market structure and r d competition abstract r d is modelled as a random draw from a set of technologies for producing a homogeneous good it is shown that both a pure monopolist and bertrand oligopolists stop r d at technology levels which are less productive than is socially desirable with bertrand competition this reservation technology level is independent of the number of firms the effort per r d project depends in general on the market structure and total r d expenditures generated in markets are smaller than the social optimum

keep on fighting the dynamics of head starts in all pay auctions abstract we investigate a model of a series of contests in which a contestant s past and present success gives a head start over a rival in the future how this advantage from winning affects contestants efforts whether the laggard gives up or keeps on fighting and how the head start develops over time are key issues we find that the expected effort of the laggard will always be higher than the rival at some stage in the series of contests and this is most likely to happen when at a large disadvantage or at a late stage in the series

substitution possibility between unpriced pulp and wastepaper in the u s paper and paperboard industry a greater use of recycled wastepaper would preserve virgin forests as well as reducing the amount of wastepaper going to landfills these environmental goals depend critically on the elasticity of substitution between pulp and wastepaper in producing paper and paperboard since most of the pulp consumed by u s paper mills and paperboard mills is transferred internally from vertically integrated pulp mills the price data on pulp is not available this paper constructs an econometric model which enables us to estimate the substitution possibility between unpriced pulp and wastepaper in the u s paper and paperboard industry empirical results show that the elasticity of substitution between unpriced pulp and wastepaper is positive but not statistically significant

market share market value and innovation in a panel of british manufacturing firms this paper examines the empirical relationship between technological innovations market share and stock market value new developments in the estimation of dynamic count data models are used to control for unobserved firm specific heterogeneity we find a robust and positive effect of market share on observable headcounts of innovations and patents although increased product market competition in the industry tends to stimulate innovative activity furthermore the impact of innovation on market value is larger for firms with higher market shares we argue that our results are consistent with models where high market share firms have incentives to pre emptively innovate

optimal management of an r d budget abstract this paper characterizes the optimal allocation of a budget between several stages of an r d project when intermediate stages are profitable the optimal allocation involves greater expenditures in early stages increasing the budget does not necessarily increase expenditures in every stage but does increase the budget that remains unspent at each stage a simple necessary and sufficient condition is given for the optimality of bold play the spending of all remaining budget on the current stage if profits are realized only after all stages are successfully completed decreasing returns in the innovation production function implies that the optimal strategy is to spread the budget evenly between the stages of the r d project

contests with multiple rounds this paper studies contests where players have the flexibility to add to their previous efforts after observing their rivals most recent effort in an intermediate stage it is found that 1 contrary to previous findings the stackelberg outcome where the underdog leads and the favorite follows cannot be an equilibrium 2 there are multiple subgame perfect equilibria all occurring on the underdog s usual one shot reaction function in between and including the one shot cournot nash and stackelberg outcome with the favorite leading 3 the total equilibrium effort is typically greater than or equal to what a one shot cournot nash play would predict and 4 in settings where players can choose whether or not to disclose their early actions to the rival both the favorite and the underdog disclose in equilibrium applications in sports lobbying and r d races are discussed

how to split the pie optimal rewards in dynamic multi battle competitions abstract multi battle competitions are ubiquitous in real life in this paper we examine the effort maximizing reward design in sequentially played multi battle competitions between two players the organizer has a fixed prize budget and rewards players contingent on the number of battles they win in a three battle contest a full spectrum of contest technologies in the tullock family is accommodated we find that the optimal design varies with the discriminatory power of the contest technology in particular when it is in the low range winner take all is optimal for the intermediate range as discriminatory power increases the optimal prize structure evolves continuously from winner take all to the proportional division rule due to the need to mitigate the growing momentum discouragement effect for the high range a wide span of prize structures extracts full surplus and is thus optimal several robustness checks confirm that mitigating the momentum discouragement effect is essential for effort maximizing prize design in dynamic multi battle contests

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

patent races and the persistence of monopoly patent races are important determinants of market structure for a new firm a patent can be an entry ticket into the market for an incumbent firm already in the market patents for related technologies can ensure that no new firm enters in this spirit recent work has explored the implications of patenting for the persistence of monopoly see for example dasgupta i982 gilbert i98i gilbert and newbery i982 much attention has been given to pre emptive patenting the strategic acquisition of patents by an incumbent firm solely to prevent potential rivals from entering the market in this context it is important to distinguish between two kinds of patent race a standard race is a competition in which a prize is awarded to the first player to reach the finishing line an asymmetrical race is a competition in which one player loses something of value if one of his rivals reaches the finishing line he is content if nobody wins but a prize is won by the first of the other players to reach the finishing line if any of them does so a patent race in which an incumbent firm s sole concern is to prevent potential rivals from entering his market is an asymmetrical race and not a standard race the distinction between the two kinds of race can be captured only in models with a sufficiently rich dynamic structure this and other advantages of a properly dynamic model are explained in section ii a model of an asymmetrical race with two firms is presented in section iii in this model the challenger wins a prize and the incumbent loses a prize if the challenger is first to reach the finishing line it is shown that the challenger is often automatically deterred from making any effort to win the race because the strategic interactions between the players are such that the incumbent would outdo any reasonable effort made by the challenger in order to stop the challenger being first to reach the finishing line then the incumbent has no need to make any effort in the race in order to maintain his existing monopoly the reason is that the incumbent unlike the challenger does not need to go all the way to the finishing line to achieve his objective on the other hand it may be truedepending on the parameters describing the firmsthat the challenger wins the patent proceeding to the finishing line just as if he were the only contender for the patent of particular interest is the case in which the firms are identical

a model of the evolution of duopoly does the asymmetry between firms tend to increase or decrease this paper is an attempt to identify some of the factors that affect the evolution of market structure in a model of dynamic competition between two firms the stochastic evolution of the state of competition depends on the respective effort rates of the firms the question is whether the current leader works harder than the laggard does the gap between firms tend to increase or decrease we show that several effects are at work the state tends to evolve in the direction where joint payoffs are greater since joint payoffs are related to joint product market profits less joint effort costs there are two classes of effect the joint profit effect and various joint cost effects the latter result in part from the pattern of profits and in part from endpoint effects that give relief from efforts asymptotic expansions illuminate these influences moreover we show by numerical simulation that there is another kind of joint cost effect the pattern of joint effort costs can influence the pattern of evolution of market structure and the evolution of the pattern of market structure can influence the pattern of efforts in a mutually self reinforcing manner in particular there may be equilibria in which this last effect means that the laggard works harder than the leader even though all the other effects work in favour of the leader

a model of rivalries with endogenous prize and strength abstract this paper extends bevia and corchon 2013 to a model with both endogenous contestable prize and endogenous relative strength such a setting is ideal for the study of intra organizational rivalries commonly observed in family sports promotion and duopoly we find that when the game starts with asymmetric players the weaker player exerts more effort than the stronger player as a result the weaker player partially overcomes the disadvantage of being weak in this setting neither domino nor avalanche effect exists

do prediction markets aid defenders in a weak link contest abstract laboratory experiments have demonstrated that prediction market prices weakly aggregate the disparate information of the traders about states moves of nature however in many practical applications one is attempting to predict the move of a strategic rival this is particularly important in aggressor defender contests this paper reports an experiment where the defender may have the advantage of observing a prediction market on the aggressor s action the results of the experiments indicate that the use of prediction markets does not increase the defender s win rate prediction markets contain reliable information regarding aggressors decisions that is not being exploited by defenders and the existence of a prediction market does not alter the behavior of the aggressor whose behavior is being forecast

a perpetual race to stay ahead this paper presents a model of dynamic competition between two firms that repeatedly engage in an innovative activity the state of competition measured by the difference between the number of innovations introduced by the firms evolves stochastically according to their effort level the structure of markov perfect equilibria is identified it is generally not true that competition is fiercest when firms are closest rather firms invest under two distinct circumstances while sufficiently ahead to outstrip their rival and secure a durable leadership while behind to regain leadership and prevent the situation from worsening to the point where their rival outstrips them industry such a market structure cannot be adequately modelled by a repeated game since history obviously affects market opportunities more precisely previous outcomes determine the range of available actions and pay offs economists have thus resorted to the study of races to gain insights into the strategic issues raised by such competition with the notable exceptions of aoki 1991 harris 1991 and budd harris and vickers 1993 most of the literature has analysed formal races displaying exogenous finishing lines or deadlines as well as final prizes and rewards and the corresponding results rely on backward induction however such assumptions do not seem to capture accurately the essential features of many markets often the rivalry only ends if at all when one of the competitors withdraws so that the deadline should be endogenized moreover benefits and losses are continuously collected additionally the emerging empirical literature on races stresses the inadequacy of standard models and the need to model r d as a race with multiple prizes in the words of cockburn and henderson 1994 our finding that the modern game theoretic literature is of only limited usefulness as an empirical guide points to the need to model r d as a race with multiple prizes the model analysed in this paper is an attempt to offer an adequate framework for this type of dynamic competition the stochastic evolution of the state of competition between two firms depends on their respective effort levels the state of competition is measured by the

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

is price flexibility stabilizing a broader perspective recent prewar postwar comparisons of united states macroeconomic performance have produced a number of stylized facts about differences in the cyclical behavior of real activity and prices across the two periods 1 among them are two that have attracted special attention the stability of real aggregate activity measured by the variance of its cyclical component has been greater in the postwar period than in the prewar period and wages and prices have been less flexible in the postwar period than in the prewar period 2 in the standard keynesian paradigms wage and price rigidity are the cause of output and employment fluctuations taken together then the observations of greater stability and reduced wage and price flexibility have puzzled some economists and prompted a reconsideration of the relationship between the flexibility of the price system and macroeconomic stability a series of recent papers3 reassesses the relationship between price flexibility and

contests with multi tasking the standard contest model in which participants compete in a single dimension is well understood and documented multi dimension extensions are possible but are liable to increase the complexity of the contest structure mitigating one of its main advantages simplicity in this paper we propose an extension in which competition ensues in several dimensions and a competitor that wins a certain number of these is awarded a prize the amount of information needed to run the contest is hence limited to the number of dimensions won by each player we look at the design of this contest from the point of view of maximising effort in the contest per dimension and totally and show that there will be a tendency to run small contests with few dimensions the standard tullock model and its results are encompassed by our framework

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

fragility of the commons under prospect theoretic risk attitudes abstract we study a common pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource to capture decision making under such uncertainty we model each player s risk preference according to the value function from prospect theory we show the existence and uniqueness of a pure nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource greater competition vis a vis the number of players increases the failure probability at the nash equilibrium we quantify this effect by obtaining bounds on the ratio of the failure probability at the nash equilibrium to the failure probability under investment by a single user we further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium

on equilibrium player ordering in dynamic team contests we study equilibrium player ordering in a dynamic all pay contest between two teams the contest lasts two periods and each team consists of two players who perform in different periods on behalf of their teams the team with the higher aggregate output wins the prize which is a public good to its players each team has one stronger player and one weaker player and the two teams can differ in their values of the prize the teams maximize their winning odds by strategically assigning their players to different periods we find that when the intrateam heterogeneity in player ability is not excessive the teams would allocate their stronger players to the late positions as the anchormen when both the intrateam ability gap and interteam heterogeneity in teams values become excessively large the team with high value always places its stronger player in the early position who will place a large bid to preempt late competition jel c7 d7 d8

competing for loyalty the dynamics of rallying support abstract we consider a class of dynamic collective action problems in which either a single principal or two competing principals vie for the support of members of a group we focus on the dynamic problem that emerges when agents negotiate and commit their support to principals sequentially we show that competition reduces agents welfare with public goods or if and only if there are positive externalities on uncommitted agents and increases agents welfare with public bads we apply the model to the study of corporate takeovers vote buying and exclusive deals jel d42 d62 d72 d82 g34 h41

the economic design of sporting contests what is the optimal number of entrants in a race or the optimal number of teams in a baseball league what is the optimal structure of prizes for a golf tournament or degree of revenue sharing for a football championship how evenly balanced should the competing teams be in the nascar or formula one championships what is the maximum number of entrants per nation to the olympic games that should be permitted what quota of qualifying teams to the soccer world cup should be allocated to the developing nations

go for broke or play it safe dynamic competition with choice of variance we consider a differential game in which the joint choices of the two players influence the variance but not the mean of the one dimensional state variable we show that a pure strategy perfect equilibrium in stationary markov strategies me exists and has the property that patient players choose to play it safe when sufficiently ahead and to take risks when sufficiently behind we also provide a simple condition that implies both players choose risky strategies when neither one is too far ahead a situation that ensures a dominant player emerges quickly

competition and growth with step by step innovation an example this paper develops a simple example to analyse the relationship between product market competition and growth in a model with step by step innovations where laggards can never leapfrog the current industry leaders but instead must first catch up with the leaders before battling for technological leadership in the future unlike in existing schumpeterian models of growth more intense product market competition and or imitations may be growth enhancing

suspense dynamic incentives in sports contests in a dynamic model of sports competition if spectators care only about contestants efforts incentive schemes depending linearly on the final score difference dominate rank order schemes based only on who wins if spectators also care about suspense defined as valuing more contestants efforts when the game is closer rank order schemes can dominate linear score difference schemes and this will be the case when the demand for suspense is sufficiently high under additional assumptions we show that the optimal rank order scheme dominates a broad class of incentive schemes sport contestants can earn substantial financial prizes total prize money at wimble don topped 10 million for the first time in 2005 the professional golf association has distributed approximately 250 million in prize money across 48 events in the pga tour even in less professional sports prize money plays an important role nearly 21 million in prize money was awarded in international track and field competitions in 2004 interestingly prize money is typically allocated on the basis of who wins and who loses more informative measures of performance such as score differences rarely matter even though they are readily available when there are several contestants in a sporting event rewards depend on who wins the most games round robin tourna ment or on the sequence of games won elimination tournament total scores and other performance measures matter only in terms of determining who the winner is not how much the winner gets although for superstar athletes prize money pales in comparison with income from sponsorship deals only about 6 million of tiger woods income of close to 90 million in 2004 was prize money sponsorship money can depend on factors such as charisma and star power other than athletic perform ance so prize money is still the main provider of incentives for efforts in a given sports event likewise in recent years contracts for players in some team sports are loaded with incentive clauses that often take on a strong piece rate flavour e g salaries for batters depending on the batting average in baseball but financial incentives for team efforts remain largely independent of relative performance measures such as score differences why do win lose rank order incentives dominate in the design of financial incentives in sports especially in individual sports the literature on optimal design of rank order tournaments that began with lazear and rosen 1981 explains how tournaments provide incentives for efforts however the literature has not shed much light on when rank order incentive schemes are preferred to schemes based on other relative performance measures particularly when the agents are risk neutral prendergast 1999 pp 36 7 reviews several reasons for using tournaments but it remains unclear why prizes in sporting events depend only on rank order of scores and not on scores themselves holmstrom 1982 casts doubt this article was originally titled suspense it was first presented at the memorial conference for sherwin

the dynamics of majoritarian blotto games abstract we study colonel blotto games with sequential battles and a majoritarian objective for a large class of contest success functions the equilibrium is unique and characterized by an even split each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player s overall budget as a consequence a player s chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player has accumulated in prior battles this result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective we also consider the equilibrium choice of an overall budget for many contest success functions if the sequence of battles is long enough the payoff structure in this extended game resembles an all pay auction without noise

incentives and problem uncertainty in innovation contests an empirical analysis contests are a historically important and increasingly popular mechanism for encouraging innovation a central concern in designing innovation contests is how many competitors to admit using a unique data set of 9 661 software contests we provide evidence of two coexisting and opposing forces that operate when the number of competitors increases greater rivalry reduces the incentives of all competitors in a contest to exert effort and make investments at the same time adding competitors increases the likelihood that at least one competitor will find an extreme value solution we show that the effort reducing effect of greater rivalry dominates for less uncertain problems whereas the effect on the extreme value prevails for more uncertain problems adding competitors thus systematically increases overall contest performance for high uncertainty problems we also find that higher uncertainty reduces the negative effect of added competitors on incentives thus uncertainty and the nature of the problem should be explicitly considered in the design of innovation tournaments we explore the implications of our findings for the theory and practice of innovation contests this paper was accepted by christian terwiesch operations management

a tug of war team contest this paper analyzes a tug of war contest between two teams in each round of the tug of war a pair of agents from the opposing teams competes in a private value all pay auction with asymmetric value distributions and effort effectiveness whichever team arrives first at a given lead in terms of battle victories over the opponent wins the tug of war there exists a unique markov perfect equilibrium in bidding strategies which depend on the respective player s valuation and the current state of the tug of war we derive rich comparative statics for this equilibrium by using the fact that the state of the tug of war evolves according to a time homogeneous absorbing markov chain

do polls create momentum in political competition abstract we explore how public opinion polls affect candidates campaign spending in political competition generally polls lead to more asymmetric behavior under a majority rule there always exists an equilibrium in which the initially more popular candidate invests more in the campaign and thereby increases her lead in expectation polls create momentum when campaigning is very effective and the race is very close a second type of equilibrium may exist the trailing candidate outspends and overtakes his opponent regardless of the type of equilibrium polls have a tendency to decrease expected total campaigning expenditures by amplifying ex ante asymmetries between candidates and thus defusing competition when candidates care also for their vote share in addition to having the majority candidates incentives crucially depend on the distribution of voters candidate preferences

innovation and cooperation under vertical product differentiation abstract this paper analyzes the strategic decisions of two identical duopolists who determine both the timing and the quality of their innovation through their research and development activities the product market is vertically differentiated and the firms choose the prices of their innovations in bertrand competition the firms interact in a two stage non cooperative game where they first decide on the quality and innovation date and then choose the prices in the second stage appropriately the existence of equilibria in pure and mixed strategies is analyzed it is shown that the firms have an incentive to form a research joint venture and to share their research know how even when research results are certain and there are no spillover effects and that cooperation is not socially desirable

racing with uncertainty a patent race experiment this paper presents an experimental test of the multi stage patent race model of harris and vickers rev econ stud 54 1987 1 tied competitors invested more when nearer the end of the race but this may have followed from a more general and unexplained pattern of a positive correlation between investment and progress in the race the relationship between investment and gap between competitors was mostly not as predicted also leaders did not invest more than not heavily lagging followers and the race did not approach monopoly as the gap between competitors widened overall the evidence brings only limited support to the theory

war and conflict in economics theories applications and recent trends we review the main economic models of war and conflict these models vary in details but their implications are qualitatively consistent highlighting key commonalities across a variety of conflict settings recent empirical literature employing both laboratory and field data in many cases confirms the basic implications of conflict theory however this literature also presents important challenges to the way economists traditionally model conflict we finish our review by suggesting ways to address these challenges

competition imitation and growth with step by step innovation is more intense product market competition and imitation good or bad for growth this question is addressed in the context of an endogenous growth model with step by step innovations in which technological laggards must first catch up with the leading edge technology before battling for technological leadership in the future in contrast to earlier schumpeterian models in which innovations are always made by outsider firms who earn no rents if they fail to innovate and become monopolies if they do innovate here we find first that the usual schumpeterian effect of more intense product market competition pmc is almost always outweighed by the increased incentive for firms to innovate in order to escape competition so that pmc has a positive effect on growth second that a little imitation is almost always growth enhancing as it promotes more frequent neck and neck competition but too much imitation is unambiguously growth reducing the model thus points to complementary roles for competition anti trust policy and patent policy

performance responses to competition across skill levels in rank order tournaments field evidence and implications for tournament design tournaments are widely used in the economy to organize production and innovation we study individual data on 2775 contestants in 755 software algorithm development contests with random assignment the performance response to added contestants varies nonmonotonically across contestants of different abilities precisely conforming to theoretical predictions most participants respond negatively whereas the highest skilled contestants respond positively in counterfactual simulations we interpret a number of tournament design policies number of competitors prize allocation and structure number of divisions open entry and assess their effectiveness in shaping optimal tournament outcomes for a designer

persistence of technological leadership emerging technologies and incremental innovation in a model of competitive innovation i derive theoretical conditions for an entrant to displace the incumbent firm by innovating in an undeveloped substitute emerging technology the main result presents conditions on profitability and innovation speed that yield a markov perfect equilibrium in which the entrant pursues the emerging technology while the incumbent chooses to persist with the established technology and collect short run profits notably this result does not require the entrant s superiority to the incumbent for innovation finally when the model is calibrated to hard drive industry data its predictions are consistent with the observed outcomes

market r d allocations when research paths are product specific a compared to the social optimum individual firms undertook too little rd b too many firms entered the competition to undertake rd2 c if the elasticity of demand were sufficiently low aggregate rd

best of three all pay auctions abstract we study a best of three all pay auction it is shown that with values of winning and without values of losing this auction is less productive the players total expected effort is smaller than the one stage all pay auction however with different values of losing over the contest s stages it may be more productive than the one stage all pay auction

multi player race abstract we present a model of race with multiple players and study players effort choices and expected prizes in equilibrium we show that in equilibrium once any two players win one battle each the remaining players do not exert any effort anymore this turns the continuation game into a two player race this is different than the results in previous two player models of race which report that all states of the game are reached with positive probabilities we also provide a set of comparative static results on the effects of the number of players and the victory threshold

intensity of competition and the incentive to innovate abstract the effects of intensity of product market competition on r d incentives are analysed in a model capturing the strategic interactions between firms with different cost levels first four axioms are proposed that a measure of intensity of competition should satisfy then the effects of intensity of competition on the value of the innovation are analysed and it is shown that the axioms imply the existence of a non monotone relation between intensity of competition and the value of an innovation

dynamic r d competition the authors study a simple two stage stochastic patent race involving two firms they examine the behavior of the participants as they gain the lead or fall behind in the race the authors find that the leader engages in rd 2 a policy of issuing patents for intermediate research results and 3 the effects of research joint ventures whereby the firms coordinate their initial research efforts and share their results copyright 1987 by royal economic society

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

the great industry gamble market structure dynamics as a survival contest industry dynamics are studied as an endogenous tournament with infinite horizon and stochastic entry in each period firms investments determine their probability of surviving into the next period this generates a survival contest which fuels market structure dynamics while the evolution of market structure constantly redefines the contest more concentrated markets endogenously generate less profit rivals that are more difficult to outlive and more entry the unique steady state distribution exhibits ongoing turbulence correlated exit and entry rates and shakeouts the model s predictions fit empirical findings in markets where firms trade off profits for smaller risk of failure e g banking

gambling in contests this paper presents a strategic model of risk taking behavior in contests formally we analyze an n player winner take all contest in which each player decides when to stop a privately observed brownian motion with drift a player whose process reaches zero has to stop the player with the highest stopping point wins unlike the explicit cost for a higher stopping time in a war of attrition here higher stopping times are riskier because players can go bankrupt we derive a closed form solution of a nash equilibrium outcome in equilibrium highest expected losses occur at an intermediate negative value of the drift

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

recognition for sale abstract i examine the consequences of letting players compete for bargaining power in a multilateral bargaining game in each period the right to propose an offer is sold to the highest bidder and all players pay their bids if players vote according to any rule in which no player has veto power then the first proposer captures the entire surplus if a full consensus is needed for an offer to be accepted then the first proposer shares the surplus with at most one other player and as the period length between offers vanishes one player may capture virtually the entire surplus in settings with a stochastic or an endogenous surplus players are unwilling to efficiently delay agreement or invest in the surplus

cognitive performance in competitive environments evidence from a natural experiment competitive situations that involve cognitive performance are widespread in labor markets schools and organizations including test taking competition for promotion in firms and others this paper studies cognitive performance in a high stakes competitive environment the analysis takes advantage of a natural experiment that randomly allocates different emotional states across professional subjects competing in a cognitive task the setting is a chess match where two players play an even number of chess games against each other alternating the color of the pieces white pieces confer an advantage for winning a chess game and who starts the match with these pieces is randomly decided the theoretical analysis shows that in this setting there is no rational reason why winning frequencies should be better than 50 50 in favor of the player drawing the white pieces in the first game yet we find that observed frequencies are about 60 40 differences in performance are also stronger when the competing subjects are more similar in cognitive skills we conclude that the evidence is consistent with the hypothesis that psychological elements affect cognitive performance in the face of experience competition and high stakes