any time on is independent of the date at which she came into play we flnd that competitive pressure is nonmonotonic over time and that private information tends to alleviate rent dissipation our results have a natural interpretation in terms of eroding reputations

how risk sharing may enhance efficiency of english auctions we investigate the possibility of enhancing efficiency by awarding premiums to a set of highest bidders in an english auction in a setting that extends maskin and riley 1984 econometrica 52 1473 1518 in three aspects i the seller can be risk averse ii the bidders can have heterogeneous risk preferences and iii the auction can have a binding reserve price our analysis reveals that the premium has an intricate joint effect on risk sharing and expected revenue which in general benefits risk averse bidders when the seller is more risk averse than the pivotal bidder a condition often verifiable by deduction prior to the auction the premium also benefis the seller and therefore leads to a pareto improvement of the english auction the advantage of such premium tactics is directly related to a the seller s degree of risk aversion b the reserve price c the riskiness of the object for sale d the degree of heterogeneity in risk preferences among the bidders and e the number of the potential bidders

reputation and imperfect information abstract a common observation in the informal literature of economics and elsewhere is that is multistage games players may seek early in the game to acquire a reputation for being tough or benevolent or something else but this phenomenon is not observed in some formal game theoretic analyses of finite games such as selten s finitely repeated chain store game or in the finitely repeated prisoners dilemma we reexamine selten s model adding to it a small amount of imperfect or incomplete information about players payoffs and we find that this addition is sufficient to give rise to the reputation effect that one intuitively expects

optimal bidding in auctions from a game theory perspective abstract the game theoretic perspective in auction bidding has provided a powerful normative framework for the analysis of auctions and it has generated an impressive volume of research contributions tracing this research we review key recent advances which have greatly expanded our understanding of the operation of auctions and produced a more accurate analysis of mechanism design and optimal bidding we follow various experimental studies which have shown that the predictive power of auction theory remains in many cases limited for this reason we concentrate on research themes which enhance the applicability of auction theory leading to more realistic descriptions of bidding behaviors we identify important innovations which expand the environment of auction bidding and carry us beyond rational decision making we conclude providing directions of future research and discussing their implications

optimality and robustness of the english auction abstract in milgrom and weber s 1982 econometrica 50 1089 1122 general symmetric model under a few additional regularity conditions the english auction maximizes the seller s expected profit within the class of all posterior implementable trading procedures and fails to do so among all interim incentive compatible procedures in which losers do not pay these results suggest that appropriate notions of robustness and simplicity which imply the optimality of the english auction for a risk neutral seller must impose bargaining like features on the set of feasible trading mechanisms journal of economic literature classification numbers d44 d82

strategic timing of adoption of new technologies under uncertainty abstract in this paper we introduce experience effects into a duopoly game of timing of adoption of new technologies which exhibit exogenous technological progress departing from the existing literature with this model we obtain continuous and downward sloping reaction functions we find that a higher level of uncertainty increases the extent of dispersion between the equilibrium timings of adoption furthermore we find that the equilibrium timings are even more dispersed when the leader takes the follower s reaction into account when firm roles are made endogenous we find that if there is an incentive to lead follow the equilibrium timings are more less dispersed finally we show that it is possible for collusive adoption to improve welfare

interdependent value auctions with insider information theory and experiment abstract we develop a model of interdependent value auctions in which two types of bidders compete insiders who are perfectly informed about their value and outsiders who are informed only about the private component of their value because the bidding strategy of outsiders cannot efficiently adjust with that of insiders the second price auction is inefficient the english auction has an equilibrium in which the information outsiders infer from the history of drop out prices enables them to bid toward attaining efficiency the presence of insiders has positive impacts on the seller s revenue a laboratory experiment confirms key theoretical predictions despite evidence of naive bidding

adoption and diffusion of an innovation of uncertain profitability the argument has frequently been made that the pattern of diffusion associated with most new innovations will typically have certain characteristics a diffusion curve for an innovation is usually defined as the proportion of its potential users who have already adopted as a function of time measured from the first adoption many empirical studies by both economists and other social scientists have shown that diffusion curves nearly always have two distinct characteristics i they are s shaped the proportion adopted is an increasing function of time which is initially convex but eventually becomes concave and ii they tend to be right hand skewed the inflection point occurs at a time corresponding to a proportion adopted which is less than one half so that the function is concave over the greatest amount of time in fact this skewing is occasionally severe enough to make the diffusion curve appear concave everywhere the focus of most empirical studies of innovation diffusion has centered on identification of either the major determinants of the speed of diffusion or the characteristics of firms which determine how long they delay adoption the seminal contributions are griliches 6 study of hybrid corn and mansfield s 121 study of 12 industrial innovations these studies and most of the similar ones following conclude that diffusion is faster for innovations with higher profitability and that large firms tend to be the earliest adopters some studies e g mansfield 121 herregat 71 have attempted to ascertain

strategic timing of adoption of new technologies under uncertainty a note abstract this note clarifies the circumstances under which ex ante identical firms will choose different dates for the adoption of new technology in particular conditions under which diffusion will arise in both open loop and closed loop games are identified furthermore it is shown that the rents of nonidentical firms are not equalized even if pre emptive adoption is possible finally an example is given in which the reduction of the uncertainty associated with the implementation of new technology leads to a postponement of the adoption by the late adopter

analysis and algorithm for the optimal investment times of new manufacturing technologies in a duopoly abstract on the basis of a dynamic and non cooperative game theoretic model the optimal timings of investments in new manufacturing technologies nmt is analysed under duopolistic competition non identical incumbents with time proportional demand always wait for some delay to invest in nmt the existence of silent timing equilibrium is addressed subsequently we show that cost reducing nmt diffuse over time within a duopoly the investments in strategic nmt however may be distributed through time or in a swarm economic interpretations of initial options and the comparative statics presented in this paper help decision makers develop strategies and make decisions under the situation they face finally a computational algorithm of optimal timings could verify this analysis and facilitate the real applications of game theoretic models

asymmetric english auctions abstract this paper studies equilibria of the n bidder single object english or open ascending price auction in a setting with interdependent values and asymmetric bidders maskin in h siebert ed privatization institut fur weltwirtschaften der universitat kiel kiel 1992 pp 115 136 showed that if the values satisfy a single crossing condition then the two bidder english auction has an efficient equilibrium in this paper two extensions of the single crossing condition the average crossing condition and the cyclical crossing condition are introduced the main result is that under either of these conditions the n bidder english auction has an efficient equilibrium

optimal bidding in auctions of mixed populations of bidders abstract a mixed population of bidders consists of two asymmetric groups members of the first group are game theoretic players who maximize their expected profit and incorrectly believe that their opponents act similarly the second group of bidders adopts an irrational strategy they either choose their bids randomly following a given probability distribution in a naive form of bidding or follow a decision theoretic approach maximizing their expected profit under the assumption that all other bids are random in a sealed bid private value procurement auction we examine the optimal strategy of a new player who has perfect knowledge of the structure of the mixed bidder population and enters the auction the optimal bid of the new bidder is derived when the cost and mark up follow a uniform distribution in 0 1 the effect of the relative size of the group of game theoretic bidders and the population size on the optimal bid price is established

reputations in the adoption of a new technology abstract this paper studies the effects of uncertainty on the timing of adoption of a new technology in a duopoly firms are uncertain of the innovative capabilities of their rivals and about the profitability of adoption these features lead to a richer and in some respects more plausible theory of adoption in which rents from delayed adoption are always realized and returns are not equalized across adoption times

bidding in a possibly common value auction abstract we analyze a second price auction with two bidders in which only one of the bidders is informed as to whether the object is valued commonly we show that any equilibrium strategy of the bidder who is uninformed must be part of an equilibrium when both bidders instead know that the auction is not common value regardless of the way in which the values are different we derive sufficient conditions for equilibrium existence

innovation in a generalized timing game we examine innovation as a market entry timing game with complete information and observable actions we characterize all pure strategy subgame perfect equilibria for the two player symmetric model allowing both the leader s and the follower s payoff functions to be multi peaked non monotonic and discontinuous we provide sufficient conditions for when the equilibria can be pareto ranked and when the equilibrium is unique economic applications discussed include process and product innovation and the timing of the sale of an asset

asymmetric information and adverse selection in mauritian slave auctions information asymmetry is a necessary prerequisite for testing adverse selection this paper applies this sequence of tests to mauritian slave auctions the theory of dynamic auctions with private and common values suggests that when an informed participant is known to be active uninformed bidders will be more aggressive and the selling price will be higher we conjecture that observable family links between buyer and seller entailed superior information and find a strong price premium when a related buyer purchased a slave indicative of information asymmetry we then test for adverse selection using sale motivation our results indicate large discounts on voluntary as compared to involuntary sales consistent with adverse selection the market anticipated that predominantly low productivity slaves would be brought to the market in voluntary sales copyright 2009 wiley blackwell

an experimental analysis of auctions with interdependent valuations abstract we study experiments in an auction setting with interdependent valuation groups of three players receive private signals and then bid for a single indivisible item valuations for the item differ within groups and depend asymmetrically on a bidder s own and other bidders signals theoretically the english auction yields efficient allocations while other standard auction formats fail to do so consistent with equilibrium predictions we find that an english auction yields significantly more efficiency than a second price sealed bid auction we also study the seller s expected revenue and the bidders expected profits and find that the experimental results are close to the theoretical predictions

the supply of children s time to disabled elderly parents i introduction in recent years economists have become increasingly interested in intergenerational transfers of both time and money 1 such transfers may be motivated by altruism or exchange models of altruism assume that a person s utility depends on the consumption or utility of other family members and her own consumption for example children may supply unpaid informal care to aging parents because their utility increases when their parents are happier one of the most striking predictions of models of altruism is that public subsidies tend to crowd out transfers by altruistic individuals especially if the subsidy is financed by taxing the altruistic individual becker 1974 in exchange models there is typically altruism but one family member such as a parent can induce a relative such as a child or kid 2 to provide more services or money than the relative would normally provide by threatening to withhold a bequest to the extent that this is so one would plausibly expect more care and attention to be provided to wealthy parents when there is more than one kid more care should be provided because the threat of disinheritance is more credible when there is competition between kids for bequests in a well known article bernheim shleifer and summers 1985 hereafter referred to as bss found empirical support for the strategic bequest motive based on an observed positive relationship between children s visits and telephone calls to elderly parents per child as the measure of attention and bequeathable wealth per child as the measure of the financial motivation for providing such attention one might expect this result to extend to decisions about direct provision of help informal care that kids may provide to parents the marginal benefit of such care is plausibly greater than the benefit derived from a visit or telephone call in a recent article however we found no evidence that the strategic bequest motive is an important determinant of the amount of informal care kids provide or a related decision whether or not to place the parent in a nursing home sloan hoerger and picone 1996 we focused on the distinction between cognitively aware parents who can threaten to disinherit their kids and cognitively unaware parents who cannot disinherit and examined whether this distinction had any effect on the probability that the parent entered a nursing home or on amounts of formal and informal care received if the parent remained in the community any strategic effects were swamped by the greater marginal benefit of care to the parent when the parent was cognitively unaware moreover among the cognitively aware richer parents actually received less informal care contrary to the strategic model s predictions unfortunately in past research on intergenerational transfers of time and money it was not possible to control for the wealth wage and other characteristics of kids to the extent that kid s wealth and wage were positively correlated with parent s wealth which was observed the parameter estimates on parent s wealth may be negatively biased although parent s wealth and kid s wealth and wage rates are plausibly positively correlated they have opposite effects on the supply of kid s time according to the strategic bequest model that is potential bequests from a parent may be less attractive to rich kids and therefore induce less care we test the strategic bequest model using information on elderly parents and their children from two linked surveys the 1989 national long term care survey nltcs for elderly individuals and the survey of informal caregivers sic for a subsample of the elderly s children using these data we can include explicit measures of kid s wealth and wage rates thereby avoiding the possible bias introduced by a correlation between parent s and kid s wealth and wages also the data sets provide information on several pertinent health cognitive and functional status variables which are not typically observed in surveys of financial status

preemptive patenting and the persistence of monopoly this article takes a different tack and inquires whether institutions such as the patent system create opportunities for firms with monopoly power to maintain their monopoly power the results apply to other situations such as brand identification spatial location and capacity expansion which share the characteristic that early or preemptive actions may lower the returns to potential competitors

information acquisition and the adoption of new technology the profitability of a new technology is rarely known with certainty at its announcement date consequently prior to making an adoption decision it behooves the firm considering the adoption of this innovation to reduce the level of uncertainty associated with its profitability the firm accomplishes this by sequentially gathering information updating its prior estimate of profitability in a bayesian manner quantifying the uncertainty regarding the innovation permits application of dynamic programming techniques criteria are derived which tell the firm when to stop collecting information and make the adoption decision it will be shown that it is optimal for the firm to continue to collect information until its estimate of profitability crosses one of two thresholds upon crossing the upper threshold the firm adopts the technology whereas the firm rejects the technology if the lower threshold is crossed the model predicts that even the manager who behaves optimally will occasionally adopt unprofitable technologies and reject profitable ones

second mover advantages in the strategic adoption of new technology under uncertainty abstract this paper introduces technological uncertainty into a timing game of new technology adoption it is shown that the timing neither necessarily involves first mover advantages in precommitment equilibria reinganum review of economic studies xlviii 1981 395 405 nor rent equalization due to the threat of preemption fudenberg and tirole review of economic studies lii 1985 383 401 rather there may be second mover advantages because of informational spillovers furthermore the model predicts that the equilibrium payoffs will typically be discontinuous and non monotonic in the probability that the new technology is profitable a welfare analysis reveals several market failures and suggests that policy intervention should adequately depend on the nature of uncertainty and the rate of technological progress

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

first price auctions in the asymmetric n bidder case i consider the first price auction when the bidders valuations may be differently distributed i show that every bayesian equilibrium is an essentially pure equilibrium formed by bid functions whose inverses are solutions of a system of differential equations with boundary conditions i then prove the existence of an equilibrium i prove its uniqueness when the valuation distributions have a mass point at the lower extremity of the support i give sufficient conditions for uniqueness when every valuation distribution is one of two atomless distributions i establish inequalities between equilibrium strategies when relations of stochastic dominance exist between valuation distributions

preemption and rent equalization in the adoption of new technology we study the adoption of a new technology to illustrate the effects of preemption in games of timing we show that the threat of preemption equalizes rents in a duopoly but that this result does not extend to the general oligopoly game if the gain to preemption is sufficiently small then the optimal symmetric outcome which involves late adoption is an equilibrium this contrasts with reinganum s result that in precommitment equilibria there must be diffusion we develop a new and richer formalism for modeling games of timing which permits a continuoustime representation of the limit of discrete time mixed strategy equilibria

timing of technology adoption and product market competition abstract this paper examines how product market competition affects firms timing of adopting a new technology as well as whether the market provides sufficient adoption incentives it demonstrates that adoption dates differ not only among symmetric firms but also among markets with different market features more specifically technology adoption can occur earlier in a market with cournot competition than in a market with bertrand competition it can also occur earlier in a market in which goods are not too close substitutes therefore this paper shows that competition toughness does not always reinforce adoption incentives when goods are sufficiently differentiated adoption occurs later than is socially optimal

strategic investment in technological innovations abstract the aim of this paper is to determine the optimal timing of technology investment of a single firm in a duopoly framework as time passes different technologies are invented which after sometime become available for the firm to adopt the question here is not only when a firm should invest but also which technology should be adopted for different scenarios the optimal technology investment decision is determined outcomes range from pre emption equilibria to equilibria with second mover advantages

full extraction of the surplus in bayesian and dominant strategy auctions we consider auctions for a single indivisible object in the case where the bidders have information about each other which is not available to the seller we show that the seller can use this information to his own benefit and we completely characterize the environ ments in which a well chosen auction gives him the same expected payoff as that obtainable were he able to sell the object with full information about each bidder s willingness to pay we provide this characterization for auctions in which the bidders have dominant strate gies and for those where the relevant equilibrium concept is bayesian nash in both set ups the existence of these auctions hinges on the possibility of constructing lotteries with the correct properties we consider the situation in which an agent the seller possesses one indivisible unit of a good to which he attaches no value but the good has value to a number of potential buyers and its transfer to one of them would increase social welfare in particular the transfer to the buyer with the highest valuation maximizes social welfare in this paper we completely characterize environments in which the seller can design an auction that will enable him to capture for himself the full increase in social welfare induced by the transfer of the good to the bidder with the highest willingness to pay if the seller had full information about the reservation prices of potential buyers his optimal selling strategy would be very simple he would announce a price equal or very close to the highest reservation value the optimal strategy for the bidder with the highest evaluation would be to accept the offer note that we are treating a situation in which the seller can commit himself to a price as a result of the exchange the utility of the seller increases by the full amount of the increase in social welfare and he has been able to fully extract the surplus in many circumstances however a seller has only imperfect knowledge of the buyers willingnesses to pay in this case he must find some mechanism or auction which will enable him to maximize his benefit from the sale of the object the auction literature starts with this observation and shows how the seller can by an astute choice of auction extract the largest possible fraction of the surplus in general the literature has shown that this proportion is strictly less than one in some circumstances the bidders will have information about each other which is not available to the seller for instance in auctions for petroleum drilling rights bidders know the results of geological tests which they have

an efficient multi unit ascending auction we provide an ascending auction that yields an e cient outcome when there are many identical units for sale and bidders have interdependent values and downward sloping demand our ascending auction both extends and generalizes ausubel s 1997 and yields the same outcome as perry and reny s 2000 generalization of vickrey s 1961 sealed bid auction there are two key components to our auction bidders are permitted both to

on the existence of monotone pure strategy perfect bayesian equilibrium in games with complementarities abstract many important economic situations such as auctions and signaling games can be modeled as dynamic games of incomplete information with strategic complementarities of actions and types in this paper we extend the results of athey 2001 and reny 2011 from static bayesian games to dynamic environments with observable actions providing conditions that guarantee the existence of monotone equilibria in types in such games a feature that distinguishes this environment from those of previous results is the endogeneity of beliefs which can complicate continuity of payoffs needed to find a fixed point to address this we perturb the strategies of the game which pins down beliefs while preserving continuity of payoffs we then provide conditions which guarantee that there will exist monotone best replies to monotone strategies of one s opponents in a dynamic environment enabling verification of existence by merely looking at the primitives of the model

on the efficiency of the first price auction we provide a natural setting in privatizations in which the equilibrium of the first price auction gives greater expected surplus than any equilibrium of the open ascending auction