the role of risk preferences in pay to bid auctions we analyze a new auction format in which bidders pay a fee each time they increase the auction price bidding fees are the primary source of revenue for the seller but produce the same expected revenue as standard auctions assuming risk neutral bidders if risk loving preferences are incorporated in the model expected revenue increases our model predicts a particular distribution of ending prices which we test against observed auction data the degree of fit depends on how unobserved parameters are chosen in particular a slight preference for risk has the biggest impact in explaining auction behavior suggesting that pay to bid auctions are a mild form of gambling this paper was accepted by peter wakker decision analysis

all pay war we study a model of conflicts and wars in which the outcome is uncertain not because of luck on the battlefield as in standard models but because countries lack information about their opponent in this model expected resource levels and production and military technologies are common knowledge but realized resource levels are private information each country decides how to allocate its resources to production and warfare the country with the stronger military wins and receives aggregate production in equilibrium both comparative and absolute advantages matter a larger resource share is allocated to warfare by the country with a comparative advantage in warfare at relatively low realized resource levels and by the country with an absolute disadvantage in warfare at relatively high realized resource levels from an ex ante perspective the country with a comparative advantage in warfare is more likely to win the war unless its military potential is much lower

two bidder all pay auctions with interdependent valuations including the highly competitive case abstract we analyze symmetric two bidder all pay auctions with interdependent valuations and discrete type spaces relaxing previous restrictions on the distribution of types and the valuation structure we present a construction that characterizes all symmetric equilibria we show how the search problem this construction faces can be complex in equilibrium randomization can take place over disjoint intervals of bids equilibrium supports can have a rich structure and non monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common particular attention is paid to the case in which an increase in a bidder s posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder such environments are highly competitive in the sense that the bidder s higher valuation also signals that the other bidder has an incentive to bid aggressively

monotone equilibrium of two bidder all pay auctions redux abstract in this paper we revisit the two bidder asymmetric all pay auction of amann and leininger 1996 by allowing interdependent values and correlated signals both values and signals are distributed on continuous supports we provide conditions for the existence and uniqueness of a monotone pure strategy equilibrium mpse and constructively characterize the mpse when it exists we find that given the marginal distributions of the signals the equilibrium allocation is solely determined by how bidders values depend on their signals in particular the equilibrium allocation does not depend on how bidders signals are correlated

incomplete information and rent dissipation in deterministic contests abstract in a deterministic contest or all pay auction all rents are dissipated when information is complete and contestants are identical as one contestant becomes stronger that is values the prize more total expenditures are known to decrease monotonically thus asymmetry among contestants reduces competition and rent dissipation recently this result has been shown to hold for other non deterministic contest success functions as well thereby suggesting a certain robustness in this paper however the complete information assumption is shown to be crucial i examine a tractable incomplete information model for which the complete information model is a special case with incomplete information regardless of how little total expenditures in a deterministic two player contest increase when one contestant becomes marginally stronger starting from a symmetric contest in fact both contestants expend resources more aggressively with complete information neither of them do so thus there is a discontinuity in the information structure

product introduction with network externalities the authors study the introduction of a new product in a market with network externalities there is a common presumption that such markets exhibit excess inertia i e that they are biased toward existing products in contrast the authors provide conditions under which equilibrium involves insufficient friction i e a tendency to rush into new incompatible technologies they also analyze the firms incentives to make their products compatible and they show that the firm introducing the new technology is biased against compatibility copyright 1992 by blackwell publishing ltd

installed base and compatibility innovation product preannouncements and predation a good is often more valuable to any user the more others use compatible goods the authors show that this effect may inhibit innovation if an installed base exists and transition to a new standard must be gradual early adopters bear a disproportionate share of transient incompatibility costs this can produce excess inertia the installed base however is stranded if the new standard is adopted this may create excess momentum these dynamic effects have strategic implications temporary price cutting can permanently prevent entry and product preannouncements can be critical in innovation these strategic actions have ambiguous welfare effects

private versus complete information in auctions abstract we show that in several but not all standard auctions i private independent values and ii complete information are payoff equivalent the first price auction generates the same revenue under i and ii the all pay auction has lower revenue under ii

asymmetric all pay auctions with incomplete information the two player case abstract we prove existence and uniqueness of bayesian equilibrium for a class of generally asymmetric all pay auctions with incomplete information due to its importance in applications some prominence is given to the first price all pay auction for which a detailed characterization of equilibrium and an approximation to equilibrium of its well studied complete information version are supplied furthermore we relate our uniqueness result to the well known multiplicity of equilibria in the war of attrition second price all pay auction which emerges as a limit point of the class of two player auction games considered journalof economic literature classification numbers d44 c62 c72

contests with small noise and the robustness of the all pay auction this paper considers all pay contests in which the relationship between bids and allocations reflects a small amount of noise prior work had focused on one particular equilibrium however there may be other equilibria to address this issue we introduce a new and intuitive measure for the proximity to the all pay auction this allows in particular to provide simple conditions under which actually any equilibrium of the contest is both payoff equivalent and revenue equivalent to the unique equilibrium of the corresponding all pay auction the results are shown to have powerful implications for monopoly licensing political lobbying electoral competition optimally biased contests the empirical analysis of rent seeking and dynamic contests

bid costs and endogenous bid caps we study contests where several privately informed agents bid for a price all bidders bear a cost of bidding that is an increasing function of their bids and moreover bids may be capped we show that regardless of the number of bidders if agents have linear or concave cost functions then setting a bid cap is not profitable for a designer who wishes to maximize the average bid on the other hand if agents have convex cost functions i e an increasing marginal cost then affectively capping the bids is profitable for a designer facing a sufficiently large number of bidders

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

compatibility standardization and network effects some policy implications given the dramatic growth of the internet and information technology industries in general and the importance of interconnection in these networks the economics of compatibility and standardization has become mainstream economics in this paper i examine several key policy aspects of standard setting in industries with network effects copyright 2002 oxford university press

bargaining over perfect complements owned separately with experimental test this paper considers the situation in which two perfect complements belong to different owners we calculate the bayesian nash equilibrium in the mechanism of k 1 price bargaining with private value and did experiment to test the theory

costly signalling in auctions this paper analyses a dynamic auction in which a fraction of each bid is sunk jump bidding is used by bidders to signal their private information bluffing respectively sandbagging occurs when a weak respectively strong player seeks to deceive his opponent into thinking that he is strong respectively weak a player with a moderate valuation bluffs by making a high bid and drops out if his bluff is called a player with a high valuation should vary his bids and should sometimes sandbag by bidding low to induce lower bids by his rival

efficiency and competition in the long run the survival of the unfit abstract in a dynamic contest the current incumbent competes against a randomly assigned entrant in a private value all pay auction each period we focus on equilibria where the beliefs about the incumbent s type and the employed strategies are stationary we show that inefficient types survive even if the entrants arrive very frequently because the entrant plays more aggressively than the incumbent allowing a low type entrant to win against a high type incumbent in an example we show that if the incumbent is challenged more often then the equilibrium type of the incumbent is higher on average when the value of the prize is the same for all players the case studied in the public choice literature the equilibrium rent of the bidders is fully dissipated as the incumbent is challenged infinitely often the technical contribution lies in showing the existence of stationary equilibrium in an incomplete information game

favoritism in asymmetric contests head starts and handicaps abstract i examine a contest with identity dependent rules in which contestants are privately informed and ex ante heterogeneous a contestant may suffer from a handicap or benefit from a head start the former reduces the contestant s score by a fixed percentage the latter is an additive bonus although total effort increases if the weak contestant is favored with a head start the optimal use of handicaps is not as clear cut depending on the nature of the asymmetry it may or may not be optimal to handicap the strong contestant moreover it is generally optimal to combine the two instruments for instance when contestants are sufficiently heterogeneous the weak contestant should be given both a head start and a handicap it may also be possible to induce higher effort and at the same time make both contestants better off ex ante

discrimination in a model of contests with incomplete information about ability we study contests with private information and identical contestants where contestants efforts and innate abilities generate output of varying qualities the designer s revenue depends on the quality of the output and she offers a reward to the contestant achieving the highest quality we characterize the equilibrium behavior outcomes and payoffs for both nondiscriminatory and discriminatory where the reward is contestant dependent contests we derive conditions under which the designer obtains a larger payoff when using a discriminatory contest and describe settings where these conditions are satisfied

a symmetric two player all pay contest with correlated information we construct both monotonic and non monotonic symmetric bayesian nash equilibria for a two player all pay contest with binary types and correlated information structures we also employ a class of parametric distributions to illustrate our equilibrium construction explicitly and to derive some comparative statics results

team contests with multiple pairwise battles abstract we consider a multi battle team contest in which players from two rival teams form pairwise matches to fight in distinct component battles which are carried out sequentially or partially

innovative activity and sunk cost abstract we analyze innovative activity in a general framework with time dependent rewards and sunk costs when firms are identical innovation is delayed by an increase in the number of firms or a decrease in the size of the reward when one firm has higher profit potential it is more likely to innovate first our framework generalizes an all pay auction however we show that under certain conditions there is qualitatively different equilibrium behavior

information alliances in contests with budget limits we study the role of information exchange that may occur in alliances in a contest without noise contestants learn their own limits of what they can spend in a contest they may also form alliances and learn the limits of all players who are within the same alliance then they decide independently about their own contest efforts alliance formation for the purpose of information exchange is beneficial for members of the same alliance and neutral for all other players also a merger between alliances is beneficial for their members further we identify and discuss the set of stable alliance combinations

uniqueness and existence of equilibrium in auctions with a reserve price abstract we prove existence and uniqueness of equilibrium for a general class of two player bidding games we apply our results to the first price auction the combination of first and second price auctions the war of attrition the all pay auction as well as combinations of the latter two auction forms we also treat the first price auction without risk neutrality our results deal with the asymmetric affiliated common values environment in the case where signals are independent our results apply to all equilibria when signals are not independent our uniqueness results hold in the class of nondecreasing strategy equilibria journal of economic literature classification number d44

the optimal allocation of prizes in contests we study a contest with multiple not necessarily equal prizes contestants have private information about an ability parameter that affects their costs of bidding the contestant with the highest bid wins the first prize the contestant with the second highest bid wins the second prize and so on until all the prizes are allocated all contestants incur their respective costs of bidding the contest s designer maximizes the expected sum of bids our main results are 1 we display bidding equlibria for any number of contestants having linear convex or concave cost functions and for any distribution of abilities 2 if the cost functions are linear or concave then no matter what the distribution of abilities is it is optimal for the designer to allocate the entire prize sum to a single first prize 3 we give a necessary and sufficient conditions ensuring that several prizes are optimal if contestants have a convex cost function

equilibria existence and characterization in auctions achievements and open questions establishing existence and characterizing equilibria is a fundamental step in the study of auctions theoretical characterizations and empirical predictions are well accepted only to the extent that they are based on equilibria however despite the fact that auctions have been extensively studied there are still many problems regarding equilibrium existence and characterization waiting for resolution in this survey we review the landmark results and highlight open questions in addition we review the standard assumptions underlying these results and discuss the suitability of the nash equilibrium solution concept we focus our review on single object auctions but also review results in multi unit divisible combinatorial and double auctions

private information group contests best shot competition abstract we model competing groups when players values for winning are private information each group s performance equals the best effort best shot of its members and the group with the best performance wins the contest at the symmetric equilibrium of symmetric contests increasing the number of competing teams may increase or decrease each team s performance but it unambiguously increases the overall expected best shot depending on the elasticity of the distribution of players values individual team and contest performance may increase or decrease with team size considering just two competing groups that differ only in size we show members of the smaller group use the more aggressive strategy but depending on the nature of uncertainty either team may be more likely to win more generally when teams value cdfs differ increasing one team s size decreases increases that team s chance of winning if its value cdf is elastic inelastic

technology adoption in the presence of network externalities we analyze technology adoption in industries where network externalities are significant the pattern of adoption depends on whether technologies are sponsored a sponsor is an entity that has property rights to the technology and hence is willing to make investments to promote it key findings include the following 1 compatibility tends to be undersupplied by the market but excessive standardization can occur 2 in the absence of sponsors the technology superior today has a strategic advantage and is likely to dominate the market 3 when one of two rival technologies is sponsored that technology has a strategic advantage and may be adopted even if it is inferior 4 when two competing technologies both are sponsored the technology that will be superior tomorrow has a strategic advantage

asymmetric all pay auctions with interdependent valuations abstract i show that a unique equilibrium exists in an asymmetric two player all pay auction with a discrete signal structure correlated signals and interdependent valuations the proof is constructive and the construction can be implemented as a computer program and be used to derive comparative statics i also characterize the set of equilibria when a reserve price is introduced

cartelization in gas markets studying the potential for a gas opec natural gas is increasingly important as a fuel for electric power generation as well as other uses due to its environmental advantage over other fossil fuels using the world gas model a large scale energy equilibrium system based on a complementarity formulation this paper analyzes possible future gas cartels and their effects on gas markets in a number of regions across the world in addition scenarios related to lower transport costs and decreased unconventional gas supply in the united states are considered

mixed strategy play in single stage first price all pay auctions with symmetric players abstract we consider sealed bid first price all pay auctions with complete information discrete strategy space budget constraint and symmetric players and then construct the equilibrium solution in mixed strategies for both fixed and variable prizes the equilibrium solution yields predictions concerning the effects of group size and value of the prize that are tested experimentally the experimental results support equilibrium play on the aggregate but not individual level adaptive learning on the individual level accounts for the major trends in the aggregate expenditures over time

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

multi stage sequential all pay auctions abstract we study multi stage sequential all pay contests auctions where heterogeneous contestants are privately informed about a parameter ability that affects their cost of effort we characterize the perfect bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants expected highest effort

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

open architecture and r d incentives in open systems firms give up their property rights to technologies and permit other companies to use these technologies we ask how an incumbent s architecture choice affects social welfare by altering r d competition among firms more specifically we ask whether an incumbent by adopting an open system can establish its socially inefficient technology as the market standard while an entrant is developing a more efficient technology it is shown that an incumbent has an incentive to preempt an entrant s competing technology by choosing an open system but that the open system might result in a premature market standard

politician preferences law abiding lobbyists and caps on political contributions the effect of a contribution cap is analyzed in a political lobbying game where the politician has a policy preference in contrast to the previous literature without politician policy preferences more restrictive binding caps always reduce expected aggregate contributions however the initial imposition of a cap increases contributions if the politician mildly favors the low valuation lobbyist s policy the introduction of policy preferences permits analysis of monied interests policy influence a more restrictive cap makes it more likely that the politician enacts the policy he would have enacted in the absence of lobbying even in cases where expected aggregate contributions increase

inefficient standard adoption inertia and momentum revisited i introduction since the establishment of the theory of network effects economists have been concerned with the question of whether a market with network effects will tend to settle on the socially optimal standard it has been postulated that markets may exhibit excess inertia once a technological standard is in place a new superior standard may not displace it because of installed base effects alternatively markets may exhibit excess momentum consumers may adopt a new standard too quickly ignoring the stranding effect they are having on previous users similar issues arise in the adoption of language and social norms the literature has investigated various conditions under which one of these inefficiencies arises such inefficiencies are of particular concern for open technologies such as the qwerty and dvorak keyboards 1 the situation is somewhat different when individual firms own standards in that case a simple argument seems to indicate that there is no possibility that an inefficient standard will persist if a new standard is superior in any objective sense there are gains to be made from switching to it once the standard has been adopted the firm can appropriate these gains therefore the firm has incentive to lower the initial price enough to induce adoption of the standard the preceding argument is made in liebowitz and margolis 1999 and repeated in spulber 2002 spulber expresses a general skepticism about the likelihood of inefficiencies when property rights are defined and markets exist critics might claim that previous models that imply inefficient standard adoption are unrealistic in some way and that if such models were modified slightly the inefficiency would disappear i reconsider the issue of inefficient standard adoption using a parsimonious yet compelling model assuming only that there are successive generations of finitely lived consumers that preferences are heterogeneous and that there are network effects among users adoption decisions can be inefficient this is true even if consumers can coordinate efficiently within a generation and a firm can act as a coordinating device across generations the model presented here generates some of the same results found in other papers collectively but in a more general setting and with more robust results if there is an established standard and a superior alternative emerges no single generation of consumers will be willing to switch to the new standard if the switching cost the loss of network benefit from breaking with past users is too high it may be that the benefits to future generations of consumers are large enough that from a social standpoint it would be efficient for one generation to adopt the new standard even if it is privately optimal for that generation to retain the old standard on the other hand the current generation considers only its own switching cost and not the cost it imposes on the previous generation leading to potential overadoption of new technology even for proprietary standards it is not clear that the incentive of the firm to induce adoption matches the social incentive in particular if consumer preferences are heterogeneous the firm will not be able to price in such a way to extract all of the additional surplus gained from the new standard on the other hand the firm will be able to appropriate some of the surplus generated by the network effect itself which is present for any standard and thus does not affect the social incentive to change standards it is not possible to address this issue with a two period model as in some of the previous literature see for example choi 1994 choi and thum 1998 katz and shapiro 1986 if a new technology is introduced in the second period but then the game ends the welfare of future generations of consumers is neglected 2 this article also differs from previous infinite horizon models of technology adoption

numerical simulations of asymmetric first price auctions abstract the standard method for computing the equilibrium strategies of asymmetric first price auctions is the backward shooting method in this study we show that the backward shooting method is inherently unstable and that this instability cannot be eliminated by changing the numerical methodology of the backward solver moreover this instability becomes more severe as the number of players increases we then present a novel boundary value method for computing the equilibrium strategies of asymmetric first price auctions we demonstrate the robustness and stability of this method for auctions with any number of players and for players with mixed types of distributions including distributions with more than one crossing finally we use the boundary value method to study large auctions with hundreds of players to compute the asymptotic rate at which large first price and second price auctions become revenue equivalent and to study auctions in which the distributions cannot be ordered according to first order stochastic dominance

a theory of competition among pressure groups for political influence this paper presents a theory of competition among pressure groups for political influence political equilibrium depends on the efficiency of each group in producing pressure the effect of additional pressure on their influence the number of persons in different groups and the deadweight cost of taxes and subsidies an increase in deadweight costs discourages pressure by subsidized groups and encourages pressure by taxpayers this analysis unifies the view that governments correct market failures with the view that they favor the politically powerful both are produced by the competition for political favors

pure strategy equilibria of single and double auctions with interdependent values we prove the existence of monotonic pure strategy equilibrium for many kinds of asymmetric auctions with n bidders and unitary demands interdependent values and independent types the assumptions require monotonicity only in the own bidder s type the payments can be a function of all bids thus we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders the generality of our setting requires the use of special tie breaking rules we present an example of a double auction with interdependent values where all equilibria are trivial that is they have zero probability of trade this is related to akerlof s market for lemmons example and to the winner s curse establishing a connection between them however we are able to provide sufficient conditions for non trivial equilibrium existence

r d in the presence of network externalities timing and compatibility two rival firms decide on the time of r d and whether the new products should be compatible i show that network externalities may induce the firms to introduce new incompatible technologies early which is socially harmful as the r d costs increase and de facto standardization becomes less likely compared with the equilibrium outcome both firms may gain by delaying the introduction of incompatible technologies by agreeing on common standards before product introduction entry is delayed and profit may increase an ex post optimal standardization policy may increase the incentives for early product introduction and consequently be an undesirable policy ex ante

all pay auctions with affiliated binary signals abstract we analyze all pay auctions with affiliated values and binary signals we analyze the unique symmetric equilibrium with any number of bidders and show that the bidders earn positive rents only if the equilibrium is monotone we also characterize the symmetric equilibrium of the closely related two player war of attrition we compare expected revenues across these formats all pay auctions result in lower expected rents to the bidders than standard auctions but they also induce inefficient allocations in some models with affiliated private values with two bidders the effect on rent extraction dominates and the all pay auctions outperform standard auctions in terms of expected revenue with many bidders standard auctions may result in higher expected revenue the war of attrition outperforms the standard auctions in terms of revenue but its ranking relative to all pay auctions is ambiguous

all pay auctions and group size grading on a curve and other applications we model contests with a fixed proportion of prizes such as a grading curve as all pay auctions where higher effort weakly increases the likelihood of a prize we find theoretical predictions for the heterogeneous effect auction size has on effort from high and low types we test our predictions in a laboratory experiment that compares behavior in two bidder one prize auctions with behavior in 20 bidder 10 prize auctions we find a statistically significant 11 8 increase in aggregate bidding when moving from the small to large auction the impact is heterogeneous as the auction size increases low types decrease effort but high types increase effort additionally the larger auction provides a stronger rank correlation between effort and ability awarding more prizes to the higher skilled and improving the efficiency of prize allocation

contests with three or more heterogeneous agents abstract we study monotone equilibrium behavior in contests with observable effort bid where three or more participants have distinct risk attitudes and the monetary value for the prize of each is drawn independently from a distinct distribution these differences can either cause a player to drop out that is always choose zero effort regardless of his valuation or use all or nothing strategies with discontinuous effort choice neither complete drop out nor discontinuous bidding with finitely many gaps is consistent with pure strategy monotone bayesian nash equilibrium in a contest with either ex ante identical players or only two distinct participants

product compatibility as a signal of quality in a market with network externalities abstract in this paper i consider the compatibility decision as a signaling device of the quality of a newly introduced technology of which users are not informed provided that firms are located sufficiently far apart in hotelling s 0 1 interval i find separating equilibria where low compatibility signals high quality this possible separation is due to the fact that low compatibility is more advantageous to the high quality entrant than to the low quality entrant since it can prevent users of the established technology from enjoying network benefits from the new technology very much

the dynamics of bidding markets with financial constraints we develop a model of bidding markets with financial constraints a la che and gale 15 in which two firms choose their budgets optimally and we extend it to a dynamic setting over an infinite horizon we provide three main results for the case in which the exogenous cash flow is not too large and the opportunity cost of budgets is positive but arbitrarily low first firms keep small budgets and markups are high most of the time second the dispersion of markups and money left on the table across procurement auctions hinges on differences both endogenous and exogenous in the availability of financial resources rather than on significant private information third we explain why the empirical analysis of the size of markups based on the standard auction model may have a bias downwards or upwards positively correlated with the availability of financial resources a numerical example illustrates that our model is able to generate a rich set of values for markups bid dispersion and concentration

the timing of product introduction and the credibility of compatibility decisions we analyze the compatibility choices of two firms which must also decide when to introduce their goods in a market characterized by network externalities we show that the firms incentives to achieve compatibility depend crucially on the time at which the degree of compatibility must be chosen this raises the possibility of time inconsistencies as a firm which initially favors compatibility might prefer incompatibility once one of the two goods has been introduced we also determine the socially optimal standardization policies both in a domestic and in an international context

bidding for a group specific public good prize abstract we examine the equilibrium effort levels of individual players and groups in a contest in which two groups compete with each other to win a group specific public good prize the players choose their effort levels simultaneously and independently and the winning group is determined by the selection rule of all pay auctions we first prove nonexistence of a pure strategy nash equilibrium and then construct a mixed strategy nash equilibrium at the nash equilibrium the only active player in each group is a player whose valuation for the prize is the highest in that group all the other players expend zero effort and the equilibrium effort levels depend solely on two values the highest valuation for the prize in each group

ranking disclosure policies in all pay auctions in this paper we study information disclosure policies in all pay auctions with incomplete information two symmetric players have either high or low private value the contest organizer observes players values ex post and can commit ex ante to four different symmetric information policies exhaustively she can fully disclose or conceal the players types and she can disclose their types if and only if when both are high or if and only if when both are low we characterize the unique equilibriums and completely rank the four policies by various criteria we find the full concealment policy extracts highest aggregate expected effort followed by the policy of disclosing types if and only if when both are high the policy of disclosing types if and only if when both are low induces least aggregate expected effort players enjoy highest expected payoffs under the policy of disclosing types if and only if when both are low the other three policies yield the same expected payoffs to players in terms of prize allocation efficiency the full concealment policy is ranked highest and the full disclosure policy is ranked lowest in between the other two policies rankings depend on the probability of high type jel c72 d44 d82 d83 j48

to deter or to moderate alliance formation in contests with incomplete information we consider two players choice about the formation of an alliance ahead of conflict in a framework with incomplete information about the strength of the potential ally when deciding on alliance formation players anticipate the self selection of other players and the informational value of own and other players choices in the absence of these signaling effects strong players have an incentive to stand alone which leads to a separating equilibrium this separating equilibrium can be destabilized by deception incentives if beliefs are updated on the basis of endogenous alliance formation choices weak players may find it attractive to appear strong in order to deter competitors from positive effort choices strong players may find it attractive to appear weak in order to give their competitors a false sense of security and then beat them with little effort moreover appearing weak allows players to free ride when alliances are formed jel d72 d74

all pay auctions with certain and uncertain prizes abstract we study all pay auctions with multiple prizes the players have the same value for all the certain prizes except for one uncertain prize for which each player has a private value we characterize the equilibrium strategy and show that independent of the ranking of the uncertain prize if the uncertain prize is not the lowest one a player s effort as well as his expected payoff increase in his value for the uncertain prize otherwise if this prize is the lowest one we obtain that a player s effort may decrease in his value for the uncertain prize but his expected utility increases

handicaps in incomplete information all pay auctions with a diverse set of bidders abstract in many contests a subset of contestants is granted preferential treatment which is presumably intended to be advantageous examples include affirmative action and biased procurement policies in this paper however i show that some of the supposed beneficiaries may in fact become worse off when the favored group is diverse the reason is that the other favored contestants become more aggressive which may outweigh the advantage that is gained over contestants who are handicapped the contest is modeled as an incomplete information all pay auction in which contestants have heterogenous and possibly non linear cost functions

public policies pressure groups and dead weight costs abstract this paper presents a model of competition among special interest groups for political influence each active group exerts pressure to affect its taxes and subsidies where activities of different groups are related by the equality between total tax collections and total tax subsidies the dead weight costs and benefits of taxes and subsidies play a major role in our model an increase in the dead weight cost of taxation encourages pressure by taxpayers while an increase in the dead weight costs of subsidies discourages pressure by recipients various applications of the analysis are discussed